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regular polygon of 2n sides... inside a circle "tends" towards the circle as n increase... Antiphon... [said] for... n sufficiently large the polygon...

isoperimetrical regular polygons, the one having the largest number of angles has the greatest area; the circle has a greater area than any regular polygon of equal...

Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order...

pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) Regular pentagon...

Wolfgang Bolyai, the formula which gave the geometric inscription of the regular polygon of 17 sides, it was with the remark that this alone could be his epitaph...

polyhedra—particularly of regular polyhedra—analogous to the trivial relation between the number of vertices and edges of polygons, namely, that there are...

Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order...

characters themselves are all in polygons. We all thought that there would be a gap would appear between when we go from polygons to movies. But then again,...

really a Circle, but only a Polygon with a very large number of very small sides. As the number of the sides increases, a Polygon approximates to a Circle;...

a polygon of double the number of sides; he then repeated the process, and maintained that, by continuing it, we should at last arrive at a polygon with...

example, they "exhausted" the area between a circle and an inscribed regular polygon, as in the work of Antiphon (c. 430 B.C.) The second general step....

determination of π by the calculation of the sides or the areas of regular polygons in- and circum-scribed to the circle. The theoretical groundwork of...

Pythagoreans knew some properties of regular polygons... how a plane can be filled by... regular triangles, squares, or regular hexagons, and space by cubes....

Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order...

introduced by Hipparchus. So...Heron gives, for finding the area of a regular polygon from the square of its side, formulae which imply a knowledge of trigonometry...

but the pieces composing them are placed side by side, and either form a polygon approaching a semicircle or are cut to bring them to a curve.  In fact...

therefore led to the conclusion that the Porismata, like the pamphlet on Polygonal Numbers, was a synthetic and not an analytic treatise. It is open, however...

Pythagoreans knew some properties of regular polygons... how a plane can be filled by... regular triangles, squares, or regular hexagons, and space by cubes....

the remark of Pappus at the beginning of his "comparisons of the five [regular solid] figures which have an equal surface," to the effect that he will...

equal segments placed end to end at equal angles, like the sides of a regular polygon, must make a complete circuit. Though Gauss clearly revealed the fallacy...