the midpoint polygon of a polygon P is the polygon whose vertices are the midpoints of the edges of P. It is sometimes called the Kasner polygon after...

the midpoint of a diagonal between opposite vertices is the polygon's center. The midpoint-stretching polygon of a cyclic polygon P (a polygon whose...

In geometry, the midpoint-stretching polygon of a cyclic polygon P is another cyclic polygon inscribed in the same circle, the polygon whose vertices are...

the triangle's sides AB, AC, BC. It is the n = 3 case of the midpoint polygon of a polygon with n sides. The medial triangle is not the same thing as the...

is tangent to every side at the midpoint. Thus a regular polygon is a tangential polygon. A regular n-sided polygon can be constructed with compass and...

regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that...

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional...

} An equilateral polygon is a polygon which has all sides of the same length (for example, a rhombus is a 4-sided equilateral polygon). To calculate the...

is planar or not. The theorem can be generalized to the midpoint polygon of an arbitrary polygon. Referring to the diagram above, triangles ADC and HDG...

polygons, the external angles total 360°. If squares are constructed all internally or all externally on the sides of an octagon, then the midpoints of...

circumscribed circle) A midpoint polygon of another polygon This disambiguation page lists articles associated with the title Inscribed polygon. If an internal...

the applied forces are arranged as the edges of a polygon of forces or force polygon (see § Polygon of forces). A body is said to be "free" when it is...

cocyclic) 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...

two possible arcs determined by the endpoints of a diameter, taking its midpoint as centre. In non-technical common usage it may mean the interior of the...

But this is the midpoint of the line segment joining two interior points of edges and hence lies in C, the interior of the polygon. This again contradicts...

infinite skew polygons with vertices alternating between two parallel lines. Infinite helical polygons are 3-dimensional infinite skew polygons with vertices...

segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices...

Greek πέντε (pente) 'five' and γωνία (gonia) 'angle') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°....

the center to the midpoint of a side of the polygon; its length, h, is less than the circle radius. Also, let each side of the polygon have length s; then...

similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes...

three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side). For other properties of a triangle's centroid, see...

180°). The dual polygon of a rectangle is a rhombus, as shown in the table below. The figure formed by joining, in order, the midpoints of the sides of...

generally, an n-sided polygon with all its vertices on the same circle, also called the circumscribed circle, is called a cyclic polygon, or in the special...

In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri...

of the midpoint. Just to the west of this peak is a pair of small craters on the floor. There is also a small crater to the south of the midpoint, and the...

In geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears...

implemented by displacing the texture coordinates at a point on the rendered polygon by a function of the view angle in tangent space (the angle relative to...

midpoints of the segments connecting the centroids of opposite triangles form another equilateral triangle.: Thm. 1  A skew hexagon is a skew polygon...

thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 degrees. The regular triacontagon is a constructible polygon, by an edge-bisection...

area as a given polygon, and regular polygons of 3, 4, or 5 sides: p. xi  (or one with twice the number of sides of a given polygon: pp. 49–50 ). But...