September 30, 2024.  © Copyright 2024 by Paul Glossop. All rights reserved.    For more information, please email: Geometer Back to the Heptagon! Back to the Heptagon!
yet another division of Geometer
Constructing the Hendecagon
The Ideal centre angle 360/11 = 32.72727 Variance of Pink angles from the ideal  (+) 3 parts in 100,000 360/11 ( )  Pink 360/11  ∙105 = –2.76177 Variance of Green angles from the ideal  (-) 7 parts in 100,000 360/11 ( )  Green 360/11  ∙105 = 7.36471 Crosscheck:  3 x Green + 8 x Pink  = 360.00000° Pink = 32.72818° Analysis of the central angles of the Hendecagon Each of the pink angle group = 32.72818° Green = 32.72486° Each of the green angle group = 32.72486° A C F H G B D L J R E O C1 C1 C1 Starting with the Key we take the construction further: Octasect REFLEX angle JOE to achieve radii intersecting C1 in A, B, C, D, F, G, H. Suppress line KO, leaving JOE and its trisection unchanged. Quadrisect KOE to achieve three radii intersecting C1 in J, R, and L. Suppress construction lines, leaving the key A C F H G B D L J R E O L J R E O L J R K V U E O K V U E O C1 C2 11∙ mKOE 4   = 359.97349° 360° 11 = 32.72727° mKOE 4 = 32.72486° mKOE = 130.89945° Constructing the Key to a Hendecagon  (Undecagon) 1.)  Presume the founding circle C1 and its circumsquare.  2.)  Draw circle C2 with centre V and radius VO to intersect the square in D 3.)  Draw line segment UD to intersect C1 in K 4.)  Angle KOE is extremely close to being 4 x the centre angle in a hendecagon K D V U E O The United States Susan B. Anthony dollar coin features hendecagons on both its obverse and reverse. The Latin E Pluribus Unum is inscribed on the reverse. It means, "Out of Many comes One." This may well reflect the sentiment of the ancient Greeks, who loved the polygons, and whose dual approach to knowledge would have embraced both synthesis — bringing together many into one — and analysis, understanding the whole by considering its parts. f y  = 2.7