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Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

In Euclidean space R^3, the curve that minimizes the distance between two points is clearly a straight line segment. This can be shown mathematically as follows using ...

A polar zonohedron is a convex zonohedron derived from the star which joins opposite vertices of any right n-gonal prism (for n even) or antiprism (for n odd). The faces of ...

All Euclidean geometric constructions can be carried out with a straightedge alone if, in addition, one is given the radius of a single circle and its center. The theorem was ...

Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, ...

An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. ...

The probability Q_delta that a random sample from an infinite normally distributed universe will have a mean m within a distance |delta| of the mean mu of the universe is ...

The radical circle of three given circles is the circle having center at the radical center of the three circles and is orthogonal to all of them. (A circle with center at ...

In the arbelos, consider the semicircles K_1 and K_2 with centers A and C passing through B. The Apollonius circle K_3 of K_1, K_2 and the large semicircle of the arbelos is ...

If the integral coefficients C_0, C_1, ..., C_(N-1) of the polynomial f(x)=C_0+C_1x+C_2x^2+...+C_(N-1)x^(N-1)+x^N are divisible by a prime number p, while the free term C_0 ...