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Returning to the basic 45 degree construction, it is found that this triangle can't help but produce Octagons when it's paired with its baseline circle, AB here. Where circle AB cuts the leg CD ( the first tier point, or altitude foot)is the basis for all this triangle geometry. The relationship it has with the host triangle is the key to Garsalian geometry. The blue circle drawn from the first tier point I've come to call the defining circle or definer.




Following this defining circle around circle AB naturally produces an Octagon, as shown here.



Where the definer circle cuts the circumcircle of triangle BCD is the centre of the green triangle shown here.




When the green circle is followed around the circumcircle it produces another Octagon, as here




When the first tier baseline circle and its definer is added it looks like this




And once again an Octagon is produced





When the two smaller Octagons are overlaid it looks like this





When all three are overlaid it looks like this. The ratio between them is 1: 1.4142.





When the sides of the largest Octagon are extended till they meet, as shown here, you get.....A Cornetto. So there you are, the secret to life, the Universe and everything is.... Mint Ice Cream (was there ever any doubt?)

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Subject Views Written By Posted
Atalanta Fugiens, emblem 21. 1220 cloister 26-Sep-18 21:55
Re: Atalanta Fugiens, emblem 21. 199 Jiri Mruzek 27-Sep-18 07:48
Re: Atalanta Fugiens, emblem 21. 159 molder 27-Sep-18 10:56
Re: Atalanta Fugiens, emblem 21. 209 cloister 27-Sep-18 12:11
Re: Atalanta Fugiens, emblem 21. 148 cloister 29-Sep-18 12:36
Re: Atalanta Fugiens, emblem 21. 178 cloister 30-Sep-18 13:51
Re: Atalanta Fugiens, emblem 21. 141 cloister 02-Oct-18 12:51
Re: Atalanta Fugiens, emblem 21. 149 cloister 03-Oct-18 18:49
Re: Atalanta Fugiens, emblem 21. 257 cloister 05-Oct-18 07:17
Re: Atalanta Fugiens, emblem 21. 132 molder 03-Oct-18 04:41
Re: Atalanta Fugiens, emblem 21. 143 cloister 03-Oct-18 05:55
Re: Atalanta Fugiens, emblem 21. 135 molder 03-Oct-18 10:48
Re: Atalanta Fugiens, emblem 21. 126 cloister 03-Oct-18 17:18
Vesica Piscis and Sacred Geometry 166 MDaines 03-Oct-18 08:20
Re: Vesica Piscis and Sacred Geometry 135 cloister 03-Oct-18 17:32


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