Obtuse triangle formed by the side and diagonals of a regular heptagon
Regular heptagon
Longer diagonals
Shorter diagonals
Each of the fourteen congruent heptagonal triangles has one green side, one blue side, and one red side.
In Euclidean geometry, a heptagonal triangle is an obtuse, scalene triangle whose vertices coincide with the first, second, and fourth vertices of a regular heptagon (from an arbitrary starting vertex). Thus its sides coincide with one side and the adjacent shorter and longer diagonals of the regular heptagon. All heptagonal triangles are similar (have the same shape), and so they are collectively known as the heptagonal triangle. Its angles have measures and and it is the only triangle with angles in the ratios 1:2:4. The heptagonal triangle has various remarkable properties.
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regular heptagon. All heptagonaltriangles are similar (have the same shape), and so they are collectively known as the heptagonaltriangle. Its angles...
regular heptagon. Apart from the heptagonal prism and heptagonal antiprism, no convex polyhedron made entirely out of regular polygons contains a heptagon as...
acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle...
rational triangle", in The Book of Numbers, 1996, Springer-Verlag, pp. 201 and 228–239. Leon Bankoff and Jack Garfunkel, "The heptagonaltriangle", Mathematics...
{1}{q}}={\frac {1}{r}}} where the denominators are squares and also for a heptagonaltriangle whose sides p , q , r {\displaystyle p,q,r} are square numbers. One...
A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed...
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples...
In addition, the ratio of the inradius to the circumradius of a heptagonaltriangle is one of the solutions of a cubic equation. The values of trigonometric...
geometry, a heptagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {7,3}, having three regular heptagons around...
48. It has 24 triangle, 24 square and 4 hexagon faces. It has 60 edges, and 24 vertices. A heptagonal antiprismatic prism or heptagonal antiduoprism is...
other inscribed square. The sides of a heptagonaltriangle, which shares its vertices with a regular heptagon, satisfy the optic equation. For a lens...
case of the heptagonal antiprism, the caps are two regular heptagons. As a result, this polyhedron has 14 vertices, and 14 equilateral triangle faces. There...
Figurate numbers representing heptagons are called heptagonal numbers. 7 is also a centered hexagonal number. A heptagon in Euclidean space is unable to...
around each vertex. For example, 7.7.7 represents the heptagonal tiling which has 3 heptagons around each vertex. It is also regular since all the polygons...
pairs of hexagon edges. Heptagonal pyramid: One face is a heptagon (usually regular), and the remaining seven faces are triangles (usually isosceles). It...
geometry, the order-3 snub heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are four triangles and one heptagon on each vertex. It has...
(grammē) meaning a line. In general, a heptagram is any self-intersecting heptagon (7-sided polygon). There are two regular heptagrams, labeled as {7/2} and...
meditation from which Triangle and Robert had to awaken him in order to deal with a threat from Orpuddex. The Dairy Sentry (an irregular heptagon) – Originally...
rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides a , {\displaystyle a,} b , {\displaystyle...
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