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| [[Image:Golygon.png|thumb|right|upright=1.5|An example of a simple 8-sided golygon]]
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| A '''golygon''' (technically referred to as a "serial isogon of 90 degrees") is any [[polygon]] with all [[right angle]]s, whose sides are consecutive integer lengths. Golygons were invented and named by [[Lee Sallows]], and popularized by [[A.K. Dewdney]] in a 1990 ''[[Scientific American]]'' column (Smith). Variations on the definition of golygons involve allowing edges to cross, using sequences of edge lengths other than the consecutive integers, and considering turn angles other than 90°.
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| In any golygon, all horizontal edges have the same [[parity (mathematics)|parity]] as each other, as do all vertical edges. Therefore, the number ''n'' of sides must allow the solution of the system of equations
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| :<math>\pm 1 \pm 3\cdots \pm (n-1) = 0</math>
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| :<math>\pm 2 \pm 4\cdots \pm n = 0.</math>
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| It follows from this that ''n'' must be a multiple of 8.
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| The number of solutions to this system of equations may be computed efficiently using generating functions {{OEIS|id=A007219}} but finding the number of solutions that correspond to non-crossing golygons seems to be significantly more difficult.
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| There is a unique eight-sided golygon (shown in the figure); it can [[tessellation|tile]] the plane by 180-degree rotation using the [[Conway criterion]].
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| ==See also==
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| *[[Rectilinear polygon]]
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| ==References==
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| *{{cite journal |author=Dewdney, A.K. |title=An odd journey along even roads leads to home in Golygon City |journal=[[Scientific American]] |volume=263 |pages=118–121 |year=1990}}
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| *{{cite journal |author=Sallows, Lee |title=New pathways in serial isogons |journal=[[The Mathematical Intelligencer]] |volume=14 |pages=55–67 |year=1992 |doi=10.1007/BF03025216 |issue=2}}
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| *{{cite journal |doi=10.2307/2690648 |author=Sallows, Lee; [[Martin Gardner|Gardner, Martin]]; [[Richard K. Guy|Guy, Richard K.]]; [[Donald Knuth|Knuth, Donald]] |title=Serial isogons of 90 degrees |jstor= 2690648 |journal=[[Mathematics Magazine]] |volume=64 |issue=5 |year=1991 |pages=315–324}}
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| *{{cite web |author=Harry J. Smith |title=What is a Golygon? |url=http://www.geocities.com/hjsmithh/Golygons/GolyWhat.html |archiveurl=http://web.archive.org/web/20091027155427/http://geocities.com/hjsmithh/Golygons/GolyWhat.html |archivedate=2009-10-27}}
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| *{{mathworld|title=Golygon|urlname=Golygon}}
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| ==External links==
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| *[http://oeis.org/search?q=golygon&language=english Golygons] at the [[On-Line Encyclopedia of Integer Sequences]]
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| [[Category:Polygons]]
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Nice to satisfy you, my name is Refugia. Puerto Rico is where he and his wife live. One of the things he loves most is ice skating but he is struggling to discover time for it. Bookkeeping is what I do.
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