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Archive of posts filed under the Appreciation category.

8/15/17 — Happy Pythagorean Triple Day!

Today we celebrate a rare Pythagorean Triple day!  And especially rare, as 8-15-17 is a primitive Pythagorean triple.  We won’t see many more of those!

Here’s an animation I made to celebrate.


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07/21/2017 — Happy Derangement Day!

Today we celebrate a Derangement Day!  Usually I call a day like today a Permutation Day because the digits of the day and month can be rearranged to form the year, but there’s something extra special about today’s date:

The numbers of the month and day are a derangement of the year:  that is, they are a permutation of the digits of the year in which no digit remains in its original place!

Derangements pop up in some interesting places, and are connected to many rich mathematical ideas.   The question “How many derangements of n objects are there?” is a fun and classic application of the principle of inclusion-exclusion.  Derangements also figure in to some calculations of e and rook polynomials.

So enjoy Derangement Day!  Today, it’s ok to be totally out of order.

07/12/2017 — Happy Permutation Day!

Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and the month can be rearranged to form the year.

Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!

 

Math Photo: Snowball Tetrahedron

I put the recent snow day, and a snowball maker, to good use!

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Math Photo: Sky Squares

What catches my attention in this photo, after the blue and white squares, is how the beams slowly bend away from center.  I suppose knowing the size of those beams, and some trigonometry, would allow you estimate the location of the camera.