Square Root of Three — 1.732 : 1 — Vesica Pisces
The Vesica Pisces is created by two identical intersecting circles, the circumference of one intersecting the center of the other. The vulva-shaped space thus created is called the Vesica Pisces.
This is the lid of the Chalice Well designed by Bligh Bond in the early part of the 20th century. It covers one of the most powerful Holy Wells in Britain. The Chalice Well has numerous examples of vesicas. Even Nature demonstrates this.
|the Gothic Arch is the top half of a Vesica Pisces - see Chartres Cathedral. It This vescia is the sacred geometric shape of the Piscean Age.||Gothic arch on the tower on the Glastonbury Tor. This site was a hermitage and retreat for early Christian monks||Gothic arch in the Gallilee of Glastonbury Abbey. Note circular Romanesque arches behind in the Mary Chapel.|
The Vesica Pisces
Two Circles share a common (AB).
Radius AB = 1
The intersecting circles create a Vesica Pisces.
The minor axis of this Vesica Pisces (AB) = 1,
The major axis (CD) = the square root of three, 1.732
Proof: in right triangle (EBC), EB = 1/2 AB, or .5
CB is also a radius of the circle whose center is B, so
CB = AB = 1. Therefore using the Pythagorean Theorem
CD is perpendicular to AB;
therefore angle CEB = 90°
CD:AB :: √3:1 CD is to AB as the square root of 3 is to 1
a2 +b2 = c2
EB2 + CE2 = CB2
52=0.25 + CE2 = (CB)=1
∴ CE2 = 0.75
CE = √0.75
CE = 0.8660254038
CE is 1/2 of the major axis CD,
∴ CD = 2 * 0.8660254038
CD = 1.7320508076∞
√3 = 1.7320508076∞
Therefore CD = 1.7320508076∞
and CD:AB :: √3:1