The Top 10 Science Experiments of All Time Discover Magazine-2019/10/08 Before he was that Isaac Newton — scientist extraordinaire and inventor of th

The Top 10 Science Experiments of All Time

Discover Magazine-2019/10/08

Before he was that Isaac Newton — scientist extraordinaire and inventor of the laws of motion, calculus and ... Unconvinced, Newton set up a prism experiment that proved color is instead an inherent property of light itself.

Every day, we conduct science experiments, posing an “if” with a “then” and seeing what shakes out. Maybe it’s just taking a slightly different route on our commute home or heating that burrito for a few seconds longer in the microwave. Or it could be trying one more variation of that gene, or wondering what kind of code would best fit a given problem. Ultimately, this striving, questioning spirit is at the root of our ability to discover anything at all. A willingness to experiment has helped us delve deeper into the nature of reality through the pursuit we call science.

A select batch of these science experiments has stood the test of time in showcasing our species at its inquiring, intelligent best. Whether elegant or crude, and often with a touch of serendipity, these singular efforts have delivered insights that changed our view of ourselves or the universe.

Here are nine such successful endeavors — plus a glorious failure — that could be hailed as the top science experiments of all time.

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Mark Marturello

Eratosthenes Measures the World

Experimental result: The first recorded measurement of Earth’s circumference

When: end of the third century B.C.

Just how big is our world? Of the many answers from ancient cultures, a stunningly accurate value calculated by Eratosthenes has echoed down the ages. Born around 276 B.C. in Cyrene, a Greek settlement on the coast of modern-day Libya, Eratosthenes became a voracious scholar — a trait that brought him both critics and admirers. The haters nicknamed him Beta, after the second letter of the Greek alphabet. University of Puget Sound physics professor James Evans explains the Classical-style burn: “Eratosthenes moved so often from one field to another that his contemporaries thought of him as only second-best in each of them.” Those who instead celebrated the multitalented Eratosthenes dubbed him Pentathlos, after the five-event athletic competition.

That mental dexterity landed the scholar a gig as chief librarian at the famous library in Alexandria, Egypt. It was there that he conducted his famous experiment. He had heard of a well in Syene, a Nile River city to the south (modern-day Aswan), where the noon sun shone straight down, casting no shadows, on the date of the Northern Hemisphere’s summer solstice. Intrigued, Eratosthenes measured the shadow cast by a vertical stick in Alexandria on this same day and time. He determined the angle of the sun’s light there to be 7.2 degrees, or 1/50th of a circle’s 360 degrees.

Knowing — as many educated Greeks did — Earth was spherical, Eratosthenes fathomed that if he knew the distance between the two cities, he could multiply that figure by 50 and gauge Earth’s curvature, and hence its total circumference. Supplied with that information, Eratosthenes deduced Earth’s circumference as 250,000 stades, a Hellenistic unit of length equaling roughly 600 feet. The span equates to about 28,500 miles, well within the ballpark of the correct figure of 24,900 miles.

Eratosthenes’ motive for getting Earth’s size right was his keenness for geography, a field whose name he coined. Fittingly, modernity has bestowed upon him one more nickname: father of geography. Not bad for a guy once dismissed as second-rate.

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Mark Marturello

William Harvey Takes the Pulse of Nature

Experimental result: The discovery of blood circulation

When: Theory published in 1628

Boy, was Galen wrong.

The Greek physician-cum-philosopher proposed a model of blood flow in the second century that, despite being full of whoppers, prevailed for nearly 1,500 years. Among its claims: The liver constantly makes new blood from food we eat; blood flows throughout the body in two separate streams, one infused (via the lungs) with “vital spirits” from air; and the blood that tissues soak up never returns to the heart.

Overturning all this dogma took a series of often gruesome experiments.

High-born in England in 1578, William Harvey rose to become royal physician to King James I, affording him the time and means to pursue his greatest interest: anatomy. He first hacked away (literally, in some cases) at the Galenic model by exsanguinating — draining the blood from — test critters, including sheep and pigs. Harvey realized that if Galen were right, an impossible volume of blood, exceeding the animals’ size, would have to pump through the heart every hour.

To drive this point home, Harvey sliced open live animals in public, demonstrating their puny blood supplies. He also constricted blood flow into a snake’s exposed heart by finger-pinching a main vein. The heart shrunk and paled; when pierced, it poured forth little blood. By contrast, choking off the main exiting artery swelled the heart. Through studies of the slow heart beats of reptiles and animals near death, he discerned the heart’s contractions, and deduced that it pumped blood through the body in a circuit.

According to Andrew Gregory, a professor of history and philosophy of science at University College London, this was no easy deduction on Harvey’s part. “If you look at a heart beating normally in its normal surroundings, it is very difficult to work out what is actually happening,” he says.

Experiments with willing people, which involved temporarily blocking blood flow in and out of limbs, further bore out Harvey’s revolutionary conception of blood circulation. He published the full theory in a 1628 book, De Motu Cordis [The Motion of the Heart]. His evidence-based approach transformed medical science, and he’s recognized today as the father of modern medicine and physiology.

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Mark Marturello

Gregor Mendel Cultivates Genetics

Experimental result: The fundamental rules of genetic inheritance

When: 1855-1863

A child, to varying degrees, resembles a parent, whether it’s a passing resemblance or a full-blown mini-me. Why?

The profound mystery behind the inheritance of physical traits began to unravel a century and a half ago, thanks to Gregor Mendel. Born in 1822 in what is now the Czech Republic, Mendel showed a knack for the physical sciences, though his farming family had little money for formal education. Following the advice of a professor, he joined the Augustinian order, a monastic group that emphasized research and learning, in 1843.

Ensconced at a monastery in Brno, the shy Gregor quickly began spending time in the garden. Fuchsias in particular grabbed his attention, their daintiness hinting at an underlying grand design. “The fuchsias probably gave him the idea for the famous experiments,” says Sander Gliboff, who researches the history of biology at Indiana University Bloomington. “He had been crossing different varieties, trying to get new colors or combinations of colors, and he got repeatable results that suggested some law of heredity at work.”

These laws became clear with his cultivation of pea plants. Using paintbrushes, Mendel dabbed pollen from one to another, precisely pairing thousands of plants with certain traits over a stretch of about seven years. He meticulously documented how matching yellow peas and green peas, for instance, always yielded a yellow plant. Yet mating these yellow offspring together produced a generation where a quarter of the peas gleamed green again. Ratios like these led to Mendel’s coining of the terms dominant (the yellow color, in this case) and recessive for what we now call genes, and which Mendel referred to as “factors.”

He was ahead of his time. His studies received scant attention in their day, but decades later, when other scientists discovered and replicated Mendel’s experiments, they came to be regarded as a breakthrough.

“The genius in Mendel’s experiments was his way of formulating simple hypotheses that explain a few things very well, instead of tackling all the complexities of heredity at once,” says Gliboff. “His brilliance was in putting it all together into a project that he could actually do.”

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Mark Marturello

Isaac Newton Eyes Optics

Experimental result: The nature of color and light

When: 1665-1666

Before he was that Isaac Newton — scientist extraordinaire and inventor of the laws of motion, calculus and universal gravitation (plus a crimefighter to boot) — plain ol’ Isaac found himself with time to kill. To escape a devastating outbreak of plague in his college town of Cambridge, Newton holed up at his boyhood home in the English countryside. There, he tinkered with a prism he picked up at a local fair — a “child’s plaything,” according to Patricia Fara, fellow of Clare College, Cambridge.

Let sunlight pass through a prism and a rainbow, or spectrum, of colors splays out. In Newton’s time, prevailing thinking held that light takes on the color from the medium it transits, like sunlight through stained glass. Unconvinced, Newton set up a prism experiment that proved color is instead an inherent property of light itself. This revolutionary insight established the field of optics, fundamental to modern science and technology.

Newton deftly executed the delicate experiment: He bored a hole in a window shutter, allowing a single beam of sunlight to pass through two prisms. By blocking some of the resulting colors from reaching the second prism, Newton showed that different colors refracted, or bent, differently through a prism. He then singled out a color from the first prism and passed it alone through the second prism; when the color came out unchanged, it proved the prism didn’t affect the color of the ray. The medium did not matter. Color was tied up, somehow, with light itself.

Partly owing to the ad hoc, homemade nature of Newton’s experimental setup, plus his incomplete descriptions in a seminal 1672 paper, his contemporaries initially struggled to replicate the results. “It’s a really, really technically difficult experiment to carry out,” says Fara. “But once you have seen it, it’s incredibly convincing.”

In making his name, Newton certainly displayed a flair for experimentation, occasionally delving into the self-as-subject variety. One time, he stared at the sun so long he nearly went blind. Another, he wormed a long, thick needle under his eyelid, pressing on the back of his eyeball to gauge how it affected his vision. Although he had plenty of misses in his career — forays into occultism, dabbling in biblical numerology — Newton’s hits ensured his lasting fame.

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Mark Marturello

Michelson and Morley Whiff on Ether

Experimental result: The way light moves

When: 1887

Say “hey!” and the sound waves travel through a medium (air) to reach your listener’s ears. Ocean waves, too, move through their own medium: water. Light waves are a special case, however. In a vacuum, with all media such as air and water removed, light somehow still gets from here to there. How can that be?

The answer, according to the physics en vogue in the late 19th century, was an invisible, ubiquitous medium delightfully dubbed the “luminiferous ether.” Working together at what is now Case Western Reserve University in Ohio, Albert Michelson and Edward W. Morley set out to prove this ether’s existence. What followed is arguably the most famous failed experiment in history.

The scientists’ hypothesis was thus: As Earth orbits the sun, it constantly plows through ether, generating an ether wind. When the path of a light beam travels in the same direction as the wind, the light should move a bit faster compared with sailing against the wind.

To measure the effect, miniscule though it would have to be, Michelson had just the thing. In the early 1880s, he had invented a type of interferometer, an instrument that brings sources of light together to create an interference pattern, like when ripples on a pond intermingle. A Michelson interferometer beams light through a one-way mirror. The light splits in two, and the resulting beams travel at right angles to each other. After some distance, they reflect off mirrors back toward a central meeting point. If the light beams arrive at different times, due to some sort of unequal displacement during their journeys (say, from the ether wind), they create a distinctive interference pattern.

