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Editor-in-Chief of Maple Transactions (www.mapletransactions.org), longtime Maple user (1st use 1981, before Maple was even released). Most obscure piece of the library that I wrote? Probably `convert/MatrixPolynomialObject` which is called by LinearAlgebra[CompanionMatrix] to compute linearizations of matrix polynomials in several different bases. Do not look at the code. Seriously. Do not look. You have been warned.

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From a tweet by Tamás Görbe : plotting Chebyshev polynomials in polar coordinates leads to some interesting pictures.  Screenshot here, link to the worksheet (and some perhaps interesting puzzles) at the end.