Information AboutHeptadecagon |
| CATEGORIES ABOUT HEPTADECAGON | |
| polygons | |
| euclidean plane geometry | |
|
In Geometry , a heptadecagon (or '''17-gon''') is a seventeen-sided Polygon . A regular heptadecagon has Internal Angle s each measuring degrees. HEPTADECAGON CONSTRUCTION The regular heptadecagon is a Constructible Polygon , as was shown by Carl Friedrich Gauss in 1796. Gauss was so pleased by this that he asked for one to be inscribed on his Tombstone . The stonemason declined, stating that the difficult construction would essentially look like a circle. Constructibility implies that Trigonometric Function s of 2π/17 can be expressed with basic Arithmetic and Square Root s alone. Gauss' book ''Disquisitiones'' contains the following equation, given here in modern notation: : The first actual method of construction was devised by Johannes Erchinger, a few years after Gauss' work, as shown step-by-step in the animation below. It takes 64 steps. SEE ALSO EXTERNAL LINKS You can see how to construct a regular 17-gon geometrically at either of :http://www.showmath.co.kr/const/polygon/rpoly17.html (Korean, flash) :http://www.geocities.com/RainForest/Vines/2977/gauss/formulae/heptadecagon.html :http://mathworld.wolfram.com/Heptadecagon.html :http://www.jimloy.com/geometry/17-gon.htm And you can see the Algebra ic aspect (by Gauss) in this book: 'Famous Problems and Other Monographs' by F.Klein et al. :http://www.mathlove.org/bbs/data/mathfb/alg17gon.ppt |
|
|