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searching for Convex polygon 69 found (165 total)

Viviani's theorem (912 words) [view diff] exact match in snippet view article find links to article

the location of the point. A necessary and sufficient condition for a convex polygon to have a constant sum of distances from any interior point to the sides

Krein–Milman theorem (2,957 words) [view diff] exact match in snippet view article find links to article

extreme points of this shape. This observation also holds for any other convex polygon in the plane R 2 . {\displaystyle \mathbb {R} ^{2}.} Throughout, X {\displaystyle

Schröder–Hipparchus number (1,391 words) [view diff] exact match in snippet view article find links to article

inserting parentheses into a sequence, and the ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin 1

Convex embedding (410 words) [view diff] exact match in snippet view article find links to article

{\displaystyle F} of a planar graph is fixed to the shape of a given convex polygon in the plane, and the remaining vertices are placed by solving a system

Tripod packing (1,409 words) [view diff] exact match in snippet view article find links to article

"2-comparability", or of finding compatible sets of triangles in a convex polygon. The best lower bound known for the number of tripods that can have

Four-vertex theorem (1,729 words) [view diff] exact match in snippet view article find links to article

obtuse with one of the two edges as its longest side. For a coherent convex polygon with at least four vertices, the cyclic sequence of circumradii of consecutive

Fundamental polygon (6,002 words) [view diff] exact match in snippet view article find links to article

of Möbius transformations. A fundamental domain for Γ is given by a convex polygon for the hyperbolic metric on H. These can be defined by Dirichlet polygons

Fat object (geometry) (4,907 words) [view diff] exact match in snippet view article

enclosing-ball-slimness of an r-separated convex polygon is at most O ( 1 / r ) {\displaystyle O(1/r)} .: 7–8 A convex polygon is called k,r-separated if: It does

Convex drawing (654 words) [view diff] exact match in snippet view article find links to article

strictly convex drawing, each vertex of the graph is also a vertex of each convex polygon describing the shape of each incident face. Every polyhedral graph has

Extreme point (2,086 words) [view diff] exact match in snippet view article find links to article

circle. The perimeter of any convex polygon in the plane is a face of that polygon. The vertices of any convex polygon in the plane R 2 {\displaystyle

Line clipping (735 words) [view diff] exact match in snippet view article find links to article

primarily intended for clipping a line in the parametric form against a convex polygon in 2 dimensions or against a convex polyhedron in 3 dimensions. The

Pestov–Ionin theorem (408 words) [view diff] exact match in snippet view article find links to article

Vigneron, Antoine (2012), "Reachability by paths of bounded curvature in a convex polygon", Computational Geometry, 45 (1–2): 21–32, arXiv:1008.4244, doi:10.1016/j

Marjorie Rice (1,524 words) [view diff] exact match in snippet view article find links to article

1975, Rice read Gardner's July column, "On Tessellating the Plane with Convex Polygon Tiles", that discussed what kinds of convex polygons can fit together

Hamiltonian path (2,043 words) [view diff] exact match in snippet view article find links to article

with cyclic commutator subgroup are Hamiltonian. The flip graph of a convex polygon or equivalently, the rotation graph of binary trees, is Hamiltonian

Minimum bounding box (510 words) [view diff] exact match in snippet view article find links to article

minimum-area or minimum-perimeter bounding box of a two-dimensional convex polygon in linear time, and of a three-dimensional point set in the time it

Conway criterion (789 words) [view diff] exact match in snippet view article find links to article

Berlin: Springer, 1963. Gardner, Martin. On tessellating the plane with convex polygon tiles “Mathematical Games” Scientific American, vol. 233, no. 1 (July

Heesch's problem (899 words) [view diff] exact match in snippet view article find links to article

of the whole plane by congruent copies of the tile. Consider the non-convex polygon P shown in the figure to the right, which is formed from a regular hexagon

Snowy River Cave (460 words) [view diff] exact match in snippet view article find links to article