The researchers protected their delicate interferometer setup from vibrations by placing it atop a solid sandstone slab, floating almost friction-free in a trough of mercury and further isolated in a campus building’s basement. Michelson and Morley slowly rotated the slab, expecting to see interference patterns as the light beams synced in and out with the ether’s direction.

Instead, nothing. Light’s speed did not vary.

Neither researcher fully grasped the significance of their null result. Chalking it up to experimental error, they moved on to other projects. (Fruitfully so: In 1907, Michelson became the first American to win a Nobel Prize, for optical instrument-based investigations.) But the huge dent Michelson and Morley unintentionally kicked into ether theory set off a chain of further experimentation and theorizing that led to Albert Einstein’s 1905 breakthrough new paradigm of light, special relativity.

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Mark Marturello

Marie Curie’s Work Matters

Experimental result: Defining radioactivity

When: 1898

Few women are represented in the annals of legendary scientific experiments, reflecting their historical exclusion from the discipline. Marie Sklodowska broke this mold.

Born in 1867 in Warsaw, she immigrated to Paris at age 24 for the chance to further study math and physics. There, she met and married physicist Pierre Curie, a close intellectual partner who helped her revolutionary ideas gain a foothold within the male-dominated field. “If it wasn’t for Pierre, Marie would never have been accepted by the scientific community,” says Marilyn B. Ogilvie, professor emeritus in the history of science at the University of Oklahoma. “Nonetheless, the basic hypotheses — those that guided the future course of investigation into the nature of radioactivity — were hers.”

The Curies worked together mostly out of a converted shed on the college campus where Pierre worked. For her doctoral thesis in 1897, Marie began investigating a newfangled kind of radiation, similar to X-rays and discovered just a year earlier. Using an instrument called an electrometer, built by Pierre and his brother, Marie measured the mysterious rays emitted by thorium and uranium. Regardless of the elements’ mineralogical makeup — a yellow crystal or a black powder, in uranium’s case — radiation rates depended solely on the amount of the element present.

From this observation, Marie deduced that the emission of radiation had nothing to do with a substance’s molecular arrangements. Instead, radioactivity — a term she coined — was an inherent property of individual atoms, emanating from their internal structure. Up until this point, scientists had thought atoms elementary, indivisible entities. Marie had cracked the door open to understanding matter at a more fundamental, subatomic level.

Curie was the first woman to win a Nobel Prize, in 1903, and one of a very select few people to earn a second Nobel, in 1911 (for her later discoveries of the elements radium and polonium).

“In her life and work,” says Ogilvie, “she became a role model for young women who wanted a career in science.”

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Mark Marturello

Ivan Pavlov Salivates at the Idea

Experimental result: The discovery of conditioned reflexes

When: 1890s-1900s

Russian physiologist Ivan Pavlov scooped up a Nobel Prize in 1904 for his work with dogs, investigating how saliva and stomach juices digest food. While his scientific legacy will always be tied to doggie drool, it is the operations of the mind — canine, human and otherwise — for which Pavlov remains celebrated today.

Gauging gastric secretions was no picnic. Pavlov and his students collected the fluids that canine digestive organs produced, with a tube suspended from some pooches’ mouths to capture saliva. Come feeding time, the researchers began noticing that dogs who were experienced in the trials would start drooling into the tubes before they’d even tasted a morsel. Like numerous other bodily functions, the generation of saliva was considered a reflex at the time, an unconscious action only occurring in the presence of food. But Pavlov’s dogs had learned to associate the appearance of an experimenter with meals, meaning the canines’ experience had conditioned their physical responses.

“Up until Pavlov’s work, reflexes were considered fixed or hardwired and not changeable,” says Catharine Rankin, a psychology professor at the University of British Columbia and president of the Pavlovian Society. “His work showed that they could change as a result of experience.”

Pavlov and his team then taught the dogs to associate food with neutral stimuli as varied as buzzers, metronomes, rotating objects, black squares, whistles, lamp flashes and electric shocks. Pavlov never did ring a bell, however; credit an early mistranslation of the Russian word for buzzer for that enduring myth.

The findings formed the basis for the concept of classical, or Pavlovian, conditioning. It extends to essentially any learning about stimuli, even if reflexive responses are not involved. “Pavlovian conditioning is happening to us all of the time,” says W. Jeffrey Wilson of Albion College, fellow officer of the Pavlovian Society. “Our brains are constantly connecting things we experience together.” In fact, trying to “un-wire” these conditioned responses is the strategy behind modern treatments for post-traumatic stress disorder, as well as addiction.

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Mark Marturello

Robert Millikan Gets a Charge

Experimental result: The precise value of a single electron’s charge

When: 1909

By most measures, Robert Millikan had done well for himself. Born in 1868 in a small town in Illinois, he went on to earn degrees from Oberlin College and Columbia University. He studied physics with European luminaries in Germany. He then joined the University of Chicago’s physics department, and even penned some successful textbooks.

But his colleagues were doing far more. The turn of the 20th century was a heady time for physics: In the span of just over a decade, the world was introduced to quantum physics, special relativity and the electron — the first evidence that atoms had divisible parts. By 1908, Millikan found himself pushing 40 without a significant discovery to his name.

The electron, though, offered an opportunity. Researchers had struggled with whether the particle represented a fundamental unit of electric charge, the same in all cases. It was a critical determination for further developing particle physics. With nothing to lose, Millikan gave it a go.

In his lab at the University of Chicago, he began working with containers of thick water vapor, called cloud chambers, and varying the strength of an electric field within them. Clouds of water droplets formed around charged atoms and molecules before descending due to gravity. By adjusting the strength of the electric field, he could slow down or even halt a single droplet’s fall, countering gravity with electricity. Find the precise strength where they balanced, and — assuming it did so consistently — that would reveal the charge’s value.

When it turned out water evaporated too quickly, Millikan and his students — the often-unsung heroes of science — switched to a longer-lasting substance: oil, sprayed into the chamber by a drugstore perfume atomizer.

The increasingly sophisticated oil-drop experiments eventually determined that the electron did indeed represent a unit of charge. They estimated its value to within whiskers of the currently accepted charge of one electron (1.602 x 10-19 coulombs). It was a coup for particle physics, as well as Millikan.

“There’s no question that it was a brilliant experiment,” says Caltech physicist David Goodstein. “Millikan’s result proved beyond reasonable doubt that the electron existed and was quantized with a definite charge. All of the discoveries of particle physics follow from that.”

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Mark Marturello

Young, Davisson and Germer See Particles Do the Wave

Experimental result: The wavelike nature of light and electrons

When: 1801 and 1927, respectively

Light: particle or wave? Having long wrestled with this seeming either/or, many physicists settled on particle after Isaac Newton’s tour de force through optics. But a rudimentary, yet powerful, demonstration by fellow Englishman Thomas Young shattered this convention.

Young’s interests covered everything from Egyptology (he helped decode the Rosetta Stone) to medicine and optics. To probe light’s essence, Young devised an experiment in 1801. He cut two thin slits into an opaque object, let sunlight stream through them and watched how the beams cast a series of bright and dark fringes on a screen beyond. Young reasoned that this pattern emerged from light wavily spreading outward, like ripples across a pond, with crests and troughs from different light waves amplifying and canceling each other.

Although contemporary physicists initially rebuffed Young’s findings, rampant rerunning of these so-called double-slit experiments established that the particles of light really do move like waves. “Double-slit experiments have become so compelling [because] they are relatively easy to conduct,” says David Kaiser, a professor of physics and of the history of science at MIT. “There is an unusually large ratio, in this case, between the relative simplicity and accessibility of the experimental design and the deep conceptual significance of the results.”

More than a century later, a related experiment by Clinton Davisson and Lester Germer showed the depth of this significance. At what is now called Nokia Bell Labs in New Jersey, the physicists ricocheted electron particles off a nickel crystal. The scattered electrons interacted to produce a pattern only possible if the particles also acted like waves. Subsequent double slit-style experiments with electrons proved that particles with matter and undulating energy (light) can each act like both particles and waves. The paradoxical idea lies at the heart of quantum physics, which at the time was just beginning to explain the behavior of matter at a fundamental level.

“What these experiments show, at their root, is that the stuff of the world, be it radiation or seemingly solid matter, has some irreducible, unavoidable wavelike characteristics,” says Kaiser. “No matter how surprising or counterintuitive that may seem, physicists must take that essential ‘waviness’ into account.”

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Mark Marturello

Robert Paine Stresses Starfish

Experimental result: The disproportionate impact of keystone species on ecosystems

When: Initially presented in a 1966 paper

Just like the purple starfish he crowbarred off rocks and chucked into the Pacific Ocean, Bob Paine threw conventional wisdom right out the window.

By the 1960s, ecologists had come to agree that habitats thrived primarily through diversity. The common practice of observing these interacting webs of creatures great and small suggested as much. Paine took a different approach.

Curious what would happen if he intervened in an environment, Paine ran his starfish-banishing experiments in tidal pools along and off the rugged coast of Washington state. The removal of this single species, it turned out, could destabilize a whole ecosystem. Unchecked, the starfish’s barnacle prey went wild — only to then be devoured by marauding mussels. These shellfish, in turn, started crowding out the limpets and algal species. The eventual result: a food web in tatters, with only mussel-dominated pools left behind.

Paine dubbed the starfish a keystone species, after the necessary center stone that locks an arch into place. A revelatory concept, it meant that all species do not contribute equally in a given ecosystem. Paine’s discovery had a major influence on conservation, overturning the practice of narrowly preserving an individual species for the sake of it, versus an ecosystem-based management strategy.

“His influence was absolutely transformative,” says Oregon State University’s Jane Lubchenco, a marine ecologist. She and her husband, fellow OSU professor Bruce Menge, met 50 years ago as graduate students in Paine’s lab at the University of Washington. Lubchenco, the administrator of the National Oceanic Atmospheric Administration from 2009 to 2013, saw over the years the impact that Paine’s keystone species concept had on policies related to fisheries management.

