Vesica Piscis--Real Sacred Geometry

[Turtle]

___I mentioned this shape & attachment in another thread, but it deserves its own for a proper exploration. I will just start by attaching my exposition, & after you look it over maybe Google Vesica Piscis or check in a dictionary.

[Qfwfq]

The story behind the Fish Bladder seems quite interesting. In the last paragraph at http://www.philomuse.com/kingfisher/lab/vp.htm I found:

"Mary herself can be equated with the goddess Aphrodite Marina"

It made me wonder if the Semitic 'Miryam' has anything to do with 'sea' in that group of languages. I looked it up and found it means 'princess'. Funny coincidence, I guess, only in Latin languages. Maria-Marina, they are both used as girl's names here.

[Turtle]

___Very interesting stuff! In my research I had not encountered the term 'mandorla'. I wonder how that may be related to a 'Mandala' as in sacred meditative image? Also, I never saw a pentagram laid out on the vesica piscis as in the drawing at this page:
http://www.philomuse.com/kingfisher/north/vpgeo.htm
I will have to check it out more closely.
___ Speaking of coincidence, I ran across the term vesica piscis in relation to one of the ancient circles laid out on Glastonbury & which is an astronomical observatory. I wish I could remember the book title...something like the "little Book of the Sun & Moon'? Anyway, they related the shape to astronomy.
___Well, I'm off to read up. Great stuff Q!

[Turtle]

___So far, the drawing with the petagram on the vesica piscis seems arbitrary, ie. I have not yet found a compass & straightedge construction that follows.
___I did negelect to point out in the original drawing that the vesica piscis also bounds 2 equalteral traingles, & inasmuch as they are the first regular polygon, this is another example of sacred (or significant) geometry in the shape.
___I have found however that a rectangle of sides 2 & 4 bounds the vesica piscis & the diagonal of this rectangle is the 2*SQR5 (sacred), & half that rectangle is a square with diagonal 2*SQR2 (sacred). I will show this in a construction when I have completed it.
___

[Infiverse8@yahoo.com]

Got interested in your vesica piscis, thought it ran a bell, so I looked around and found a reference in John Michell's 'The New View over Atlantis'. They are talking about alchemy and sacred numbers. The number 1746 is mentioned as a 'number of fusion.' I'll quote, "... the profile of the Pyramid is placed in association with that basic igure of sacred geometry and architecture known as the 'vesica piscis' or vessel of the fish. ... It is not merely a figure of abstract geometry, for it occurs in many of the patterns of nature. It represents a state of perfect equilibrium between two equal forces, and in the symbolic vocabulary of the old geometers it was an image of the interpenetrating worlds of heaven and earth, spirit and matter, and other such complementary elements." He also says the shape also taked the form of a magnetic field, of which I have no knowledge.
Anyway, its a neat shape.

[Qfwfq]

I wouldn't bet my savings on there being a connection between Mandala and mandorla, though you never know... Probably coincidence, like Mary and sea/marine, which are very close in Italian and Latin; as a name, Marina may well originate as a diminutive of Maria and just happen to coincide with the adjective, I'm not sure, I would need to look it up. As for the origin of the name, it seems to be not so much Semitic but Egyptian: Myrhiam, meaning princess.

[Turtle]

___Infiverse8@yahoo.com quoted Mitchell saying, "... It is not merely a figure of abstract geometry, ..."
___This comment is very much to the point, ie. this simple to construct shape 'encodes' some very complex mathematical values. As to magnetic fields, other than in general exhibiting curves, I don't know of any specific magnetic field the shape represents. If you find more on this I'd love to hear about it.
___So Q, are you saying you think 'mandora' is related to 'Myrhiam', or that you found since that 'Mary, Maria' is related to 'Myrhiam'? I love etymology hunts!
___I haven't done any more with the construction yet as far as finding a pentagram encoded in the vesica piscis. While it's possible, it seems unlikely as the principle angles at work in a pentagram are 72deg & 36deg, & the principle angles in the vesica piscis are 90deg, 60deg, 45deg, &30deg;inasmuch as it is impossible to trisect an angle with compass & straightedge, no bisections of the angles present generate the angles needed.
___Now if the pentagram were to derive, we would have the sacred geometry of phi, the Golden Ratio/Mean in the vesica piscis as well as SQR2, SQR3, & SQR5.
___Great comments folks; thanks.

[Turtle]

___Here is my construction relating SQR's of 2 & 5 to the vesica piscis. Please don't hesitate to point out any errors, although in general it is correct.

[Turtle]

___A short addendum. In post #4 I said the rectangle "bounds" the vesica piscis;the rectangle only "bounds" 2 sides & "surrounds" the other 2.
___I realized the error just now, when I saw that the beginning circle bounds a hexagon. Extend the sides of said hexagon & you have the 6-pointed star. I botched up my drawing so I have to redo it; it will of course have the proof.
___PS Feel free to post it before I (challenge?)

Any geometers out there?

[Turtle]

___The promised construction demonstrating the six-pointed star stemming from the vesica piscis.