Euclidean plane geometry

relation in Euclidean geometry among the three sides of a right triangle

thumb|400px|right|Some polygons of different kinds: open (excluding its boundary), boundary only (excluding interior), closed (including both boundary and interior), and self-intersecting. In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain.

ratio between two quantities whose sum is at the same ratio to the larger one

flat, infinite two-dimensional surface

geometric problem

theorem

theorem

theorem in planar Euclidean geometry

theorem

In geometry, a heptadecagon, septadecagon or 17-gon is a seventeen-sided polygon.

angle formed in the interior of a circle

geometric problem of constructing a cube with twice the volume of a given cube

construction of an angle equal to one third a given angle

theorem describing a relation between the lengths of the sides and the length of a cevian in a triangle

graphics that use a two-dimensional representation of geometric data

theorem

formula that the area of a planar polygon whose vertices all have integer coordinates equals the number of interior integer points plus half the number of boundary integer points minus one

theorem that two triangles are in perspective axially if and only if they are in perspective centrally

relative distance of a point from a circle

region of the plane defined by the axes of a two-dimensional Cartesian system

construct circles that are tangent to three given circles in a plane

theorem

term in geometry

geometric concept of a 2D space with a "point at infinity" adjoined

theorem that, if the vertices of a hexagon lie alternately on two lines, then the three pairs of opposite sides meet in three collinear points

theorem that the three long diagonals of a hexagon that is tangent to a conic section meet in a single point

geometric construction used in Ancient Greek mathematics

theorem

a family of circles where every one intersects every circle in a second family of circles orthogonally

real number that can be geometrically constructed with compass and straightedge from a unit segment in a finite number of steps

In geometry, a 65537-gon is a polygon with 65,537 (216 + 1) sides. The sum of the interior angles of any non-self-intersecting is 11,796,300°.

method of interpolating functions on a 2D grid

construction in geometry, which, given to a conic, associates a line (“polar”) to a point and a point (“pole”) to a line

theorem that, in a right triangle, the altitude equals the geometric mean of the the two line segments on the hypotenuse created by the altitude

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

theorem

theorem that every finite set of points in the plane, not all collinear, has a line through exactly two points

statement in plane geometry, used implicitly by Euclid, which cannot be derived from the postulates as Euclid gave them

In geometry, a 257-gon is a polygon with 257 sides. The sum of the interior angles of any non-self-intersecting 257-gon is 45,900°.

theorem

theorem that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant

theorem that the intersections of the 3 pairs of external tangent lines to 3 circles are collinear

regular polygon that can be constructed with compass and straightedge

Relates areas of three parallelograms attached to three sides of an arbitrary triangle

mathematical problem

given a circle and its centre, the problem of dividing the circle into four equal arcs using only a compass

circle in a coordinate plane associated with a quadratic equation

subdivision of the plane into polygons that are all regular

theorem

right triangle with an additional feature beyond the right angle making calculations on the triangle even easier

type of region of the Cartesian plane

incidence geometry theorem

theorem

bound on the number of incidences between points and lines in the plane

point defined in a quadrangle

graph defined from a set of points in the Euclidean plane

isometry of the Eluclidean plane

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