To preface, I am not a mathematician. I can hold my own in most college-level math (I’ve taken 3 years of algebra, trig, geometry, 3 years of calculus, and 1 year linear algebra: where is all that knowledge now?), but I’m still easily impressed.
I’ve been working through an algorithm textbook (more on that later), which mentions a number of very interesting mathematical equalities:
I.
13 = 1
23 = 3 + 5
33 = 7 + 9 + 11
43 = 13 +15 + 17
etc.
II.
13 + 23 + … + n3 = (1 + 2 + … + n)2
III.
12 = 1
22 = 1 + 3
32 = 1 + 3 + 5
42 = 1 + 3 + 5 + 7
etc.
To be honest, when I first read these it blew my mind. There is a beautiful correspondence demonstrated in these ancient forumlas that is nearly breathtaking when you first learn of them.
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I love it! Perhaps I “knew” this eons ago. Now it seems especially significant. Those brilliant Ancients!