Lubchenco and Menge credit Paine’s inquisitiveness and dogged personality for changing their field. “A thing that made him so charismatic was almost a childlike enthusiasm for ideas,” says Menge. “Curiosity drove him to start the experiment, and then he got these spectacular results.”

Paine died in 2016. His later work had begun exploring the profound implications of humans as a hyper-keystone species, altering the global ecosystem through climate change and unchecked predation.

https://discovermagazine.com/2019/november/the-top-10-science-experiments-of-all-time

不可能とされてきたゼロ除算について 自然な解釈でゼロ除算が可能になる事を発見しました：

とても興味深く読みました

ゼロ除算の発見は日本です：

∞？？？

∞は定まった数ではない????

人工知能はゼロ除算ができるでしょうか：5年 ゼロ除算の発見と重要性をした：再生核研究所 2014年2月2日

https://www.researchgate.net/project/division-by-zero

https://lnkd.in/fH799Xz

https://lnkd.in/fKAN-Tq

https://lnkd.in/fYN_n96

https://note.mu/ysaitoh/n/nf190e8ecfda4

ゼロ除算の発見は日本です：

∞？？？

∞は定まった数ではない????

人工知能はゼロ除算ができるでしょうか：5年 ゼロ除算の発見と重要性をした：再生核研究所 2014年2月2日

再生核研究所声明 382 (2017.9.11)： ニュートンを越える天才たちに－育成する立場の人に

次のような文書を残した： いま思いついたこと：ニュートンは偉く、ガウス、オイラーなども 遥かに及ばないと 何かに書いてあると言うのです。それで、考え、思いついた。 ガウス、オイラーの業績は とても想像も出来なく、如何に基本的で、深く、いろいろな結果がどうして得られたのか、思いもよらない。まさに天才である。数学界にはそのような天才が、結構多いと言える。しかるに、ニュートンの業績は 万有引力の法則、運動の法則、微積分学さえ、理解は常人でも出来き、多くの数学上の結果もそうである。しかるにその偉大さは 比べることも出来ない程であると表現されると言う。それは、どうしてであろうか。確かに世界への甚大な影響として 納得できる面がある。－ 初めて スタンフォード大学を訪れた時、確かにニュートンの肖像画が 別格高く掲げられていたことが、鮮明に想い出されてくる。－ 今でもそうであろうか？（２０１７．９．８．１０：４２）。

万物の運動を支配する法則、力、エネルギーの原理、長さ、面積、体積を捉え、傾き、勾配等の概念を捉えたのであるから、森羅万象のある基礎部分をとらえたものとして、世界史における影響が甚大であると考えれば その業績の大きさに驚かされる。

世界史における甚大な影響として、科学上ではないが、それらを越える、宗教家の大きな存在に まず、注意を喚起して置きたい。数学者、天文学者では ゼロを数として明確に導入し、負の数も考え、算術の法則（四則演算）を確立し、ゼロ除算0/0=0を宣言したBrahmagupta (598 -668 ?) の 偉大な影響 にも特に注意したい。

そのように偉大なるニュートンを発想すれば、それを越える偉大なる歴史上の存在の可能性を考えたくなるのは人情であろう。そこで、天才たちやそれを育成したいと考える人たちに 如何に考えるべきかを述べて置きたい。

万人にとって近い存在で、甚大な貢献をするであろう、科学的な分野への志向である。鍵は 生命と情報ではないだろうか。偉大なる発見、貢献であるから具体的に言及できるはずがない。しかしながら、科学が未だ十分に達しておらず、しかも万人に甚大な影響を与える科学の未知の分野として、生命と情報分野における飛躍的な発見は ニュートンを越える発見に繋がるのではないだろうか。

生物とは何者か、どのように作られ、どのように活動しているか、本能と環境への対応の原理を支配する科学的な体系、説明である。生命の誕生と終末の後、人間精神の在り様と物理的な世界の関係、殆ど未知の雄大な分野である。

情報とは何か、情報と人間の関係、影響、発展する人工知能の方向性とそれらを統一する原理と理論。情報と物の関係。情報が物を動かしている実例が存在する。

それらの分野における画期的な成果は ニュートンを越える世界史上の発見として出現するのではないだろうか。

これらの難解な課題においてニュ－トンの場合の様に常人でも理解できるような簡明な法則が発見されるのではないだろうか。

人類未だ猿や動物にも劣る存在であるとして、世界史を恥ずかしい歴史として、未来人は考え、評価するだろう。世の天才たちの志向について、またそのような偉大なる人材を育成する立場の方々の注意を喚起させたい。偉大なる楽しい夢である。

それにはまずは、世界史を視野に、人間とは何者かと問い、神の意思を捉えようとする真智への愛を大事に育てて行こうではないか。

以 上

再生核研究所声明 505（2019.10.11）ゼロ除算の簡単な解説：（新数学、新世界の出現）

ゼロで割る問題、新しい考え方が 中々受け容れられない状況が続いている。そこで、少し時間が持てたので、できるだけ簡単な解説を試みたい。 簡単で、基本的な関数 y=f(x) =1/x を考えます。高校生も反比例の式や、直角双曲線関数として学ぶ関数です。 問題はその関数を考えて 原点 x=0 での値を考えると どうなるかです。 正の方からゼロに近づけばプラス無限大に近づき、負の方向から近づけば 負の無限大に近づき、原点での値は分からない、 定まらない、考えられない というのが、我々以外の 世界の考え方でした。２０１４．２．２以来 その値を 世界的に注目して来ましたが、その関数値は 原点でゼロであるという事を述べた文献は 無いようです。 逆に、おかしい、おかしいという意見が現在でも 相当続いています。

何十年もゼロで割る問題を考えてきた人も、今朝になっても (2019.10.10) 分からず、おかしなことを言っているありさまです。

世の混乱を おさめ きちんとするために、この問題、多くの人が知っている、基本関数の原点での値を 説明したい。 高校生の教科書にも載っている基本関数です。その関数の原点での値が有るとすれば、高校生の教科書を変える事件に繋がり、世の膨大な文献と世の考え方を変えることに繋がります。

その基本関数の原点での値は ゼロです。 沢山の理由を与えて来ました:

これらの数学の素人向きの解説は ５５カ月に亘って 次で与えられている：

数学基礎学力研究会公式サイト 楽しい数学

www.mirun.sctv.jp/~suugaku/

数学的な解説論文は 次で公表されている：

viXra:1904.0408 submitted on 2019-04-22 00:32:30,

What Was Division by Zero?; Division by Zero Calculus and New World

美しい関数のグラフを考えて下さい。プラス無限大とマイナス無限大の間。 その値がゼロならば、原点は そのグラフの中心で 美しいと発想できます。ゼロは 周辺の平均値であるとも考えられます。 関数は、奇関数だから f(―x) = ―f(x) で、 x=0 で f(0)=0 でなければならないなどと 言われてみれば 納得できる人は 多いのではないでしょうか。

ところが、それがどうしても受け入れられないのは、誠に畏れ多くも アリストテレス の連続性に対する強い思い入れや ゼロや無を嫌ってきた 永いギリシャ文化の影響が 欧米の精神の基礎にあるからと その根強い理由が考えられます。－ 実際、我々の結果を聞くと、多くの人が、異様に表情を変えたことが 回想されます。

プラス無限とマイナス無限が 離れている。

あるいは、正の方向からゼロに近づくと 無限大に大きくなっていくのに、ゼロ点で突然に ゼロに落ちている。そんなことは あり得ない と考えてしまう。

そこで、クテシビオスの法則を考えてみます。ギリシャの紀元前２００年くらい前の方です。 非常に分かりやすい例です。想像してください、一様の太さでない管を流れる流体を考えます。 ある平面で切った断面の面積をＳとして、その面で流体の速度vは一定とします。 どの断面でも 一定時間にその断面を流れる流体は一定 (すなわち、Sv:一定）と考えられます。このことは、離れた２つの断面で考えれば、それらの間で、入った流体の量は 同じ量出て行かなければならい事からうなずけるでしょう。 ホースで断面を小さくすると、水の出は激しくなる、速くなる現象から簡単に想像できるでしょう。 ここは実際の物理的な現象ではなくて 理想的に （数学ではある意味で 何時でも 理想的な状態で考える）そのような状況を想像するという事です。

そこで面白いのは、断面を どんどん小さくすると そこを流れる流体の速度vがどんどん大きく（速く）なる、Ｓを小さくしていくと速度が 無限大に近づくという事で、関数y=１/xで ｘが ゼロに近づいた状況に似ています。

しかしながら、そこで、Ｓがゼロの場合、どうなるでしょうか。流体は流れず、したがって速度はゼロになってしまいます。 突然、管が閉じてしまって 流体が流れません。

微妙なこと、理解できるのではないでしょうか。図を見ると図を想像すると分かり易いです。

それでも 原点の値は飛んでいて 気持ちが受け容れられないと感じられる方は多いのではないでしょうか。ところが驚嘆すべき新しい世界が現れました。実はゼロ点と無限遠点は接していたというのです。すると、双曲線関数の像はその上で２つの閉曲線に写り、実は美しいグラフをその世界、ホーントーラス上で描く事になります。この新世界はドイツの元お医者さんが２０年来愛し、拘って来た世界です。美しい図を見て、新世界を確認して下さい。２０００年来のユークリッド空間に代わる新数学、新世界の出現です：

https://www.horntorus.com/manifolds/horntorusmapping.html

Daeumler, Wolfgang, private publication (2019),

https://www.horntorus.com/manifolds/conformalmapping.pdf

さて、除算とは 割算のことです。1/0 とは 何だろうかが、それが ゼロ除算の本質的な問題で、ゼロで割ることを考えることです。算術の確立者ブラーマグプタは 0/0=0 と１３００年も前に 算術の確立と同時に考えましたが、一般にゼロで割ることは考えられませんでした。それもそのはずです、直ぐに ゼロ除算は 不可能であることが、証明されてしまいます。 それで、この考えは１３００年を越えて現在に至っています。ところが物理法則に ゼロ分の公式が沢山現れ、実際 アインシュタインの最大の懸案の問題 とされていました。また、今でも何とかならないかと 結構な人が 真剣に考えています。不可能な事を考える。思えば、数学では できないことを できるように 考え方を広げて 可能にしてきた歴史が有り、数学の歴史がそうであったと述べて、ゼロ除算も可能になるだろう と予見していた数学の歴史家もいました。

