Convex and concave polygons - Wikipedia, the free encyclopedia
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In geometry, a polygon can be either convex or concave . A convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to c...
en.wikipedia.org/wiki/Convex_and_concave_polygons
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Bob Jenkin's half-bath has a beautiful tiling based on the Hirschhorn Medalion. This is one pentagon in the Chaos Tiles. Bob Jenkins and Mike Korn have both made pages about non-convex pentagons. Marjorie Rice has a page here.
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www.mathpuzzle.com/tilepent.html
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The rectifiable polyominoes are well studied, but the convexifiable iamonds (hexagonifiable?) are not. How many of the enneiamonds are n-convex? The last is the only other class of n-vex convex pentagon I was able to find.
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www.mathpuzzle.com/convex.html
www.mathpuzzle.com/convex.html
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Description: Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry. Source: Florida Center for Instructional Technology Clipart (Tampa: University of South Florida, 2007) ;
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etc.usf.edu/clipart/42600/42609/irregpent_42609.htm
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Description: Illustration of an irregular convex pentagon. Source: Florida Center for Instructional Technology Clipart (Tampa: University of South Florida, 2007) ; Keywords: polygon, geometric shape, pentagon, five sided, 5 sides, irregular, convex;
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etc.usf.edu/clipart/42600/42614/irregpent_42614.htm
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Subject: Re: Angles in a convex pentagon? ... You can get an angle approaching pi + arccos(1/4) > pi + pi/3 by the following method: 1) Construct an equilateral not-strictly-convex pentagon with EA and AB colinear, and BC and CD colinear. 2) Wiggle it. (shrink the appropriate edges slightly, causing slight changes in...
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valis.cs.uiuc.edu/~sariel/research/CG/compgeom/msg00423...
valis.cs.uiuc.edu/~sariel/research/CG/compgeom/msg00423.html
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Subject: Angles in a convex pentagon? ... Does anyone know whether the following is true in a convex pentagon ABCDE: Given that EA>AB>BC and CD<DE<EA, the angle sum DEA+EAB is at most 4*pi/3. ... Next by thread: Re: Angles in a convex pentagon?
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valis.cs.uiuc.edu/~sariel/research/CG/compgeom/msg00421...
valis.cs.uiuc.edu/~sariel/research/CG/compgeom/msg00421.html
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In 1985, a fourteenth type of tessellating pentagon was discovered by Rolf Stein, a German graduate student. Are all the types of convex pentagons that tessellate now known? The tessellating pentagon problem remains unsolved.
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britton.disted.camosun.bc.ca/jbperplex.htm
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However, the non-convex pentagon on the right is a trickier case. If we have the figure on the page, we can always find a way to draw segments to divide the pentagon into 3 triangles, but how can we prove this in all cases?
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www.math.washington.edu/~king/coursedir/m444a00/syl/cla...
www.math.washington.edu/~king/coursedir/m444a00/syl/class/wk5/regpentagon/index.html
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