Posted on April 8, 2015 by amca01

You can find the full post at my numbersandshapes.net blog, but if you don’t want to follow the link, the integrals (for , the number of derangements of order , are:

and

This last integral can be equivalently written, of course as

or

I think that derangements having an integral representation is rather splendid!

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Posted on December 6, 2014 by amca01

Constructing a regular heptagon is a very elegant and delightful exercise in geometry and algebra, and which requires the trisection of an angle. There are plenty of discussions all over the web but *mine, *which is available at Numbers and Shapes, I think is the clearest, with its LaTeXed mathematics, and diagrams drawn with TiKZ.

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Posted on December 4, 2014 by amca01

This post, containing a nice slew of methods of trisecting a general angle using neusis methods, can be found at Numbers and Shapes.

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Posted on December 4, 2014 by amca01

You can find this post, introducing geometric constructions which allow the use of a straight-edge with two marks, at my new site Numbers and Shapes.

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Posted on October 30, 2014 by amca01

This post, which is on my new site here:

http://www.numbersandshapes.net/?p=2520

shows how a cubic equation can be solved by origami. This is not a new result by any means, but it’s hard to find a simple proof of how the construction works.

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Posted on September 11, 2014 by amca01

Posted on August 13, 2014 by amca01

As I explained on the page Numbers and Shapes, this blog is moving to a new home, and you’ll find this post there: The foolishness of signature images

Enjoy!

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