Passage, contains the fourth largest cave footprint (the area within a convex polygon that encloses the known cave passages) in the USA. The Bureau of Land

Barrow's inequality (541 words) [view diff] exact match in snippet view article find links to article

triangle. Barrow's inequality can be extended to convex polygons. For a convex polygon with vertices A 1 , A 2 , … , A n {\displaystyle A_{1},A_{2},\ldots

Curve sketching (798 words) [view diff] exact match in snippet view article find links to article

the diagram. This method considers all lines which bound the smallest convex polygon which contains the plotted points (see convex hull). Streamline tracing

Unknot (589 words) [view diff] exact match in snippet view article find links to article

particular unknotted linkage that cannot be reconfigured into a flat convex polygon. Like crossing number, a linkage might need to be made more complex

Geometric graph theory (934 words) [view diff] exact match in snippet view article find links to article

higher-dimensional triangulations. The flip graph of triangulations of a convex polygon forms the skeleton of the associahedron or Stasheff polytope. The flip

Kovner–Besicovitch measure (467 words) [view diff] exact match in snippet view article find links to article

the Reuleaux triangle. The Kovner–Besicovitch measure of any given convex polygon with n {\displaystyle n} vertices can be found in time O ( n log ⁡ n

List of formulae involving π (8,342 words) [view diff] exact match in snippet view article find links to article

angles of a regular convex polygon with n sides: S = ( n − 2 ) π {\displaystyle S=(n-2)\pi } Area A of a regular convex polygon with n sides and side

Star domain (1,062 words) [view diff] exact match in snippet view article find links to article

from a set Radial set – Topological set Star polygon – Regular non-convex polygon Symmetric set – Property of group subsets (mathematics) Star-shaped

Spatial network (1,111 words) [view diff] exact match in snippet view article find links to article

sight and access' through open space, and a convex space the 'maximal convex polygon' that can be drawn in open space. Each of these elements is defined

Dynamic convex hull (769 words) [view diff] exact match in snippet view article find links to article

the overall algorithm. For example, the point in polygon query for a convex polygon represented by the ordered set of its vertices may be answered in logarithmic

Steinmetz solid (1,549 words) [view diff] exact match in snippet view article find links to article

the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous

SMAWK algorithm (706 words) [view diff] exact match in snippet view article find links to article

computational geometry, in finding the farthest point from each point of a convex polygon, and in finding optimal enclosing polygons. Subsequent research found

Fáry's theorem (1,261 words) [view diff] exact match in snippet view article find links to article

that its edges are straight line segments and an outside face is a convex polygon (Tutte 1963). It is so called because such an embedding can be found

Hartlaub's spurfowl (1,528 words) [view diff] exact match in snippet view article find links to article

of one bird in 1.43 ha. There was no significant difference in outer convex polygon areas determined by call sites and radio-telemetry. However, core ranges

Alexandrov's uniqueness theorem (1,743 words) [view diff] exact match in snippet view article find links to article

space may be degenerate: it may form a doubly-covered two-dimensional convex polygon (a dihedron) rather than a fully three-dimensional polyhedron. In this

List of conjectures by Paul Erdős (1,448 words) [view diff] exact match in snippet view article find links to article

number of points needed to ensure that a point set contains a large convex polygon. The Erdős–Turán conjecture on additive bases of natural numbers. A

Stellation (2,189 words) [view diff] exact match in snippet view article find links to article

and n are coprime (have no common factor). The case m = 1 gives the convex polygon {n}. m also must be less than half of n; otherwise the lines will either

Lusitanian pine vole (1,107 words) [view diff] exact match in snippet view article find links to article

metres. Estimates of home range size vary by method, with the minimum convex polygon method indicating ranges around 1,042 square metres for males and 862

