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Orthogonal circles are orthogonal curves, i.e., they cut one another at right angles. By the Pythagorean theorem, two circles of radii r_1 and r_2 whose centers are a ...

A statement which appears self-contradictory or contrary to expectations, also known as an antinomy. Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent ...

Percolation theory deals with fluid flow (or any other similar process) in random media. If the medium is a set of regular lattice points, then there are two main types of ...

The Petersen family of graphs, not to be confused with generalized Petersen graphs, are a set of seven graphs obtained from the Petersen graph (or complete graph K_6) by del ...

pi may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the ...

A planar hypotraceable graph is a hypotraceable graph that is also planar. A number of planar hypotraceable graphs are illustrated above. Using a theorem of Thomassen (1974), ...

A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. Fáry (1948) showed that ...

Let p(d) be the probability that a random walk on a d-D lattice returns to the origin. In 1921, Pólya proved that p(1)=p(2)=1, (1) but p(d)<1 (2) for d>2. Watson (1939), ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

A polyomino tiling is a tiling of the plane by specified types of polyominoes. Tiling by polyominoes has been investigated since at least the late 1950s, particularly by S. ...