Appreciation

8/17/15: Happy Right Triangle Day!

It’s 8/17/15, or as I like to think of it, Right Triangle Day!

Since

$8^2 + 15^2 = 17^2$

we know that 8, 15, and 17 are the lengths of the sides of a right triangle. Informally, we say this is true because of the Pythagorean Theorem, but technically it’s true because of the converse of the Pythagorean Theorem.

It’s been a while since we’ve celebrated a Right Triangle day, and it won’t be long before we get to celebrate another. To commemorate this numerical novelty, the Museum of Mathematics is teaming up with the Pacific Science Center to pythagorize Seattle’s Triangle Pub. They certainly had fun pythagorizing the Flatiron building in NYC on 5/12/13!

Enjoy being right today!

By MrHonner, 11 yearsAugust 17, 2015 ago

Math Photo: Hexagonal Rabbits

The tilling station is one of my favorite exhibits at the Museum of Mathematics. These rabbit tiles create a hexagonal tiling of the plane. Pick any rabbit, and you’ll notice six rabbits all around it; this is exactly how hexagons fit together to tile the plane.

What I really like about this tiling is the the various levels of triangles that emerge. Triangles of rabbits, one of each color, mutually intersect at ears and paws. And I can’t help but seeing the monochromatic rabbit triangles!

By MrHonner, 11 yearsJuly 19, 2015 ago

Appreciation Photography

Math Photo: Circular Refraction

$Circular Refraction$

This simple exhibit at the New York Hall of Science demonstrates a lot of interesting trigonometry. As the light hits the boundary of the semi-circular glass block, it bends back toward the central axis of the system. I can’t look at this without seeing tangents, normals, and angles of incidence and refraction. I wish I had brought my protractor!

By MrHonner, 11 yearsJune 28, 2015 ago

Appreciation Numbers

05/21/2015 — 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.

By MrHonner, 11 yearsMay 21, 2015 ago

3D Printing Appreciation Geometry