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A region in a knot or link projection plane surrounded by a circle such that the knot or link crosses the circle exactly four times. Two tangles are equivalent if a sequence ...

Take any triangle with polygon vertices A, B, and C. Pick a point A_1 on the side opposite A, and draw a line parallel to BC. Upon reaching the side AC at B_1, draw the line ...

The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

A transformation T (a.k.a., map, function) over a domain D takes the elements X in D to elements Y in T(D), where the range (a.k.a., image) of T is defined as ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The two-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the line ...

A paradox also known as the surprise examination paradox or prediction paradox. A prisoner is told that he will be hanged on some day between Monday and Friday, but that he ...

The distribution for the sum X_1+X_2+...+X_n of n uniform variates on the interval [0,1] can be found directly as (1) where delta(x) is a delta function. A more elegant ...

If ABB^' and AC^'C are straight lines with BC and B^'C^' intersecting at D and AB+BD=AC^'+C^'D, then AB^'+B^'D=AC+CD. The origin and some history of this theorem are ...

A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials (Hoffman and Kunze p. 114), and the ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...