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The most well known and oldest proof of irrationality is a proof that √2 is irrational. I see that that's already posted here. Here's another proof of that same result: Suppose it is rational, i.e. √2 = n / m. We can take n and m to be positive and the fraction to be in lowest terms.
Oct 19, 2023 · These numbers are known today as rational numbers. The name ‘irrational numbers’ does not literally mean that these numbers are ‘devoid of logic’. Any number that couldn’t be expressed in a similar fashion is an irrational number. Such a number could easily be plotted on a number line, such as by sketching the diagonal of a square.
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Let's look at their history. Hippassus of Metapontum, a Greek philosopher of the Pythagorean school of thought, is widely regarded as the first person to recognize the existence of irrational numbers. Supposedly, he tried to use his teacher's famous theorem a^ {2}+b^ {2}= c^ {2} a2 + b2 = c2 to find the length of the diagonal of a unit square.
Jun 13, 2024 · The ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is ...
May 22, 2020 · With more than 4,000 participants in 19 countries, nearly every question in the original paper was answered the same way by people today as they were by their 1970s counterparts. Back to the beginning
- Cathleen O'grady
Apr 2, 2019 · Princeton University Press, Apr 2, 2019 - History - 330 pages. A fascinating history that reveals the ways in which the pursuit of rationality often leads to an explosion of irrationality It’s a story we can’t stop telling ourselves. Once, humans were benighted by superstition and irrationality, but then the Greeks invented reason.
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Apr 25, 2019 · Humans, he says, are hardly rational, and in fact, irrationality has defined much of human life and history. And the point is not merely academic. “The desire to impose rationality, to make ...
