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[1] [2] It is also related to the densest circle packing of the plane, in which every circle is tangent to six other circles, which fill just over 90% of the area of the plane. The case when the problem is restricted to a square grid was solved in 1989 by Jaigyoung Choe who proved that the optimal figure is an irregular hexagon.
For example, the perimeter of a rectangle of width 0.001 and length 1000 is slightly above 2000, while the perimeter of a rectangle of width 0.5 and length 2 is 5. Both areas are equal to 1. Proclus (5th century) reported that Greek peasants "fairly" parted fields relying on their perimeters. [ 2 ]
A magic polygon, also called a perimeter magic polygon, [1] [2] is a polygon with an integers on its sides that all add up to a magic constant. [3] [4] It is where positive integers (from 1 to N) on a k-sided polygon add up to a constant. [1] Magic polygons are a generalization of other magic shapes [5] such as magic triangles. [6]
In the 3-dimensional euclidean space, a cell of such a honeycomb is said to be a space-filling polyhedron. [2] A necessary condition for a polyhedron to be a space-filling polyhedron is that its Dehn invariant must be zero, [3] [4] ruling out any of the Platonic solids other than the cube.
Basic topics in elementary mathematics include polygons, circles, perimeter and areas. A polygon is a shape that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular ...
A regular digon has both angles equal and both sides equal and is represented by Schläfli symbol {2}. It may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune. The digon is the simplest abstract polytope of rank 2. A truncated digon, t{2} is a square, {4}. An alternated digon, h{2} is a ...