詳しい解説は、上記文献で詳しく述べていますが、結論を、本質を言えば、上記関数の f(0)=0 の事実を 1/0 の定義として、1/0=0 の意味であるとしました。 ゼロ除算の最大の問題は、実は、ゼロ除算の定義、意味に有りました。世の多くの誤解は、ゼロ除算の意味を捉えず、ゼロ除算をきちんと定義することなく、議論してきたことに有ります。

私たちは、いろいろなゼロ除算の定義を与えて来ましたが、この定義がゼロ除算の本質であると考えています。 この定義で、割る意味が現れていると考えられるでしょうか。

以 上

再生核研究所声明 ５００（2019.7.2８） 数学の令和革新と日本の挑戦、東京オリンピック

日本を取り巻く国際環境は、日本にとって 面白くない状況が有るようである。 日本が被害感情 抑圧されているように感じられて 鬱積感情が高まっているように感じられる。日本固有の美しい文化も 失われないかとの危惧の気持ちも湧いてくる。

そこで、東京オリンピックを意識して、日本発の 数学の令和革新を断行して、世界の数理科学や世界史の進化に貢献して 日本国の矜持を 高めたい。

そんなことで、人間は良いのか、世界史は良いのか。 我々はそれらの進化を願っている。

令和革新は 初めの１０年 情報をしっかり世界に発信して、その後１０年くらいで 数学の内容の発展と研究を充実させ、千年を越える数理の文化の基礎を 令和時代に確立したい。

志向する内実は、既に歴然である：

ユークリッド幾何学は 無限の彼方について、いわばどこまでもどこまでも一様に続いているとの考え、思想を実現させているので、無限遠点の考えを用いない範囲では 従来の幾何学はすべて正しい。 しかしながら、無限の先を考えるときに新しい世界、現象が現れて驚嘆すべき結果や、世界が現れる。その意味で、 ユークリッド幾何学は 本質的な発展がなされる。 従来の結果に新しい結果が加わる。

ところが、従来の有限の世界での結果でも、沢山の新しい美しい結果が導かれてきた。 例えば、一般の三角形で成り立つ公式が 特別に、２等辺三角形や直角三角形、あるいは退化した三角形で成り立たないような公式になっている場合でも 公式が例外なく成り立つようになるなど、美しい、完全な結果になる現象さえ沢山発見されてきた（沢山の具体例が挙げられるが、ここでは式を用いない表現を試みている）。 沢山の実例が、奥村先生たちによって創刊された雑誌などに どんどん出版され、躍動する状況がある。

我が国の名著、高木貞治氏の解析概論、世界的な名著L. V. Ahlfors の, Complex Analysis などの基礎数学は 基本的な変更が要求されることとなった。

それはそもそもゼロ除算、ゼロで割ってはならないの 数学十戒第一： 汝ゼロで割ってはいけないが覆され、ゼロで割って新しい世界が現れてきたことによる。 そこから現れた、現象とは、無限遠点が曖昧であった、無限ではなく、実はゼロで表されるという事実をもたらした。 それゆえに、直線は原点を代数的に通り、その意味で平行線の公理は成り立たず、しかもいわゆる非ユークリッド幾何学とも違う世界を示している。解析関数は、孤立特異点で固有の値をとり、ピカールの定理さえ変更が求められる。いわゆる直角座標系で y軸の勾配はゼロであり、\tan(\pi/2) =0 である。基本関数 y=1/x の原点における値は ゼロである。リーマン球面のモデルは、ホーントーラスのモデルに変更されるべきである。 微分係数の概念や、特異積分の概念さえ変更されるべきである。 微分方程式論には本質的な欠陥があり、２次曲線論や解析幾何学、複素解析学さえ本質的な欠陥を有している。このような変更は、数学史上かつてなかった事件であり、それ故に 令和革新を 求めている：

そこで、初等数学の 令和革新 を広く提案して、将来 数学での日本発の世界文化遺産 になるように努力したい。

東京オリンピックに絡んで言及した理由は次のようである。

日本を訪れた人々は、日本の美しさ、親切さ、日本人の細やかさに感動して高質なお土産を購入して感銘を受けて帰国するだろう。

その際、日本発の文化として、 汝ゼロで割ってはならないの数学十戒第一は覆されて、ゼロで割って、新世界が現れた、ゼロで割ることができて、アリストテレス、ユークリッド以来の新数学が現れたことを伝えたい。 象徴的な例は、

1/0=0/0=z/0= tan(\pi/2) =log 0 =0,

基本的な関数 y=1/x の原点に於ける値はゼロである。無限遠点がゼロで表される。ゼロの意味の新しい発見である。

我々は、象徴的に提案できるTシャッツ、お菓子などへの刻印、デザインの例を そのために いろいろ提供できる。

そのような活用を図って、上記 目標の実現を志向したい。 日本発の文化を世界に展開したい。ゼロ除算の発見は、人間の愚かさを世界の人々に教え、新時代を志向させるだろう。 未だ混乱する世界を哀しく示すだろう。

万物流転、世に令和革新を断行して、世界史に日本指導の文化の基礎を築こう。 革新には 真智への愛の熱情が必要であり、それ故に 多様な人々による できるところでの参画を呼び掛けたい。

世界史が、この声明の行く末を、趨勢を見ているのは 歴然である。

これらの数学の素人向きの解説は ５５カ月に亘って 次で与えられている：

数学基礎学力研究会公式サイト 楽しい数学

www.mirun.sctv.jp/~suugaku/

数学的な解説論文は 次で公表されている：

viXra:1904.0408 submitted on 2019-04-22 00:32:30,

What Was Division by Zero?; Division by Zero Calculus and New World

我々は 初等数学には基本的な欠陥がある と述べている。ゼロ除算は数学者ばかりではなく 人類の、世界史の恥である と述べている。その真相を明らかにしたいと 人々は思われないでしょうか。 マスコミの皆さん、世界は未だ混乱している。何故、真相を究めようとされないのでしょうか。

次も参照：

再生核研究所声明490: 令和革新の大義、 趣旨 ー 初等数学

再生核研究所声明493： ゼロ除算 分らない、回答 － 初等数学の 令和革新 の意味

再生核研究所声明495：ゼロ除算 は 何故理解が難しいのか － 再生核研究所声明493（2019.7.1） ゼロ除算 分らない、回答 － 初等数学の 令和革新 の意味 の前段階

再生核研究所声明496（2019.7.8） 初等数学の 令和革新 の意味 - 数学嫌いな一般の方 向き

再生核研究所声明 497（2019.7.9） ゼロ除算は何故難しいか、なぜ当たり前か

再生核研究所声明 498（2019.7.11） ゼロ除算は 何故 驚きか

以 上

God’s most important commandment

never-divide-by-zero-meme-66

Even more important than “thou shalt not eat seafood”

Published by admin, on October 18th, 2011 at 3:47 pm. Filled under: Never Divide By Zero Tags: commandment, Funny, god, zero ? Comments Off on God’s most important commandment

https://thedistractionnetwork.com/.../never-divide.../page/4/

1/0=0、0/0=0、z/0=0

https://ameblo.jp/syoshinoris/entry-12276045402.html

1/0=0、0/0=0、z/0=0

https://ameblo.jp/syoshinoris/entry-12263708422.html

1/0=0、0/0=0、z/0=0

https://ameblo.jp/syoshinoris/entry-12272721615.html

Division By Zero（ゼロ除算）1/0=0、0/0=0、z/0=0

https://ameblo.jp/syoshinoris/entry-12392596876.html

ゼロ除算（ゼロじょざん、division by zero）1/0=0、0/0=0、z/0=0

https://ameblo.jp/syoshinoris/entry-12394775733.html

再生核研究所声明371（2017.6.27）ゼロ除算の講演― 国際会議 https://sites.google.com/site/sandrapinelas/icddea-2017 報告

ソクラテス?プラトン?アリストテレス その他

https://ameblo.jp/syoshinoris/entry-12328488611.html

Ten billion years ago DIVISION By ZERO：

https://www.facebook.com/notes/yoshinori-saito/ten-billion-years-ago-division-by-zero/1930645683923690/

One hundred million years ago DIVISION By ZERO

https://www.facebook.com/.../one-hundred-million-years-ago

https://ameblo.jp/syoshinoris/entry-12370907279.html

平成の30年

かってカトリック教会は、過去にガリレオでひどい間違いを犯した。

科学の問題に権威を振りかざし、「太陽が地球の周りを回っている」と宣言したのだ。

さらには地動説を唱える学者を火あぶりの刑にさえしている。

それから数世紀を経て教会の総本山ヴァチカンは、専門家を招いて宇宙論について意見を求めた。

1981年のことである。

ステーヴン?W?ホーキングもここに出席した。

会議の最後に、参加者は教皇への拝謁が許された。この時、教皇はおごそかに

「ビッグバン以後の宇宙の進化を研究することは結構だが、

ビッグバン自体を突き詰めてはいけない」

と述べたという。なぜか?

「ビッグバンは創造の瞬間であり、したがって神の業だから」

それが、理由である。

またもやヴァチカンは、科学の分野に口出しをしてきたではないか。

で、ホーキングは、この時のことを非常に謎めいた言葉でその著書「宇宙の始まりと終わり」に書き残している。

「それを聞いてホッとしました。私が会議で話したテーマを教皇は知らなかったからです。」

…ムムッ????? と言うことはもしかして、すでにホーキングはビッグバン自体をテーマにその原理などを科学的根拠を元に講演をしたのか??

