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Arguments in analysis are notorious for their profusion of ε’s. In sophisticated arguments, one ends up managing many ε₁₄, ε₈₂, ε₁₁₃, …. This art is not terribly difficult—it basically requires you to keep track of which quantities are “small”, “very small”, “very very small”, and so on … but these arguments are lengthy, tedious, and unpleasant to read.
Terence Tao
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(via Almanacco: scrittrici nate il 15 gennaio)
Weierstrass functions.
Quoting Wikipedia, “In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for Karl Weierstrass. The relation between the sigma, zeta, and p-functions is analogous to that between the sine, cotangent, and squared cosecant functions: the logarithmic derivative of the sine is the cotangent, whose derivative is negative the squared cosecant.”
The stunning colors come from domain coloring.
Mathematics is beautiful. <3
From function to fractal, Weierstrass showcases short Wolfram Language code: https://wolfr.am/gCB8JxNv
Roommate: I hate techniques of integration. Why do we need to know them? They are only useful before they invented computers.
Me: Well, I mean...you are not going to have a computer when you write your exam, right? So they are kind of useful...
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It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician. -Karl Weierstrass Science Art - 5 simple equations: Weierstrass quote on mathematical beauty and Euler's identity vinyl wall decal by Cut'n'Paste
Es ist wahr, ein Mathematiker, der nicht etwas Poet ist, wird nimmer ein vollkommener Mathematiker sein.
Karl Weierstrass (1815-1897)
