• ## The shape of the Wankel rotor

I’ve written a number of posts about curvilinear triangles that are not the Reuleaux triangle, including MIT’s Kresge Auditorium, triforce string art, valve covers, a patio table, and the logo of Whale Cove, Nunavut. I’ve long intended to write about another obvious topic in this theme, the curved-triangle rotor of the Wankel engine, but was finally pushed into doing so by seeing that two recent popular mathematics books, How Round Is Your Circle? (2008) and Icons of Mathematics (2011) repeat the falsehood that Wankel rotors are Reuleaux triangles. They are not.

• ## Sorting with integer offsets

Here’s a cute exercise for the next time you’re teaching radix sorting in an algorithms class:

• ## Subpract

I’ve written here before about subtraction games, two-player games in which the players remove tokens from a pile of tokens, the number of removed tokens is required to belong to a designated subtraction set, and the goal is to make the last move. For instance, subtract a square, a game I studied at FUN 2018, is of this type, with the subtraction set being the square numbers.

• ## Infinite threshold graphs, four different ways

One of the difficulties of extending results from finite graphs to infinite ones is that it is not always obvious how to extend the definitions. A single class of finite graphs may correspond, in the infinite graph world, to several different natural classes of infinite graphs. One of the ways this can happen is through orderings: if a class of graphs has a natural ordering on its vertices (say, through a construction in which graphs in this class are built up by adding one vertex at a time) then we might get several classes of infinite graphs with different ways of restricting or not restricting this vertex ordering.