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Two links can be continuously deformed into each other iff any diagram of one can be transformed into a diagram of the other by a sequence of Reidemeister moves.

dN^^+kappa_idr=0, where N^^ is the unit normal vector and kappa_i is one of the two principal curvatures.

If a triangle is inscribed in a conic section, any line conjugate to one side meets the other two sides in conjugate points.

An operator T which commutes with all shift operators E^a, so TE^a=E^aT for all real a in a field. Any two shift-invariant operators commute.

External (or positive) and internal (or negative) similarity points of two circles with centers C and C^' and radii r and r^' are the points E and I on the lines CC^' such ...

A nonzero ring S whose only (two-sided) ideals are S itself and zero. Every commutative simple ring is a field. Every simple ring is a prime ring.

A Skolem sequence of order n is a sequence S={s_1,s_2,...,s_(2n)} of 2n integers such that 1. For every k in {1,2,...,n}, there exist exactly two elements s_i,s_j in S such ...

The small world problem asks for the probability that two people picked at random have at least one acquaintance in common.

A roll of two 1s (the lowest roll possible) on a pair of six-sided dice. The probability of rolling snake eyes is 1/36, or 2.777...%.

Let A and B be two *-algebras. An algebraic homomorphism phi:A->B is called *-homomorphism if it satisfies phi(a^*)=phi(a)^* for each a in A.