Prismanes (560 words) [view diff] exact match in snippet view article find links to article

some of the cyclobutanes can be fused anti to each other, giving a non-convex polygon base. These are geometric isomers of the prismanes. Two isomers of [12]prismane

List of shapes with known packing constant (387 words) [view diff] exact match in snippet view article find links to article

Ruth (1990). "Packing and covering the plane with translates of a convex polygon". Journal of Algorithms. 11 (4): 564–580. doi:10.1016/0196-6774(90)90010-C

Antiprism (2,763 words) [view diff] exact match in snippet view article find links to article

rotational symmetry. Thus: Retrograde star antiprisms with regular convex polygon bases cannot have all equal edge lengths, and so cannot be uniform.

Reconfiguration (1,182 words) [view diff] exact match in snippet view article find links to article

into another. The same state space also models the triangulations of a convex polygon, and moves that "flip" one triangulation into another by removing one

List of circle topics (2,408 words) [view diff] exact match in snippet view article find links to article

Steiner chain – Set of circles related by tangency Tangential polygon – Convex polygon that contains an inscribed circle Tangential quadrilateral Roulettes

Erdős–Mordell inequality (1,106 words) [view diff] exact match in snippet view article find links to article

2017) Let A 1 A 2 . . . A n {\displaystyle A_{1}A_{2}...A_{n}} be a convex polygon, and P {\displaystyle P} be an interior point of A 1 A 2 . . . A n {\displaystyle

Schwarz triangle (10,933 words) [view diff] exact match in snippet view article find links to article

when a, b and c are greater than 2. The original triangle Δ gives a convex polygon P1 with 3 vertices. At each of the three vertices the triangle can be

Normal (geometry) (2,664 words) [view diff] exact match in snippet view article

\mathbf {T} ={\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} s}}} For a convex polygon (such as a triangle), a surface normal can be calculated as the vector

3D modeling (3,314 words) [view diff] no match in snippet view article find links to article

described by each triangle is planar, so the projection is always convex). Polygon representations are not used in all rendering techniques, and in these

NP-intermediate (1,534 words) [view diff] exact match in snippet view article find links to article

binary trees or the flip distance between two triangulations of the same convex polygon is below a given threshold The turnpike problem of reconstructing points

Dov Dori (1,086 words) [view diff] case mismatch in snippet view article find links to article

1080/05695558208974578. Dori, Dov; Ben-Bassat, Moshe (1983). "Circumscribing a Convex Polygon by a Polygon of Fewer Sides with Minimal Area Addition". Computer Vision

Flip graph (1,723 words) [view diff] exact match in snippet view article find links to article

flips between them, is a natural generalization of the flip graph of a convex polygon, as the two flip graphs coincide when A {\displaystyle {\mathcal {A}}}

Axiality (geometry) (1,043 words) [view diff] exact match in snippet view article

(2006), Finding the largest inscribed axially symmetric polygon for a convex polygon (PDF), Masters thesis, Department of Electrical Engineering and Computer

Two ears theorem (1,127 words) [view diff] exact match in snippet view article find links to article

anthropomorphic polygons. Repeatedly finding and removing a mouth from a non-convex polygon will eventually turn it into the convex hull of the initial polygon

Steinitz's theorem (5,973 words) [view diff] exact match in snippet view article find links to article

have a unique solution in which each face of the graph is drawn as a convex polygon. Intuitively, this solution describes the pattern that would be obtained

Metafont (3,205 words) [view diff] exact match in snippet view article find links to article

equivalent to a "(transformation) matrix" in PostScript/PDF. Pen: a convex polygon, representing the shape of a "pen" used for drawing. Picture: a raster

LP-type problem (4,687 words) [view diff] exact match in snippet view article find links to article

find a point of maximal Tukey depth for the uniform distribution on a convex polygon. The discovery of linear time algorithms for linear programming and

Richard Schwartz (mathematician) (1,457 words) [view diff] exact match in snippet view article

concept of the pentagram map. According to Schwartz's conception, a convex polygon would be inscribed with diagonal lines inside it, by drawing a line

