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    Re: Sacred Geometry

    Quote Originally Posted by Darkhawk View Post
    I think the most relevant to my particular dabblings in sacred geometry is phi, though - the golden ratio.

    https://en.wikipedia.org/wiki/Golden_ratio

    It crops up a lot in classical art and architecture, with humanity reaching for the sorts of arcs one gets with the Fibonacci sequence found in nature.
    Phi is fabulous--a nice mathematical representation of "As above, so below"--but it gets a little tortured in its use, IMHO. I approach claims for phi in nature, art, or architecture with skepticism; the nautilus shell is an infamous example of phi overreach.

    The "Fibonacci Flim-Flam" site does some strong debunking. While I might not agree with everything in it, it's worth reading:

    https://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm

    I'm much more interested in logarithmic progressions (of which things like the golden spiral are a subset), which do indeed recur in nature and are governed by the mathematical constant e.

    https://en.wikipedia.org/wiki/E_(mathematical_constant)

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    Re: Sacred Geometry

    Quote Originally Posted by Aster Breo View Post
    You've also reminded me that I need to read your wonderful book! :-D
    When you do, keep your eyes peeled for subtle sacred geometry references scattered sporadically throughout (subtle, because I didn't want anyone to think they need to know math to read the book, because they absolutely do not!)

    In fact, I tried to take it one step beyond sacred geometry by employing a broader use of math symbolically. There's a profound equation woven into the text, one that goes to the heart of the book and, I think, of nature-based paganism.

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    Re: Sacred Geometry

    Quote Originally Posted by Altair View Post
    When you do, keep your eyes peeled for subtle sacred geometry references scattered sporadically throughout (subtle, because I didn't want anyone to think they need to know math to read the book, because they absolutely do not!)

    In fact, I tried to take it one step beyond sacred geometry by employing a broader use of math symbolically. There's a profound equation woven into the text, one that goes to the heart of the book and, I think, of nature-based paganism.
    I remember some of that from my first read of the book, but a lot has faded from my memory. And I don't think I ever did solve the overall riddle. :-P
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    Re: Sacred Geometry

    Quote Originally Posted by Altair View Post
    The "Fibonacci Flim-Flam" site does some strong debunking. While I might not agree with everything in it, it's worth reading:

    https://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm
    I've been reading through a lot of the threads here, but this thread was the one that made me register.

    I love sacred geometry and spend a lot of time with Pythagoras. I read the article you linked to as well as your article here. I understand you also wrote a book on the subject? I'd be interested in reading that as well.

    I've always believed that mathematics is the language of God and I've been a pattern-seeker from childhood.

    I've seen different pictorial versions of the monad through decad. The Pythagorean Sourcebook and Library differs significantly from those you showed. I've just always found it fascinating using geometry to convey ideas and of course, numbers were so much more to the Pythagoreans than mere counters.

    Some of the things I've played with is moving things from 2d to 3d and what symbols or shapes emerge. I've also played with Pythagoras' Table of Opposites, taking them into 3d, showing that in 3d, it boils down to the relative position of the viewer. Another thing I've played with is working with the Tetraktys and the Kabbalah in 3d forms.

    When I was in organic chemistry in college, I had the molecule models but I think I spent more time using them exploring sacred geometry. I couldn't do as much as I wanted because the angles off the carbon atom would only do the angles of the tetrahedron. When I bought my son Magnetix (the magnetic sticks and ball bearings), I was in heaven playing with SG.

    Something kind of cool that some pagans can use for an on-the-go altar is to get a set of gaming dice that has the platonic solids. The shapes correspond to the the points of the pentacle: tetrahedron--fire; cube--earth; octahedron--air; dodecahedron--aither; and icosahedron--water.

    Well, as you can tell, I love this stuff and would love to discuss this more if y'all are interested.

    Oh, and speaking of phi, this is an elegant video of the Golden Key I think you'll like:

    http://www.youtube.com/watch?v=rgmHjEfYsl0

    ~Gnowan

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    Re: Sacred Geometry

    Quote Originally Posted by Gnowan View Post
    I've been reading through a lot of the threads here, but this thread was the one that made me register.
    Welcome to TC!

    Thank you for responding in such depth, and thank you for the link. I'm looking forward to watching the video as soon as I can.

    Do you have a recommendation for reasonably easy to understand resources on Pythagoras's work? I saw you mentioned a Pythagorean Sourcebook. Would that be a good place for a beginner to start? I'm totally NOT a mathematician in any sense. :-P

    Also, to clarify: Altair's book is not *about* sacred geometry. It's an amazing and beautiful journey through his unique take on myth, in which he incorporates ideas about the universal meaning of math. As I said, I'm not a mathematician, so I'm sure I don't understand all of how he's interwoven these concepts. Nevertheless, I absolutely LOVED the book on my first reading and it's next in line on my Kindle for a second reading (which I almost never do).

    Songs of the Metamythos: https://www.amazon.com/dp/0986296406..._2zMNwbW0YPY1G

    I can't recommend it highly enough.
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    Re: Sacred Geometry

    Quote Originally Posted by Aster Breo View Post
    Welcome to TC!
    Thank you for the welcome!

    A book I would recommend for you is Divine Harmony. It's 159 p. "Reader's Digest" version of Pythagoras' life and teachings. Easy read but still pretty thorough.

    I hope you enjoy the short video. The creator did a beautiful job of pictorially depicting the relationships of phi.

    And thank you for the link to the book. I will look that up!

    ~Gnowan

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    Re: Sacred Geometry

    Quote Originally Posted by Gnowan View Post
    I've been reading through a lot of the threads here, but this thread was the one that made me register.

    I love sacred geometry and spend a lot of time with Pythagoras. I read the article you linked to as well as your article here. I understand you also wrote a book on the subject? I'd be interested in reading that as well.

