Square of Hypotenuse of Pythagorean Triangle is Difference of two Cubes/Historical Note
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Historical Note on Square of Hypotenuse of Pythagorean Triangle is Difference of two Cubes
The statement:
- The square of the hypotenuse of a right-angled triangle is also the difference of $2$ cubes; thus, $13^2 = 8^3 - 7^3$.
appears in the $1997$ edition of Curious and Interesting Numbers, 2nd ed. by David Wells.
There is no record of where he may have found this statement, but it is demonstrably false.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$