Occupancy–abundance relationship (3,942 words) [view diff] exact match in snippet view article find links to article

see Fig. 2 and ALA). The EOO can best be thought of as the minimum convex polygon encompassing all known normal occurrences of a particular species and

Filling area conjecture (1,710 words) [view diff] exact match in snippet view article find links to article

{d} _{x}f_{i}} are vertices, listed in counterclockwise order, of a convex polygon inscribed in the dual unit ball B x ∗ {\displaystyle B_{x}^{*}} . The

Tessellation (6,057 words) [view diff] exact match in snippet view article find links to article

city or post office.) The Voronoi cell for each defining point is a convex polygon. The Delaunay triangulation is a tessellation that is the dual graph

Heilbronn triangle problem (2,575 words) [view diff] exact match in snippet view article find links to article

These points are an affine transformation of a regular hexagon, but for larger numbers of points the optimal solution does not form a convex polygon.

Relative convex hull (1,112 words) [view diff] exact match in snippet view article find links to article

contain P {\displaystyle P} , as the smallest Q {\displaystyle Q} -convex polygon that contains P {\displaystyle P} , or as the minimum-perimeter simple

List of Martin Gardner Mathematical Games columns (355 words) [view diff] exact match in snippet view article find links to article

nim, meander, dodgem and rex 1975 Jul On tessellating the plane with convex polygon tiles 1975 Aug More about tiling the plane: the possibilities of polyominoes

Matrix chain multiplication (2,665 words) [view diff] exact match in snippet view article find links to article

(June 1981). "An O(n) algorithm to find a near-optimum partition of a convex polygon". Journal of Algorithms. 2 (2): 122–138. doi:10.1016/0196-6774(81)90014-6

Shoelace formula (3,779 words) [view diff] exact match in snippet view article find links to article

of positive trapezoids, which are outside the polygon. In case of a convex polygon (in the diagram the upper example) this is obvious: The polygon area

Polygon covering (2,229 words) [view diff] exact match in snippet view article find links to article

point p, such that for every point q in P, there is an orthogonally convex polygon containing p and q. The problem of covering a polygon with star polygons

List of unsolved problems in mathematics (20,026 words) [view diff] exact match in snippet view article find links to article

for example showing that outer billiards relative to almost every convex polygon have unbounded orbits. Quantum unique ergodicity conjecture on the distribution

Prime number (14,179 words) [view diff] exact match in snippet view article find links to article

+ 1 {\displaystyle 2^{a}3^{b}+1} ⁠. It is possible to partition any convex polygon into ⁠ n {\displaystyle n} ⁠ smaller convex polygons of equal area and

Topological graph (3,579 words) [view diff] exact match in snippet view article find links to article

Vasilis; Pach, János (1992), "A Turán-type theorem on chords of a convex polygon", Journal of Combinatorial Theory, Series B, 56 (1): 9–15, doi:10

Approximations of π (12,075 words) [view diff] no match in snippet view article find links to article

the calculation of π based on the idea that the perimeter of any (convex) polygon inscribed in a circle is less than the circumference of the circle

Tilings and patterns (1,465 words) [view diff] exact match in snippet view article find links to article

tiling, pentagonal tiling, hexagonal tiling, parallelogon, §9.2 non-convex polygon tilings, §9.3 anisohedral tiling, §9.4 polyomino, heptomino, polyiamond

Timeline of manifolds (1,178 words) [view diff] exact match in snippet view article find links to article

theorem on polyhedra "triangulating" the 2-sphere. The subdivision of a convex polygon with n sides into n triangles, by means of any internal point, adds

Geometric rigidity (5,449 words) [view diff] exact match in snippet view article find links to article

where: the vertices of G {\displaystyle G} are realized as a strictly convex polygon; the bars form a Hamilton cycle on the boundary of this polygon; and