√2 (Pythagoras' Constant)

★☆☆☆☆Elementary

📖Definition

√2 is the diagonal length of a unit square. The first discovered irrational number, it shocked the Pythagorean school.

√2 = 1.41421356237...

Value of √2

√2 = 1 + \cfrac1{2 + \cfrac12 + \cfrac12 + ...}

Continued fraction

((p)/(q))² ≠ 2 (for all integers p, q )

Irrationality proof

예제 1

What is the diagonal of a square with side 5?

예제 2

Prove √2 is irrational.

Discovered by: Pythagorean school (Hippasus) (c. 5th century BCE)

First irrational number discovered, shattering Pythagorean belief that all numbers are rational.

Diagonals, squares

A4 paper ratio (1:√2)

Semitone ratio

#루트2#무리수#sqrt2#Pythagoras