As part of a personal musicology project I found myself with the mathematical model of a geometry which utilizes the equation(adsbygoogle = window.adsbygoogle || []).push({});

a*(a/b)^{sin(pi*x)}

The only problem with this is that I need to take the integral from -1/2 <= x <= 1/2, and according to Wolfram Alpha no such integral exists. I can take the derivative, of course, which is

cos(x)*ln(a)*a^{sin(x)}

and I can graph the thing and approximate the area under the curve, but it's incredibly annoying. Is it for situations such as these why Riemann Sums are even taught? (Not bashing on Riemann, it's just incredibly irritating.)

I can approximate the equation itself with

(1/2)[(a-a^{-1})*sin(x)+(a+a^{-1})

but it doesn't do it justice. Math people, please rectify this. XD

It's like it has a modulating frequency or something... like a 'chorus' effect for guitar.

Imagine drawing 'a/b' on a circle, including the dividing line between the numerator and denominator, and then slowly rotating it.

The equation came about when I was trying to calculate the length of chord segments when pivoting the initial chord around a point a certain distance from the center of a circle. What it results in is a fraction that changes like a rotating wheel... as though the concept of the equation has a 'visio-mechanical' aspect to it...

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# 'Wheel-like' Mathematics (Modulating Trig Functions?)

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