Vesicula & Vesica Piscis - Proportions
02Jan2007 10:13 PM
Today,
following a polytopia post, I happened upon a
website with the proportions of the
vesicula (a term coined by
colleague Aya who I met in
Sedona in February 2004 with his fabulous large
mandala canvases.) The "vesicula" is the "sliver"
composed of two back-to-back sides of the
3-sided Reuleaux
Triangle...
I confirmed the proportions here (using the URL above; the proportion is 4: (2*(4-4cos30)) which is
1.0717968, so simplifying by dividing both sides by 4 (to give the proportion for a circle with radius =1);
1
2*(1-cos30)) = .2679492 (according
to my calculator)... Another proportion to add
to the list of somehow cosmically significant
proportions! I have a diagram which shows the area
calculations for the more familiar Vesica
Piscis, which has a
square root of 3 proportion, in terms of its
aspect ratio.
I confirmed the proportions here (using the URL above; the proportion is 4: (2*(4-4cos30)) which is
1.0717968, so simplifying by dividing both sides by 4 (to give the proportion for a circle with radius =1);
1
2*(1-cos30)) = .2679492 (according
to my calculator)... Another proportion to add
to the list of somehow cosmically significant
proportions! I have a diagram which shows the area
calculations for the more familiar Vesica
Piscis, which has a
square root of 3 proportion, in terms of its
aspect ratio.
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