さらに続けて言う。

「わたしはガリレオと同じ運命(注1)をたどりたくはありませでした。もっともわたしは、彼の死から300年後に生まれたこともあり、ガリレオにはおおいに親近感を抱いています」。

そう述懐しています。

(注1)地動説を唱えたガリレオは第2回異端審問所審査で、ローマ教皇庁検邪聖省から有罪の判決を受け、終身刑を言い渡されている。

ビッグバンは起こるべきして起こった。それは科学的根拠によって説明できる。理論はこうであるなどと科学者であるホーキングがヴァチカンで講演していたとしたら…。

もしかしてホーキングは教皇の不興を買って異端審問所にかけられ、神への冒瀆罪によって火あぶりの刑に処せられたかも知れないのだ。(時代が違うか)

ホーキングが考えるように教皇は、彼の発言を本当に知らなかったのか。

実は知っていた。カチンと来た教皇は、警告の意味で「ビッグバン自体には今後一切触れるな」と命じたのではなだろうか。

そう推理も出来る。またそう考えるが自然だ。それから数世紀を経て教会の総本山ヴァチカンは、専門家を招いて宇宙論について意見を求めた。

https://blog.goo.ne.jp/.../b5cd6cf92591fa651dd923d642156d4b

再生核研究所は、ゼロ除算算法の公認を求めていますが、

典型的な具体例をして、 ｙ軸の勾配はゼロ、 まっすぐに立った電柱の勾配は ゼロである、

tan(\pi/2) = 0の公認 を求め、小学生以降の教科書、学術書の変更を求めている。

それらの公認にどのくらいかからるかを楽しみにしている。

既に Isabelle/HOL は その結果の妥当性を保証している。

計算機の認識は 世の理解を超えている。

２０１９．４．１４．１１：０５

最終的に１９９２年、ローマ教皇ヨハネ?パウロ２世が誤りを認め、ガリレオに謝罪しました。ガリレオの死から３５０年後のことでした。

これは まずいのでは？ 真理を愛する、真実を求めるのが、人間として生きる意義では ないでしょうか。

人の生きるは、真智への愛 にある。 真実を知りたいということですが、それは 神の意志 を知りたいとも表現できます。

西洋と東洋の「0」への考え方：

(1)「0」を嫌う西洋（キリスト教社会）

「空虚」すなわち「0」を嫌うアリストテレスの影響を受け、「0」を認めない。

「0」を認めることは、「神様なんていないよ」と言うことと同じくらいの罪。

(2)「0」を受け入れた東洋（イスラム教社会）

「空虚」を受け入れ、「0」を取り入れる。

また、図形にとらわれない数学や、分数を小数に直して計算しやすくするなど計算技術を高めた。

https://enjoymath.pomb.org/?p=1829

再生核研究所声明 470 (2019.2.2)

ゼロ除算 1/0=0/0=z/0=\tan(\pi/2)=0 発見５周年を迎えて

アインシュタインも解決できなかった「ゼロで割る」問題

https://matome.naver.jp/odai/2135710882669605901

Title page of Leonhard Euler, Vollst?ndige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

https://notevenpast.org/dividing-nothing/

私は数学を信じない。 アルバート?アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。

1423793753.460.341866474681。

Einstein's Only Mistake: Division by Zero

https://refully.blogspot.jp/.../einsteins-only-mistake...

Albert Einstein:

Blackholes are where God divided by zero.

I don’t believe in mathematics.

George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that "it is well known to students of high school algebra" that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} [1]：

1. Gamow, G., My World Line (Viking, New York). p 44, 1970.

無限遠点は、実は数で0で表されていた。

ケンブリッジ大学とミュンヘン工科大学のIsabelle 計算機システムはゼロ除算ｘ/0=0 を導いた。

その後 質問に対して 回答があり、 添付のように 信じられないほどに ソフトが完成されていることを見て、驚嘆させられています。

責任者とは交流がありましたが、大したことではない と 言っていましたが、 実は 相当なことを 大きなグループで 完成していたと 考えられます。

2値や 大事な \tan(\pi/2)=0 も できているので、驚嘆です。

Black holes are where God divided by 0：Division by zero：1/0=0/0=z/0=\tan(\pi/2)=0 発見５周年を迎えて

You cannot divide by zero.Ever.

the story of science aristotle leads the way P220 より

If division by Zero were possible,then the result would exceed every integer

An Early Reference to Division by Zero C. B. Boyer：

https://www.fen.bilkent.edu.tr/~franz/M300/zero.pdf

4/6

７歳の少女が、当たり前である（100/0=0、0/0=0）と言っているゼロ除算を 多くの大学教授が、信じられない結果と言っているのは、まことに奇妙な事件と言えるのではないでしょうか。

1/0=0、0/0=0、z/0=0

division by zero（a?0 ）ゼロ除算 1/0=0、0/0=0、z/0=0

1/0=0/0=z/0= \tan (\pi/2)=0.

小学校以上で、最も知られている基本的な数学の結果は何でしょうか???

ゼロ除算（1/0=0、0/0=0、z/0=0）かピタゴラスの定理（a2 + b2 = c2 ）ではないでしょうか。

https://www.pinterest.com/pin/234468724326618408/

1+0=1 1－0=1 1×0=0 では、1/0?????????幾つでしょうか。

0??? 本当に大丈夫ですか?????0×0=1で矛盾になりませんか????

数学で「A÷０」（ゼロで割る）がダメな理由を教えてください。 https://detail.chiebukuro.yahoo.co.jp/.../ques.../q1411588849 #知恵袋_

割り算を掛け算の逆だと定義した人は、誰でしょう？？？

Title page of Leonhard Euler, Vollst?ndige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

https://notevenpast.org/dividing-nothing/

multiplication?????増える 掛け算（×） 1より小さい数を掛けたら小さくなる。 大きくなるとは限らない。

0×0=0?????????だから0で割れないと考えた。

唯根拠もなしに、出鱈目に言っている人は世に多い。

加（+）?減（-）?乗（×）?除（÷）

除法（じょほう、英: division）とは、乗法の逆演算????間違いの元

乗（×）は、加（+）

除（÷）は、減（-）

https://detail.chiebukuro.yahoo.co.jp/.../q14.../a37209195...

https://www.mirun.sctv.jp/.../%E5%A0%AA%E3%82%89%E3%81%AA...

何とゼロ除算は、可能になるだろうと April 12, 2011 に 公に 予想されていたことを 発見した。

多くの数学で できないが、できるようになってきた経緯から述べられたものである。

０を引いても引いたことにならないから：

君に０円の月給を永遠に払いますから心配しないでください：

変化がない：引いたことにはならない：

â„–1027

Dividing by Nothing by Alberto Martinez

Title page of Leonhard Euler, Vollst?ndige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

https://notevenpast.org/dividing-nothing/ より

The Road

Fig 5.2. Isaac Newton (1643-1727) and Gottfried Leibniz (1646-1716) were the culprits, ignoring the first commandment of mathematics not to divide by zero. But they hit gold, because what they mined in the process was the ideal circle.

https://thethirty-ninesteps.com/page_5-the_road.php より

mercredi, juillet 06, 2011

0/0, la célèbre formule d'Evariste Galois !

https://divisionparzero.blogspot.jp/2011/07/00-la-celebre-formule-devariste-galois.html より

無限に関する様々な数学的概念：無限大 ：記号∞ （アーベルなどはこれを 1 / 0 のように表記していた）で表す。 大雑把に言えば、いかなる数よりも大きいさまを表すものであるが、より明確な意味付けは文脈により様々である。https://ja.wikipedia.org/wiki/%E7%84%A1%E9%99%90 より

リーマン球面：無限遠点が、実は 原点と通じていた。

https://ja.wikipedia.org/wiki/%E3%83%AA%E3%83%BC%E3%83%9E%E3%83%B3%E7%90%83%E9%9D%A2 より

https://jestingstock.com/indian-mathematician-brahmagupta-image.html より

ブラーマグプタ（Brahmagupta、598年 – 668年?）はインドの数学者?天文学者。ブラマグプタとも呼ばれる。その著作は、イスラーム世界やヨーロッパにインド数学や天文学を伝える役割を果たした。

628年に、総合的な数理天文書『ブラーマ?スプタ?シッダーンタ』（????????????????????? Brāhmasphu?asiddhānta）を著した。この中の数章で数学が扱われており、第12章はガニタ（算術）、第18章はクッタカ（代数）にあてられている。クッタカという語は、もとは「粉々に砕く」という意味だったが、のちに係数の値を小さくしてゆく逐次過程の方法を意味するようになり、代数の中で不定解析を表すようになった。この書では、 0 と負の数にも触れていて、その算法は現代の考え方に近い（ただし 0 ÷ 0 ＝ 0 と定義している点は現代と異なっている）

https://ja.wikipedia.org/wiki/%E3%83%96%E3%83%A9%E3%83%BC%E3%83%9E%E3%82%B0%E3%83%97%E3%82%BFより

ブラーマ?スプタ?シッダーンタ (Brahmasphutasiddhanta) は、7世紀のインドの数学者?天文学者であるブラーマグプタの628年の著作である。表題は宇宙の始まりという意味。

数としての「0（ゼロ）の概念」がはっきりと書かれた、現存する最古の書物として有名である。https://ja.wikipedia.org/wiki/%E3%83%96%E3%83%A9%E3%83%BC%E3%83%9E%E3%83%BB%E3%82%B9%E3%83%97%E3%82%BF%E3%83%BB%E3%82%B7%E3%83%83%E3%83%80%E3%83%BC%E3%83%B3%E3%82%BF より

ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて６２８年になされているが、既にそのとき、正解1/0が期待されていたと言う。しかし、理論づけられず、その後１３００年を超えて、不可能である、あるいは無限、無限大、無限遠点とされてきたものである。

An Early Reference to Division by Zero C. B. Boyer

https://www.fen.bilkent.edu.tr/~franz/M300/zero.pdf

Impact of ‘Division by Zero’ in Einstein’s Static Universe and Newton’s Equations in Classical Mechanics：https://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/2084 より

神秘的に美しい3つの公式：

面白い事にゼロ除算については、いろいろな説が現在存在します

しかし、間もなく決着がつくのではないでしょうか。

ゼロ除算は、なにもかも当たり前ではないでしょうか。

ラース?ヴァレリアン?アールフォルス（Lars Valerian Ahlfors、1907年4月18日-1996年10月11日）はフィンランドの数学者。リーマン面の研究と複素解析の教科書を書いたことで知られる。https://ja.wikipedia.org/wiki/%E3%83%A9%E3%83%BC%E3%82%B9%E3%83%BB%E3%83%B4%E3%82%A1%E3%83%AC%E3%83%AA%E3%82%A2%E3%83%B3%E3%83%BB%E3%82%A2%E3%83%BC%E3%83%AB%E3%83%95%E3%82%A9%E3%83%AB%E3%82%B9

フィールズ賞第一号

COMPLEX ANALYSIS, 3E (International Series in Pure and Applied Mathematics) (英語) ハードカバー – 1979/1/1

Lars Ahlfors (è‘—)

https://www.amazon.co.jp/COMPLEX-ANALYSIS-International-Applied-Mathematics/dp/0070006571/ref=sr_1_fkmr1_1?ie=UTF8&qid=1463478645&sr=8-1-fkmr1&keywords=Lars+Valerian+Ahlfors%E3%80%80%E3%80%80COMPLEX+ANALYSIS

原点の円に関する鏡像は、実は 原点であった。

本では、無限遠点と考えられていました。

Ramanujan says that answer for 0/0 is infinity. But I'm not sure it's ...

https://www.quora.com/Ramanujan-says-that-answer-for-0-0-is-infi...

