(geometry) A theorem stating that it is not possible to dissect a square into an odd number of triangles of equal area.

(set theory) A theorem that describes the largest possible families of finite sets none of which contain any other sets in the family.

Synonym of Price equation

(mathematics) A theorem in probability theory that extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables.

(geometry) A result in geometry concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides.

(computing theory) A theorem stating that it is impossible for a distributed data store to simultaneously provide more than two of three guarantees: consistency (every read receives the most recent write or an error), availability (every request receives a non-error response, without the guarantee that it contains the most recent write), and partition tolerance (the system continues to operate despite an arbitrary number of messages being dropped or delayed between nodes).

(geometry) A theorem on convex sets, stating that any set of d + 2 points in Rᵈ can be partitioned into two sets whose convex hulls intersect.

(geometry) A basic result in discrete geometry on the intersection of convex sets, which gave rise to the notion of a Helly family.

A theorem stating that, for any deterministic process of collective decision, at least one of the following three properties must hold: (i) the process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome; (ii) the process limits the possible outcomes to two options only; (iii) the process encourages agents to think strategically: once an agent has identified their preferences, they have no action at their disposal that would best defend their opinions in any situation.

(number theory) A theorem stating that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime.