Square Root of 2 is Irrational/Historical Note
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Historical Note on Square Root of 2 is Irrational
This result Square Root of 2 is Irrational is attributed to Pythagoras of Samos, or to a student of his.
Some legends have it that it is due to Hippasus of Metapontum who was thrown off a boat by his angry fellow Pythagoreans and drowned.
The ancient Greeks prior to Pythagoras believed that irrational numbers did not exist in the real world.
However, from the Pythagorean Theorem, a square with sides of length $1$ has a diagonal of length $\sqrt 2$.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies
- 1939: E.G. Phillips: A Course of Analysis (2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Number: $1.1$ Introduction
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 41421 \, 35623 \, 73095 \, 04880 \, 16887 \, 24209 \, 69807 \, 85697 \ldots$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $10$
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.2$: Pythagoras (ca. $\text {580}$ – $\text {500}$ B.C.)
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 41421 \, 35623 \, 73095 \, 04880 \, 16887 \, 24209 \, 69807 \, 85697 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10$
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: Pythagoras