You can see from the other answers, that from the concept of limits, 0/0 can approach any value, even infinity. ... So, let me take a system where division by zero is actually defined, that is, you can multiply or divide both sides of an equation by ...

https://www.quora.com/Ramanujan-says-that-answer-for-0-0-is-infinity-But-Im-not-sure-its-correct-Can-anyone-help-me

Abel Memorial in Gjerstad

Discussions: Early History of Division by Zero

H. G. Romig

The American Mathematical Monthly

Vol. 31, No. 8 (Oct., 1924), pp. 387-389

Published by: Mathematical Association of America

DOI: 10.2307/2298825

Stable URL: https://www.jstor.org/stable/2298825

Page Count: 3

ロピタルの定理 (ロピタルのていり、英: l'H?pital's rule) とは、微分積分学において不定形 (en) の極限を微分を用いて求めるための定理である。綴りl'H?pital / l'Hospital、カタカナ表記ロピタル / ホスピタルの揺れについてはギヨーム?ド?ロピタルの項を参照。ベルヌーイの定理 (英語: Bernoulli's rule) と呼ばれることもある。本定理を (しばしば複数回) 適用することにより、不定形の式を非不定形の式に変換し、その極限値を容易に求めることができる可能性がある。https://ja.wikipedia.org/wiki/%E3%83%AD%E3%83%94%E3%82%BF%E3%83%AB%E3%81%AE%E5%AE%9A%E7%90%86

Ein aufleuchtender Blitz: Niels Henrik Abel und seine Zeit

https://books.google.co.jp/books?isbn=3642558402 -

Arild Stubhaug - 2013 - ?Mathematics

Niels Henrik Abel und seine Zeit Arild Stubhaug. Abb. 19 a–c. a. ... Eine Kurve, die Abel studierte und dabei herausfand, wie sich der Umfang inn gleich gro?e Teile aufteilen l?sst. ... Beim Integralzeichen statt der liegenden ∞ den Bruch 1/0.

https://books.google.co.jp/books?id=wTP1BQAAQBAJ&pg=PA282&lpg=PA282&dq=Niels+Henrik+Abel%E3%80%80%E3%80%80ARILD+Stubhaug%E3%80%80%E3%80%80%EF%BC%91/0%EF%BC%9D%E2%88%9E&source=bl&ots=wUaYL6x6lK&sig=OX1Yk_HxbCMm_FACotHYlgrbfsg&hl=ja&sa=X&ved=0ahUKEwj8-pftm-PPAhXIzVQKHX7ZCMEQ6AEISTAG#v=onepage&q=Niels%20Henrik%20Abel%E3%80%80%E3%80%80ARILD%20Stubhaug%E3%80%80%E3%80%80%EF%BC%91%2F0%EF%BC%9D%E2%88%9E&f=false

Indeterminate: the hidden power of 0 divided by 0

2016/12/02 に公開

You've all been indoctrinated into accepting that you cannot divide by zero. Find out about the beautiful mathematics that results when you do it anyway in calculus. Featuring some of the most notorious "forbidden" expressions like 0/0 and 1^∞ as well as Apple's Siri and Sir Isaac Newton.

https://www.youtube.com/watch?v=oc0M1o8tuPo より

ゼロ除算の論文：

file:///C:/Users/saito%20saburo/Downloads/P1-Division.pdf より

Eulerのゼロ除算に関する想い：

file:///C:/Users/saito%20saburo/Downloads/Y_1770_Euler_Elements%20of%20algebra%20traslated%201840%20l%20p%2059%20(1).pdf より

An Approach to Overcome Division by Zero in the Interval Gauss Algorithm

https://link.springer.com/article/10.1023/A:1015565313636

Carolus Fridericus Gauss：https://www.slideshare.net/fgz08/gauss-elimination-4686597

Archimedes：Arbelos

https://www.math.nyu.edu/~crorres/Archimedes/Stamps/stamps.html より

Archimedes Principle in Completely Submerged Balloons: Revisited

Ajay Sharma：

file:///C:/Users/saito%20saburo/Desktop/research_papers_mechanics___electrodynamics_science_journal_3499.pdf

ï¼»PDF]Indeterminate Form in the Equations of Archimedes, Newton and Einstein

https://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/3222

このページを訳す

0. 0 . The reason is that in the case of Archimedes principle, equations became feasible in. 1935 after enunciation of the principle in 1685, when ... Although division by zero is not permitted, yet it smoothly follows from equations based upon.

Thinking ahead of Archimedes, Newton and Einstein - The General ...

gsjournal.net/Science-Journals/Communications.../5503

このページを訳す

old Archimedes Principle, Newton' s law, Einstein 's mass energy equation. E=mc2 . .... filled in balloon becomes INDETERMINATE (0/0). It is not justified. If the generalized form Archimedes principle is used then we get exact volume V .....

https://gsjournal.net/Science-Journals/Communications-Mechanics%20/%20Electrodynamics/Download/5503

Find circles that are tangent to three given circles (Apollonius’ Problem) in C#

https://csharphelper.com/blog/2016/09/find-circles-that-are-tangent-to-three-given-circles-apollonius-problem-in-c/ より

ゼロ除算に関する詩：

The reason we cannot devide by zero is simply axiomatic as Plato pointed out.

https://mathhelpforum.com/algebra/223130-dividing-zero.html より

声明505

Fallacy of division | Revolvy

https://www.revolvy.com/page/Fallacy-of-division

このページを訳す

In the philosophy of the ancient Greek Anaxagoras, as claimed by the Roman atomist Lucretius,[1] it was assumed that the atoms .... For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a ...

https://www.revolvy.com/page/Fallacy-of-division

ソクラテス?プラトン?アリストテレス その他

2017年11月15日(水)

テーマ：社会

The null set is conceptually similar to the role of the number ``zero'' as it is used in quantum field theory. In quantum field theory, one can take the empty set, the vacuum, and generate all possible physical configurations of the Universe being modelled by acting on it with creation operators, and one can similarly change from one thing to another by applying mixtures of creation and anihillation operators to suitably filled or empty states. The anihillation operator applied to the vacuum, however, yields zero.

Zero in this case is the null set - it stands, quite literally, for no physical state in the Universe. The important point is that it is not possible to act on zero with a creation operator to create something; creation operators only act on the vacuum which is empty but not zero. Physicists are consequently fairly comfortable with the existence of operations that result in ``nothing'' and don't even require that those operations be contradictions, only operationally non-invertible.

It is also far from unknown in mathematics. When considering the set of all real numbers as quantities and the operations of ordinary arithmetic, the ``empty set'' is algebraically the number zero (absence of any quantity, positive or negative). However, when one performs a division operation algebraically, one has to be careful to exclude division by zero from the set of permitted operations! The result of division by zero isn't zero, it is ``not a number'' or ``undefined'' and is not in the Universe of real numbers.

Just as one can easily ``prove'' that 1 = 2 if one does algebra on this set of numbers as if one can divide by zero legitimately3.34, so in logic one gets into trouble if one assumes that the set of all things that are in no set including the empty set is a set within the algebra, if one tries to form the set of all sets that do not include themselves, if one asserts a Universal Set of Men exists containing a set of men wherein a male barber shaves all men that do not shave themselves3.35.

It is not - it is the null set, not the empty set, as there can be no male barbers in a non-empty set of men (containing at least one barber) that shave all men in that set that do not shave themselves at a deeper level than a mere empty list. It is not an empty set that could be filled by some algebraic operation performed on Real Male Barbers Presumed to Need Shaving in trial Universes of Unshaven Males as you can very easily see by considering any particular barber, perhaps one named ``Socrates'', in any particular Universe of Men to see if any of the sets of that Universe fit this predicate criterion with Socrates as the barber. Take the empty set (no men at all). Well then there are no barbers, including Socrates, so this cannot be the set we are trying to specify as it clearly must contain at least one barber and we've agreed to call its relevant barber Socrates. (and if it contains more than one, the rest of them are out of work at the moment).

Suppose a trial set contains Socrates alone. In the classical rendition we ask, does he shave himself? If we answer ``no'', then he is a member of this class of men who do not shave themselves and therefore must shave himself. Oops. Well, fine, he must shave himself. However, if he does shave himself, according to the rules he can only shave men who don't shave themselves and so he doesn't shave himself. Oops again. Paradox. When we try to apply the rule to a potential Socrates to generate the set, we get into trouble, as we cannot decide whether or not Socrates should shave himself.