    I've always believed that mathematics is the language of God and I've been a pattern-seeker from childhood.

    I've seen different pictorial versions of the monad through decad. The Pythagorean Sourcebook and Library differs significantly from those you showed. I've just always found it fascinating using geometry to convey ideas and of course, numbers were so much more to the Pythagoreans than mere counters.

    Some of the things I've played with is moving things from 2d to 3d and what symbols or shapes emerge. I've also played with Pythagoras' Table of Opposites, taking them into 3d, showing that in 3d, it boils down to the relative position of the viewer. Another thing I've played with is working with the Tetraktys and the Kabbalah in 3d forms.

    When I was in organic chemistry in college, I had the molecule models but I think I spent more time using them exploring sacred geometry. I couldn't do as much as I wanted because the angles off the carbon atom would only do the angles of the tetrahedron. When I bought my son Magnetix (the magnetic sticks and ball bearings), I was in heaven playing with SG.

    Something kind of cool that some pagans can use for an on-the-go altar is to get a set of gaming dice that has the platonic solids. The shapes correspond to the the points of the pentacle: tetrahedron--fire; cube--earth; octahedron--air; dodecahedron--aither; and icosahedron--water.

    Well, as you can tell, I love this stuff and would love to discuss this more if y'all are interested.

    Oh, and speaking of phi, this is an elegant video of the Golden Key I think you'll like:

    http://www.youtube.com/watch?v=rgmHjEfYsl0

    ~Gnowan
    Thanks for this post, Gnowan, as I've learned all kinds of things from it. The Tetraktys in particular resonates with my metaphysical worldview.

    The decad brings to mind the related but simpler hexagon within a circle. (Does that form have a special name?) I used that to create my personal sigil, which most people mistake for a rune but is actually a stylized bird in flight, using the geometric symbolism of the circle-circumscribed hexagon to say something about myself. I lifted the three up-pointing triangles to be found in the hexagon to form the wings and tail; up-pointing triangles being associated with masculine energy. The fact their points fall on the circle is my way of saying I strive to be in touch with the divine.





    As for the video, some of it worked for me (the established mathematics: the recursive phi relationships, the golden spirals, etc.), some of it didn't (the phi relationships supposedly imposed on organisms, etc.--I find myself much like the Fibonacci Flim-Flam guy on that score). But all of it was beautiful to look at!

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    Re: Sacred Geometry

    Quote Originally Posted by Altair View Post
    Thanks for this post, Gnowan, as I've learned all kinds of things from it. The Tetraktys in particular resonates with my metaphysical worldview.

    The decad brings to mind the related but simpler hexagon within a circle. (Does that form have a special name?) I used that to create my personal sigil, which most people mistake for a rune but is actually a stylized bird in flight, using the geometric symbolism of the circle-circumscribed hexagon to say something about myself. I lifted the three up-pointing triangles to be found in the hexagon to form the wings and tail; up-pointing triangles being associated with masculine energy. The fact their points fall on the circle is my way of saying I strive to be in touch with the divine.





    As for the video, some of it worked for me (the established mathematics: the recursive phi relationships, the golden spirals, etc.), some of it didn't (the phi relationships supposedly imposed on organisms, etc.--I find myself much like the Fibonacci Flim-Flam guy on that score). But all of it was beautiful to look at!
    Yeah, the nature stuff was definitely flim-flam. But the beauty of the original part of the video was so elegant. I love mathematics and I don't care about how the real world fits in. When it works, it truly is elegant.

    Pythagoras stated that:

    Arithmetic = Number in itself
    Geometry = Number in space
    Music or Harmonics = Number in time
    Astronomy = Number in space and time

    I've always loved math. I never liked applied math. I've just always found the beauty in numbers. Maybe I wore a toga in my previous lives!

    Looking at your sig, I'd like to see it in a circle (where YOU see it in the circle) so I can see what angles you chose and how they fit into the circle. Triangles and circles... this is what we're made of.

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    Re: Sacred Geometry

    Quote Originally Posted by Altair View Post
    Thanks for this post, Gnowan, as I've learned all kinds of things from it. The Tetraktys in particular resonates with my metaphysical worldview.

    The decad brings to mind the related but simpler hexagon within a circle. (Does that form have a special name?) I used that to create my personal sigil, which most people mistake for a rune but is actually a stylized bird in flight, using the geometric symbolism of the circle-circumscribed hexagon to say something about myself. I lifted the three up-pointing triangles to be found in the hexagon to form the wings and tail; up-pointing triangles being associated with masculine energy. The fact their points fall on the circle is my way of saying I strive to be in touch with the divine.





    As for the video, some of it worked for me (the established mathematics: the recursive phi relationships, the golden spirals, etc.), some of it didn't (the phi relationships supposedly imposed on organisms, etc.--I find myself much like the Fibonacci Flim-Flam guy on that score). But all of it was beautiful to look at!
    The closest shape I see for this is an icosphere. Again, it's all about the triangles.

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    Re: Sacred Geometry

    Quote Originally Posted by Gnowan View Post
    Pythagoras stated that:

    Arithmetic = Number in itself
    Geometry = Number in space
    Music or Harmonics = Number in time
    Astronomy = Number in space and time

    That's beautifully stated and has the ring of truth to me. But I'm still pondering it to see if it holds up to harder scrutiny (particularly the last one, astronomy). But certainly on a poetic level (and yes, I think there can be poetry in math), it works.

    Have you considered adding to the sacred geometry wiki here at The Cauldron? Some of the stuff you're familiar with may fall outside of geometry strictly speaking, but it's definitely relevant to math mysticism (for lack of a better term) more generally.

    Maybe a "Beyond Sacred Geometry" section on Pythagorean concepts like the tetraktys?

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