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!
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!
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.
My most successful 3D print so far: a Chmutov surface!
Chmutov surfaces are algebraic surfaces that have interesting properties involving their singular points. This surface has equation
And in addition to being quite beautiful, this Chmutov surface is already coming in handy!
Today we celebrate the third Permutation Day of the year! 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!
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