Note that there is no problem at all in the existential set theory being proposed. In that set theory either Socrates must shave himself as All Men Must Be Shaven and he's the only man around. Or perhaps he has a beard, and all men do not in fact need shaving. Either way the set with just Socrates does not contain a barber that shaves all men because Socrates either shaves himself or he doesn't, so we shrug and continue searching for a set that satisfies our description pulled from an actual Universe of males including barbers. We immediately discover that adding more men doesn't matter. As long as those men, barbers or not, either shave themselves or Socrates shaves them they are consistent with our set description (although in many possible sets we find that hey, other barbers exist and shave other men who do not shave themselves), but in no case can Socrates (as our proposed single barber that shaves all men that do not shave themselves) be such a barber because he either shaves himself (violating the rule) or he doesn't (violating the rule). Instead of concluding that there is a paradox, we observe that the criterion simply doesn't describe any subset of any possible Universal Set of Men with no barbers, including the empty set with no men at all, or any subset that contains at least Socrates for any possible permutation of shaving patterns including ones that leave at least some men unshaven altogether.

https://webhome.phy.duke.edu/.../axioms/axioms/Null_Set.html

I understand your note as if you are saying the limit is infinity but nothing is equal to infinity, but you concluded corretly infinity is undefined. Your example of getting the denominator smaller and smalser the result of the division is a very large number that approches infinity. This is the intuitive mathematical argument that plunged philosophy into mathematics. at that level abstraction mathematics, as well as phyisics become the realm of philosophi. The notion of infinity is more a philosopy question than it is mathamatical. The reason we cannot devide by zero is simply axiomatic as Plato pointed out. The underlying reason for the axiom is because sero is nothing and deviding something by nothing is undefined. That axiom agrees with the notion of limit infinity, i.e. undefined. There are more phiplosphy books and thoughts about infinity in philosophy books than than there are discussions on infinity in math books.

https://mathhelpforum.com/algebra/223130-dividing-zero.html

ゼロ除算の歴史：ゼロ除算はゼロで割ることを考えるであるが、アリストテレス以来問題とされ、ゼロの記録がインドで初めて６２８年になされているが、既にそのとき、正解1/0が期待されていたと言う。しかし、理論づけられず、その後１３００年を超えて、不可能である、あるいは無限、無限大、無限遠点とされてきたものである。

An Early Reference to Division by Zero C. B. Boyer

https://www.fen.bilkent.edu.tr/~franz/M300/zero.pdf

OUR HUMANITY AND DIVISION BY ZERO

Lea esta bitácora en espa?ol

There is a mathematical concept that says that division by zero has no meaning, or is an undefined expression, because it is impossible to have a real number that could be multiplied by zero in order to obtain another number different from zero.

While this mathematical concept has been held as true for centuries, when it comes to the human level the present situation in global societies has, for a very long time, been contradicting it. It is true that we don’t all live in a mathematical world or with mathematical concepts in our heads all the time. However, we cannot deny that societies around the globe are trying to disprove this simple mathematical concept: that division by zero is an impossible equation to solve.

Yes! We are all being divided by zero tolerance, zero acceptance, zero love, zero compassion, zero willingness to learn more about the other and to find intelligent and fulfilling ways to adapt to new ideas, concepts, ways of doing things, people and cultures. We are allowing these ‘zero denominators’ to run our equations, our lives, our souls.

Each and every single day we get more divided and distanced from other people who are different from us. We let misinformation and biased concepts divide us, and we buy into these aberrant concepts in such a way, that we get swept into this division by zero without checking our consciences first.

I believe, however, that if we change the zeros in any of the “divisions by zero” that are running our lives, we will actually be able to solve the non-mathematical concept of this equation: the human concept.

>I believe deep down that we all have a heart, a conscience, a brain to think with, and, above all, an immense desire to learn and evolve. And thanks to all these positive things that we do have within, I also believe that we can use them to learn how to solve our “division by zero” mathematical impossibility at the human level. I am convinced that the key is open communication and an open heart. Nothing more, nothing less.

Are we scared of, or do we feel baffled by the way another person from another culture or country looks in comparison to us? Are we bothered by how people from other cultures dress, eat, talk, walk, worship, think, etc.? Is this fear or bafflement so big that we much rather reject people and all the richness they bring within?

How about if instead of rejecting or retreating from that person—division of our humanity by zero tolerance or zero acceptance—we decided to give them and us a chance?

How about changing that zero tolerance into zero intolerance? Why not dare ask questions about the other person’s culture and way of life? Let us have the courage to let our guard down for a moment and open up enough for this person to ask us questions about our culture and way of life. How about if we learned to accept that while a person from another culture is living and breathing in our own culture, it is totally impossible for him/her to completely abandon his/her cultural values in order to become what we want her to become?

Let’s be totally honest with ourselves at least: Would any of us really renounce who we are and where we come from just to become what somebody else asks us to become?

If we are not willing to lose our identity, why should we ask somebody else to lose theirs?

I believe with all my heart that if we practiced positive feelings—zero intolerance, zero non-acceptance, zero indifference, zero cruelty—every day, the premise that states that division by zero is impossible would continue being true, not only in mathematics, but also at the human level. We would not be divided anymore; we would simply be building a better world for all of us.

Hoping to have touched your soul in a meaningful way,

Adriana Adarve, Asheville, NC

https://adarvetranslations.com/…/our-humanity-and-division…/

5000年？？？？？

2017年09月01日(金)NEW !

テーマ：数学

Former algebraic approach was formally perfect, but it merely postulated existence of sets and morphisms [18] without showing methods to construct them. The primary concern of modern algebras is not how an operation can be performed, but whether it maps into or onto and the like abstract issues [19–23]. As important as this may be for proofs, the nature does not really care about all that. The PM’s concerns were not constructive, even though theoretically significant. We need thus an approach that is more relevant to operations performed in nature, which never complained about morphisms or the allegedly impossible division by zero, as far as I can tell. Abstract sets and morphisms should be de-emphasized as hardly operational. My decision to come up with a definite way to implement the feared division by zero was not really arbitrary, however. It has removed a hidden paradox from number theory and an obvious absurd from algebraic group theory. It was necessary step for full deployment of constructive, synthetic mathematics (SM) [2,3]. Problems hidden in PM implicitly affect all who use mathematics, even though we may not always be aware of their adverse impact on our thinking. Just take a look at the paradox that emerges from the usual prescription for multiplication of zeros that remained uncontested for some 5000 years 0 0 ? 0 ) 0 1=1 ? 0 ) 0 1 ? 0 1) 1e? ? ?T1 e0aT This ‘‘fact’’ was covered up by the infamous prohibition on division by zero [2]. How ingenious. If one is prohibited from dividing by zero one could not obtain this paradox. Yet the prohibition did not really make anything right. It silenced objections to irresponsible reasonings and prevented corrections to the PM’s flamboyant axiomatizations. The prohibition on treating infinity as invertible counterpart to zero did not do any good either. We use infinity in calculus for symbolic calculations of limits [24], for zero is the infinity’s twin [25], and also in projective geometry as well as in geometric mapping of complex numbers. Therein a sphere is cast onto the plane that is tangent to it and its free (opposite) pole in a point at infinity [26–28]. Yet infinity as an inverse to the natural zero removes the whole absurd (0a), for we obtain [2] 0 ? 1=1 ) 0 0 ? 1=12 > 0 0 e0bT Stereographic projection of complex numbers tacitly contradicted the PM’s prescribed way to multiply zeros, yet it was never openly challenged. The old formula for multiplication of zeros (0a) is valid only as a practical approximation, but it is group-theoretically inadmissible in no-nonsense reasonings. The tiny distinction in formula (0b) makes profound theoretical difference for geometries and consequently also for physical applications. T

https://www.plover.com/misc/CSF/sdarticle.pdf

とても興味深く読みました：

10,000 Year Clock

by Renny Pritikin

Conversation with Paolo Salvagione, lead engineer on the 10,000-year clock project, via e-mail in February 2010.

For an introduction to what we’re talking about here’s a short excerpt from a piece by Michael Chabon, published in 2006 in Details: ….Have you heard of this thing? It is going to be a kind of gigantic mechanical computer, slow, simple and ingenious, marking the hour, the day, the year, the century, the millennium, and the precession of the equinoxes, with a huge orrery to keep track of the immense ticking of the six naked-eye planets on their great orbital mainspring. The Clock of the Long Now will stand sixty feet tall, cost tens of millions of dollars, and when completed its designers and supporters plan to hide it in a cave in the Great Basin National Park in Nevada, a day’s hard walking from anywhere. Oh, and it’s going to run for ten thousand years. But even if the Clock of the Long Now fails to last ten thousand years, even if it breaks down after half or a quarter or a tenth that span, this mad contraption will already have long since fulfilled its purpose. Indeed the Clock may have accomplished its greatest task before it is ever finished, perhaps without ever being built at all. The point of the Clock of the Long Now is not to measure out the passage, into their unknown future, of the race of creatures that built it. The point of the Clock is to revive and restore the whole idea of the Future, to get us thinking about the Future again, to the degree if not in quite the way same way that we used to do, and to reintroduce the notion that we don’t just bequeath the future—though we do, whether we think about it or not. We also, in the very broadest sense of the first person plural pronoun, inherit it.

Renny Pritikin: When we were talking the other day I said that this sounds like a cross between Borges and the vast underground special effects from Forbidden Planet. I imagine you hear lots of comparisons like that…

Paolo Salvagione: (laughs) I can’t say I’ve heard that comparison. A childhood friend once referred to the project as a cross between Tinguely and Fabergé. When talking about the clock, with people, there’s that divide-by-zero moment (in the early days of computers to divide by zero was a sure way to crash the computer) and I can understand why. Where does one place, in one’s memory, such a thing, such a concept? After the pause, one could liken it to a reboot, the questions just start streaming out.

RP: OK so I think the word for that is nonplussed. Which the thesaurus matches with flummoxed, bewildered, at a loss. So the question is why even (I assume) fairly sophisticated people like your friends react like that. Is it the physical scale of the plan, or the notion of thinking 10,000 years into the future—more than the length of human history?

PS: I’d say it’s all three and more. I continue to be amazed by the specificity of the questions asked. Anthropologists ask a completely different set of questions than say, a mechanical engineer or a hedge fund manager. Our disciplines tie us to our perspectives. More than once, a seemingly innocent question has made an impact on the design of the clock. It’s not that we didn’t know the answer, sometimes we did, it’s that we hadn’t thought about it from the perspective of the person asking the question. Back to your question. I think when sophisticated people, like you, thread this concept through their own personal narrative it tickles them. Keeping in mind some people hate to be tickled.

