Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve or the volume of a solid . Two different regions may have the same area ; by synecdoche, "area" sometimes is used to refer to the region, as in a "polygonal area".
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.
In geometry, a polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
In geometry, a hexagon is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. A kite may also be called a dart, particularly if it is not convex.
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
In geometry, a set of points are said to be concyclic if they lie on a common circle. A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing circle or circumcircle. All concyclic points are equidistant from the center of the circle.
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides. It is the only regular polygon whose internal angle, central angle, and external angle are all equal (90°), and whose diagonals are all equal in length. A square with vertices ABCD would be denoted ABCD.
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon. Equivalently, a polygon is convex if every line that does not contain any edge intersects the polygon in at most two points.
In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumradius. The circumcenter is the point of intersection between the three perpendicular bisectors of the triangle's sides, and is a triangle center.
In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point. They are in contrast to parallel lines.
In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. To say that "figure F is inscribed in figure G" means precisely the same thing as "figure G is circumscribed about figure F". A circle or ellipse inscribed in a convex polygon is tangent to every side or face of the outer figure. A polygon inscribed in a circle, ellipse, or polygon has each vertex on the outer figure; if the outer figure is a polygon or polyhedron, there must be a vertex of the inscribed polygon or polyhedron on each side of the outer figure. An inscribed figure is not necessarily unique in orientation; this can easily be seen, for example, when the given outer figure is a circle, in which case a rotation of an inscribed figure gives another inscribed figure that is congruent to the original one.
In geometry, a centre or center ; of an object is a point in some sense in the middle of the object. According to the specific definition of center taken into consideration, an object might have no center. If geometry is regarded as the study of isometry groups, then a center is a fixed point of all the isometries that move the object onto itself.
In geometry, a Robbins pentagon is a cyclic pentagon whose side lengths and area are all rational numbers.
In geometry, a bicentric polygon is a tangential polygon which is also cyclic — that is, inscribed in an outer circle that passes through each vertex of the polygon. All triangles and all regular polygons are bicentric. On the other hand, a rectangle with unequal sides is not bicentric, because no circle can be tangent to all four sides.
There are many terms in mathematics that begin with cyclic:
In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.
In geometry, a pentagon is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.
In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle. This is a circle that is tangent to each of the polygon's sides. The dual polygon of a tangential polygon is a cyclic polygon, which has a circumscribed circle passing through each of its vertices.
