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A compact set W_infty with area mu(W_infty)=8/9(24)/(25)(48)/(49)...=pi/4 created by punching a square hole of length 1/3 in the center of a square. In each of the eight ...

Let P be a finite partially ordered set. A chain in P is a set of pairwise comparable elements (i.e., a totally ordered subset). The partial order length of P is the maximum ...

Given a polygon with an even number of sides, the derived polygon is obtained by joining the points which are a fractional distance r along each side. If r=1/2, then the ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a path polynomial whose coefficients are the numbers of paths of ...

The diameter of a polygon is the largest distance between any pair of vertices. In other words, it is the length of the longest polygon diagonal (e.g., straight line segment ...

Let v(G) be the number of vertices in a graph G and h(G) the length of the maximum cycle in G. Then the shortness exponent of a class of graphs G is defined by sigma(G)=lim ...

For any positive integer k, there exists a prime arithmetic progression of length k. The proof is an extension of Szemerédi's theorem.

An equichordal point is a point p for which all the chords of a curve C passing through p are of the same length. In other words, p is an equichordal point if, for every ...

The Markström graph is a cubic planar graph on 24 vertices which lacks cycles of length 4 and 8 but contains cycles of length 16. (In particular, it contains cycles of ...

Prince Rupert's cube is the largest cube that can be made to pass through a given cube. In other words, the cube having a side length equal to the side length of the largest ...