Search results
Results from the WOW.Com Content Network
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [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. [4] [5]
The Battle for Wesnoth, a hex grid based computer game. A hex map, hex board, or hex grid is a game board design commonly used in simulation games of all scales, including wargames, role-playing games, and strategy games in both board games and video games. A hex map is subdivided into a hexagonal tiling, small regular hexagons of identical size.
The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter. The optimal three-dimensional structure for making honeycomb (or rather, soap bubbles) was investigated by Lord Kelvin , who believed that the Kelvin structure (or body-centered cubic lattice) is ...
Apothem of a hexagon Graphs of side, s; apothem, a; and area, A of regular polygons of n sides and circumradius 1, with the base, b of a rectangle with the same area. The green line shows the case n = 6. The apothem (sometimes abbreviated as apo [1]) of a regular polygon is a line segment from the center to the midpoint of one of its sides.
In geometric measure theory the area formula relates the Hausdorff measure of the image of a Lipschitz map, while accounting for multiplicity, to the integral of the Jacobian of the map. It is one of the fundamental results of the field that has connections, for example, to rectifiability and Sard's theorem .
A short elementary proof of Pascal's theorem in the case of a circle was found by van Yzeren (1993), based on the proof in (Guggenheimer 1967). This proof proves the theorem for circle and then generalizes it to conics. A short elementary computational proof in the case of the real projective plane was found by Stefanovic (2010).
As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members. The method of exhaustion typically required a form of proof by contradiction, known as reductio ad absurdum. This amounts to finding an area of a ...