beatley · HackerTrans

3 jaar geledendiscuss

If I'm not mistaken, the square wave case should in essence be the limiting case of the general case you get when looking at "trigonometric" functions which don't arise as the parametrisation of xˆ2 + yˆ2 = 1, but xˆn + yˆn = 1 for n > 2. It turns out that people have looked at that, and the study of those functions have been given the funny name "squigonometry". There's a Springer textbook out there.

beatley

3 jaar geledendiscuss

Before the 19th and 20th century, much of the basis of modern math was entirely leisurely and recreational. Even today that still rings true. I recommend reading Barry Mazur's "Number Theory as Gadfly" to add some context to that claim.

beatley

3 jaar geledendiscuss

A lot of modern technical marvels were built on top of the leisurely work done by people who were just playing.

"I wonder what would happen if the square root of -1 existed"

"I wonder what happens if numbers were cyclic"

"Can you actually cross all the bridges of Köningsberg without walking any of them twice"

The impetus to solve these problems was that they were fun to think about, not that they a century or several centuries later would enable us to do harmonic analysis, invent the basis for cryptosystems or spectral graph theory. Which are billion or even trillion dollar inventions.

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