21–24 of 24 posts
The caption "The equation 1⁰² + 1¹² + 1²² = 1³² + 1⁴², whose answer is that both sides equal 365, was immortalized in a different form in this 1895 painting: “Mental Arithmetic. In the Public School of S. Rachinsky.” (NIKOLAY BOGDANOV-BELSKY)" has funky exponents. Medium requires that I make an account to say that, so I am saying it here.
I thought this was going to help me with Project Euler 261 [0], but it's not exactly the same, so no luck so far. Cool article anyway; linking geometry and algebra is always satisfactory. [0] https://projecteuler.net/problem=261
Brute force search of 10^10 (with some automatic monitoring of how wide a range of 'm' to scan at each candidate) is a lot but not a lot of a lot, if you code in a CPU efficient language and maybe use parallel computation and are willing to wait a while.
Pythagoreans believed that the world was made of math -- and that the harmonies of mathematics revealed the harmonies of the universe. Pretty good for 6th century BC.
I thought this was going to help me with Project Euler 261 [0], but it's not exactly the same, so no luck so far. Cool article anyway; linking geometry and algebra is always satisfactory. [0] https://projecteuler.net/problem=261
How much CPU time and number theory do problems in that range generally require? Brute force search of 10^10 (with some automatic monitoring of how wide a range of 'm' to scan at each candidate) is a lot but not a lot of a lot, if you code in a CPU efficient language and maybe use parallel computation and are willing to wait a while.