RP: Can you give an example of a question that redirected the plan? That’s really so interesting, that all you brainiacs slaving away on this project and some amateur blithely pinpoints a problem or inconsistency or insight that spins it off in a different direction. It’s like the butterfly effect.

PS: Recently a climatologist pointed out that our equation of time cam, (photo by Rolfe Horn) (a cam is a type of gear: link) a device that tracks the difference between solar noon and mundane noon as well as the precession of the equinoxes, did not account for the redistribution of water away from the earth’s poles. The equation-of-time cam is arguably one of the most aesthetically pleasing parts of the clock. It also happens to be one that is fairly easy to explain. It visually demonstrates two extremes. If you slice it, like a loaf of bread, into 10,000 slices each slice would represent a year. The outside edge of the slice, let’s call it the crust, represents any point in that year, 365 points, 365 days. You could, given the right amount of magnification, divide it into hours, minutes, even seconds. Stepping back and looking at the unsliced cam the bottom is the year 2000 and the top is the year 12000. The twist that you see is the precession of the equinoxes. Now here’s the fun part, there’s a slight taper to the twist, that’s the slowing of the earth on its axis. As the ice at the poles melts we have a redistribution of water, we’re all becoming part of the “slow earth” movement.

RP: Are you familiar with Charles Ray’s early work in which you saw a plate on a table, or an object on the wall, and they looked stable, but were actually spinning incredibly slowly, or incredibly fast, and you couldn’t tell in either case? Or, more to the point, Tim Hawkinson’s early works in which he had rows of clockwork gears that turned very very fast, and then down the line, slower and slower, until at the end it approached the slowness that you’re dealing with?

PS: The spinning pieces by Ray touches on something we’re trying to avoid. We want you to know just how fast or just how slow the various parts are moving. The beauty of the Ray piece is that you can’t tell, fast, slow, stationary, they all look the same. I’m not familiar with the Hawkinson clockwork piece. I’ve see the clock pieces where he hides the mechanism and uses unlikely objects as the hands, such as the brass clasp on the back of a manila envelope or the tab of a coke can.

RP: Spin Sink (1 Rev./100 Years) (1995), in contrast, is a 24-foot-long row of interlocking gears, the smallest of which is driven by a whirring toy motor that in turn drives each consecutively larger and more slowly turning gear up to the largest of all, which rotates approximately once every one hundred years.

PS: I don’t know how I missed it, it’s gorgeous. Linking the speed that we can barely see with one that we rarely have the patience to wait for.

RP: : So you say you’ve opted for the clock’s time scale to be transparent. How will the clock communicate how fast it’s going?

PS: By placing the clock in a mountain we have a reference to long time. The stratigraphy provides us with the slowest metric. The clock is a middle point between millennia and seconds. Looking back 10,000 years we find the beginnings of civilization. Looking at an earthenware vessel from that era we imagine its use, the contents, the craftsman. The images painted or inscribed on the outside provide some insight into the lives and the languages of the distant past. Often these interpretations are flawed, biased or over-reaching. What I’m most enchanted by is that we continue to construct possible pasts around these objects, that our curiosity is overwhelming. We line up to see the treasures of Tut, or the remains of frozen ancestors. With the clock we are asking you to create possible futures, long futures, and with them the narratives that made them happen.

https://openspace.sfmoma.org/2010/02/10000-year-clock/

ダ?ヴィンチの名言 格言｜無こそ最も素晴らしい存在

https://systemincome.com/7521

ゼロ除算の発見はどうでしょうか：

Black holes are where God divided by zero：

再生核研究所声明371（2017.6.27）ゼロ除算の講演― 国際会議

https://ameblo.jp/syoshinoris/entry-12287338180.html

1/0=0、0/0=0、z/0=0

https://ameblo.jp/syoshinoris/entry-12276045402.html

1/0=0、0/0=0、z/0=0

https://ameblo.jp/syoshinoris/entry-12263708422.html

1/0=0、0/0=0、z/0=0

https://ameblo.jp/syoshinoris/entry-12272721615.html

ソクラテス?プラトン?アリストテレス その他

https://ameblo.jp/syoshinoris/entry-12328488611.html

ドキュメンタリー 2017: 神の数式 第２回 宇宙はなぜ生まれたのか

https://www.youtube.com/watch?v=iQld9cnDli4

〔NHKスペシャル〕神の数式 完全版 第3回 宇宙はなぜ始まったのか

https://www.youtube.com/watch?v=DvyAB8yTSjs&t=3318s

〔NHKスペシャル〕神の数式 完全版 第1回 この世は何からできているのか

https://www.youtube.com/watch?v=KjvFdzhn7Dc

NHKスペシャル 神の数式 完全版 第4回 異次元宇宙は存在するか

https://www.youtube.com/watch?v=fWVv9puoTSs

再生核研究所声明 411(2018.02.02): ゼロ除算発見4周年を迎えて

https://ameblo.jp/syoshinoris/entry-12348847166.html

再生核研究所声明 416(2018.2.20): ゼロ除算をやってどういう意味が有りますか。何か意味が有りますか。何になるのですか － 回答

再生核研究所声明 417(2018.2.23): ゼロ除算って何ですか － 中学生、高校生向き 回答

再生核研究所声明 418(2018.2.24): 割り算とは何ですか？ ゼロ除算って何ですか － 小学生、中学生向き 回答

再生核研究所声明 420(2018.3.2): ゼロ除算は正しいですか，合っていますか、信用できますか － 回答

2018.3.18．午前中 最後の講演： 日本数学会 東大駒場、函数方程式論分科会 講演書画カメラ用 原稿

The Japanese Mathematical Society, Annual Meeting at the University of Tokyo. 2018.3.18.

https://ameblo.jp/syoshinoris/entry-12361744016.html ã‚ˆã‚Š

*057 Pinelas,S./Caraballo,T./Kloeden,P./Graef,J.(eds.): Differential and Difference Equations with Applications: ICDDEA, Amadora, 2017. (Springer Proceedings in Mathematics and Statistics, Vol. 230) May 2018 587 pp.

再生核研究所声明 424(2018.3.29): レオナルド?ダ?ヴィンチとゼロ除算

再生核研究所声明 427(2018.5.8): 神の数式、神の意志 そしてゼロ除算

アインシュタインも解決できなかった「ゼロで割る」問題

https://matome.naver.jp/odai/2135710882669605901

Title page of Leonhard Euler, Vollst?ndige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

https://notevenpast.org/dividing-nothing/

私は数学を信じない。 アルバート?アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。

1423793753.460.341866474681。

Einstein's Only Mistake: Division by Zero

https://refully.blogspot.jp/2012/05/einsteins-only-mistake-division-by-zero.html

ゼロ除算は定義が問題です：

再生核研究所声明 １４８（2014.2.12） 100/0=0, 0/0=0 － 割り算の考えを自然に拡張すると ― 神の意志 https://blogs.yahoo.co.jp/kbdmm360/69056435.html

再生核研究所声明１７１（2014.7.30）掛け算の意味と割り算の意味 ― ゼロ除算100/0=0は自明である？https://reproducingkernel.blogspot.jp/2014/07/201473010000.html

アインシュタインも解決できなかった「ゼロで割る」問題

https://matome.naver.jp/odai/2135710882669605901

Title page of Leonhard Euler, Vollst?ndige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.

https://notevenpast.org/dividing-nothing/

私は数学を信じない。 アルバート?アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。1423793753.460.341866474681。

Einstein's Only Mistake: Division by Zero

https://refully.blogspot.jp/2012/05/einsteins-only-mistake-division-by-zero.html

#divide by zero

TOP DEFINITION

Genius

A super-smart math teacher that teaches at HTHS and can divide by zero.

Hey look, that genius’s IQ is over 9000!

#divide by zero #math #hths #smart #genius

by Lawlbags! October 21, 2009

divide by zero

Dividing by zero is the biggest epic fail known to mankind. It is a proven fact that a succesful division by zero will constitute in the implosion of the universe.

You are dividing by zero there, Johnny. Captain Kirk is not impressed.

Divide by zero?!?!! OMG!!! Epic failzorz

#4 chan #epic fail #implosion #universe #divide by zero

3

divide by zero

Divide by zero is undefined.

Divide by zero is undefined.

#divide #by #zero #dividebyzero #undefined

by JaWo October 28, 2006

division by zero

1) The number one ingredient for a catastrophic event in which the universe enfolds and collapses on itself and life as we know it ceases to exist.

2) A mathematical equation such as a/0 whereas a is some number and 0 is the divisor. Look it up on Wikipedia or something. Pretty confusing shit.

3) A reason for an error in programming

Hey, I divided by zero! ...Oh shi-

a/0

Run-time error: '11': Division by zero

#division #0 #math #oh shi- #divide by zero

by DefectiveProduct September 08, 2006

dividing by zero

When even math shows you that not everything can be figured out with math. When you divide by zero, math kicks you in the shins and says "yeah, there's kind of an answer, but it ain't just some number."

It's when mathematicians become philosophers.

Math:

Let's say you have ZERO apples, and THREE people. How many apples does each person get? ZERO, cause there were no apples to begin with

Not-math because of dividing by zero:

Let's say there are THREE apples, and ZERO people. How many apples does each person get? Friggin... How the Fruitcock should I know! How can you figure out how many apples each person gets if there's no people to get them?!? You'd think it'd be infinity, but not really. It could almost be any number, cause you could be like "each person gets 400 apples" which would be true, because all the people did get 400 apples, because there were no people. So all the people also got 42 apples, and a million and 7 apples. But it's still wrong.

#math #divide by zero #divide #dividing #zero #numbers #not-math #imaginary numbers #imaginary. phylosophy

by Zacharrie February 15, 2010

https://www.urbandictionary.com/tags.php?tag=divide%20by%20zero

https://ameblo.jp/syoshinoris/entry-12370907279.html