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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?)

Subject Views Written By Posted
Atalanta Fugiens, emblem 21. 1309 cloister 26-Sep-18 21:55
Re: Atalanta Fugiens, emblem 21. 226 Jiri Mruzek 27-Sep-18 07:48
Re: Atalanta Fugiens, emblem 21. 173 molder 27-Sep-18 10:56
Re: Atalanta Fugiens, emblem 21. 220 cloister 27-Sep-18 12:11
Re: Atalanta Fugiens, emblem 21. 159 cloister 29-Sep-18 12:36
Re: Atalanta Fugiens, emblem 21. 190 cloister 30-Sep-18 13:51
Re: Atalanta Fugiens, emblem 21. 157 cloister 02-Oct-18 12:51
Re: Atalanta Fugiens, emblem 21. 163 cloister 03-Oct-18 18:49
Re: Atalanta Fugiens, emblem 21. 289 cloister 05-Oct-18 07:17
Re: Atalanta Fugiens, emblem 21. 142 molder 03-Oct-18 04:41
Re: Atalanta Fugiens, emblem 21. 168 cloister 03-Oct-18 05:55
Re: Atalanta Fugiens, emblem 21. 144 molder 03-Oct-18 10:48
Re: Atalanta Fugiens, emblem 21. 137 cloister 03-Oct-18 17:18
Vesica Piscis and Sacred Geometry 180 MDaines 03-Oct-18 08:20
Re: Vesica Piscis and Sacred Geometry 145 cloister 03-Oct-18 17:32

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