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A gyrobicupola is a bicupola in which the bases are in opposite orientations.

If the first case of Fermat's last theorem is false for the prime exponent p, then 3^(p-1)=1 (mod p^2).

A bicupola in which the bases are in the same orientation.

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

A number traditionally associated with bad luck. A so-called baker's dozen is equal to 13. Fear of the number 13 is called triskaidekaphobia. There are 13 Archimedean solids. ...

An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German), is a single tile ...

The numbers three and four appear prominently in the game of baseball. There are three strikes for an out, three outs per half-inning (i.e., teams switch after three outs, ...

(dy)/(dx)+p(x)y=q(x)y^n. (1) Let v=y^(1-n) for n!=1. Then (dv)/(dx)=(1-n)y^(-n)(dy)/(dx). (2) Rewriting (1) gives y^(-n)(dy)/(dx) = q(x)-p(x)y^(1-n) (3) = q(x)-vp(x). (4) ...

An n-bridge knot is a knot with bridge number n. The set of 2-bridge knots is identical to the set of rational knots. If L is a 2-bridge knot, then the BLM/Ho polynomial Q ...

The Christmas stocking theorem, also known as the hockey stick theorem, states that the sum of a diagonal string of numbers in Pascal's triangle starting at the nth entry ...