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Given collinear points W, X, Y, and Z, Y and Z are harmonic conjugates with respect to W and X if (|WY|)/(|YX|)=(|WZ|)/(|XZ|). (1) W and X are also harmonic conjugates with ...

The haversine, also called the haversed sine, is a little-used entire trigonometric function defined by hav(z) = 1/2vers(z) (1) = 1/2(1-cosz) (2) = sin^2(1/2z), (3) where ...

A purple cow is a confirming instance of the hypothesis that all crows are black.

A polyiamond composed of six equilateral triangles. The 12 hexiamonds are illustrated above. They are given the names bar, crook, crown, sphinx, snake, yacht, chevron, ...

Home plate in the game of baseball is an irregular pentagon with two parallel sides, each perpendicular to a base. It seems reasonable to dub such a figure (i.e., a rectangle ...

As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

The hyperbolic volume of the knot complement of a hyperbolic knot is a knot invariant. Adams (1994) lists the hyperbolic volumes for knots and links. The hyperbolic volume of ...

A riffle shuffle, in which the top half of the deck is placed in the left hand, and cards are then alternatively interleaved from the left and right hands. Using an ...

An intrinsically linked graph is a graph having the property that any embedding of it in three dimensions contains a nontrivial link. A graph is intrinsically linked iff it ...

If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...