While finding a polynomial P(x) for sin(x) isn't the main result of Euler's solution to the Basel problem [1], it is still pretty amazing that it can be done. Even more mind-boggling is the Weierstrass Factorization Theorem [2] itself, which tells us that this can be done for a wide variety of functions.

See https://davidmeyer.github.io/qc/basel.pdf for a bit more detail. And as always, questions/comments/corrections/* are greatly appreciated.

#math #maths #baselproblem #euler

References
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[1] "Basel problem", https://en.wikipedia.org/wiki/Basel_problem

[2] "Weierstrass Factorization Theorem", https://en.wikipedia.org/wiki/Weierstrass_factorization_theorem

Here's a crazy thing. This beautiful formula for π was devised by John Wallis in 1655. It says that π/2 is equal to the infinite product of even numbers squared divided by the product of their adjacent odd numbers, and is sometimes known as the Wallis product.

A few of my notes are here: https://davidmeyer.github.io/qc/basel.pdf. The LaTeX source is here: https://www.overleaf.com/read/xsnvysdcfcvd.

See https://en.wikipedia.org/wiki/Wallis_product for more.

#math #baselproblem #wallisproduct

#onthisday in 1460 Pope Pius II founded the University of Basel [1].

Basel has a special place in #mathematics. One example: the Basel problem.

I wrote a bit about the Basel problem and Euler's solution of it here: https://davidmeyer.github.io/qc/basel.pdf. The LaTex source is here: https://www.overleaf.com/read/xsnvysdcfcvd.

As always, questions/comments/corrections/* greatly appreciated.

#math #baselproblem

References
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[1] "University of Basel", https://en.wikipedia.org/wiki/University_of_Basel

An interesting consequence of Euler's derivation of the polynomial for sin x (and hence his proof of the Basel problem) is the Wallis Product [1], a beautiful expression for π/2.

My notes here: https://davidmeyer.github.io/qc/basel.pdf.

As always, questions/comments/corrections/* greatly appreciated.

#math #baselproblem

References
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[1] "Wallis's Product", https://proofwiki.org/wiki/Wallis's_Product See less

@mysticshadow I wrote a bit about the Wallis product in the context of Euler's solution to the Basel problem here: https://davidmeyer.github.io/qc/basel.pdf,

The #LaTeX source is here: https://www.overleaf.com/read/xsnvysdcfcvd,

As always, questions/comments/correction/* greatly appreciated. #baselproblem #wallisproduct