Discrete geometry

Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid, one with Xs and the other with Os. A player wins when they mark all three spaces of a row, column, or diagonal of the grid, whereupon they traditionally draw a line through those three marks to indicate the win. It is a solved game, with a forced draw assuming best play from both players.

type of plane partition

non-periodic tiling of the plane

branch of geometry that studies combinatorial properties and constructive methods of discrete geometric objects

mathematical theorem about sphere packing

mathematical problem about moving the largest possible shape around a 90° corner

problem about proving that five points in the plane will have a subset forming the vertices of a convex quadrilateral

dense arrangement of congruent spheres in an infinite, regular arrangement

(as a form of proximity search (metric space)) optimization problem of finding the point in a given set that is closest (or most similar) to a given point

mathematical problem of tiling an integral square using only other integral squares

an arrangement of non-overlapping spheres within a containing space

thumb|upright|All 8 one-sided tetracubes – if chirality is ignored, the bottom 2 in grey are considered the same, giving 7 free tetracubes in total thumb|right|A puzzle involving arranging nine L tricubes into a 3×3×3 cube

problem of determining the maximum number of non-overlapping spheres that can be simultaneously tangent to another sphere of the same size

mathematical problem

the problem of partitioning a given shape into pieces that can be rearranged to form a second given shape

mathematical problem

triangle with integer side lengths

conjecture

a sequence of moves on a lattice that does not visit the same point more than once

type of tiling in geometry

theorem that states that a regular hexagonal grid is the best way to divide a surface into regions of equal area with the least total perimeter

problem in discrete geometry

unsolved geometry problem

Symmetric tessellation of a closed surface

shape containing unit line segments in all directions

process of producing small rectangular items of fixed dimensions

method in geometry

thumb|A 6-equidissection of a square

Unsolved geometry problem about planar regions

geometry; how many 3-point lines can n points form