By Marina Cohen
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Extra info for 3-D Shapes
This is the essential difference between the division of Unity by the square root of 2 and its division by 4 , both of which are geometrical proportions. As the geometry of the former shows, through the creation of J2 we are immediately propelled outside the original square (see Workbook 1). This marks the beginning of an endless, ever expanding progression and proliferation, leading further and further away from the original Unity. There is no possible way with J2 to have a geometric internal division of Unity.
Join these points to determine the midpoint of 3 continue the the circle's radius at 3. 3. 17557. 809. 3a that the relationship between the side of a pentagon and its diagonal is 1 :4. 90211. 809. The diagonal of the pentagon is the geometric mean between the diameter of the circumscribing circle and the height of the pentagon. 4b. Draw diagonal EB and height AT. 587785, and the hypotenuse of TC = OC = 1, the radius of the circle. The ratio 18/19 is of interest since it is one of the ratios used to define the semitone in music and is also the ratio that determines the lunar and solar year in the eclipse cycle.
This area and shape is known as the Vesica Piscis. 1. 3. Geometric proof of theJ3 proportion within the Vesica Piscis. Draw the major and minor axes C D and AB. Draw CA, AD, DB and BC. By swinging arcs of our given radius from either centre A o r B we trace along the vesica tg points C and D, thus verifying that lines AB, BC, CA, BD and A D are equal to one another and to the radius common to both circles. We now have two identical equilateral triangles emerging from within the Vesica Piscis. Extend lines CA and CB to intersect circles A and B at points G and F.
3-D Shapes by Marina Cohen