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Day 18 | LThMath Advent Calendar

In today's post I wanted to share a little creative way of showing some digits of square root of 2. The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property.

General Information

It is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem.

It was probably the first number known to be irrational. The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of √2 in four sexagesimal figures which is accurate to about six decimal digits. Another early approximation is given in ancient Indian mathematical texts, the Sulbasutras (c. 800–200 BC).

Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational. Little is known with certainty about the time or circumstances of this discovery, but the name of Hippasus of Metapontum is often mentioned. For a while, the Pythagoreans treated as an official secret the discovery that the square root of two is irrational, and, according to legend, Hippasus was murdered for divulging it. The square root of two is occasionally called Pythagoras's number or Pythagoras's constant, for example by Conway & Guy (1996).

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