The area of a regular heptagon can be expressed in terms of the roots of a cubic.
2.
The illustration shows an example in which the seven points are the vertices of a regular heptagon.
3.
Deeper truncations of the regular heptagon and heptagrams can produce isogonal ( vertex-transitive ) intermediate tetradecagram forms with equally spaced vertices and two edge lengths.
4.
Thabit's translation of a work by Archimedes which gave a construction of a regular heptagon was discovered in the 20th century, the original having been lost.
5.
A regular heptagon or higher number of sides, used as a base, with equilateral triangles, would have gaps, and not form a pyramid at all.
6.
The heptagonal triangle, with sides coinciding with a side, the shorter diagonal, and the longer diagonal of a regular heptagon, is obtuse, with angles \ pi / 7, 2 \ pi / 7, and 4 \ pi / 7.
7.
The area of a regular heptagon inscribed in a circle of radius " R " is \ tfrac { 7R ^ 2 } { 2 } \ sin \ tfrac { 2 \ pi } { 7 }, while the area of the circle itself is \ pi R ^ 2; thus the regular heptagon fills approximately 0.8710 of its circumscribed circle.
8.
The area of a regular heptagon inscribed in a circle of radius " R " is \ tfrac { 7R ^ 2 } { 2 } \ sin \ tfrac { 2 \ pi } { 7 }, while the area of the circle itself is \ pi R ^ 2; thus the regular heptagon fills approximately 0.8710 of its circumscribed circle.
मोबाइल