Monday 3 August 2009

Sacred geometry

The vesica piscis is one of the most important figures in sacred geometry, and symbolically speaking an image of the source of life. It may best be described as a lens shape formed by intersection of two circles with the same radius, intersecting in such a way that the center of each circle lies on the circumference of the other. The name in Latin means the bladder of the fish. The shape is also called, somewhat more poetically, mandorla ("almond" in Italian).

The Mandorla halo, often seen in religious art enclosing Christ or his Mother, is also often taken to represent the womb, and to have been associated with the power of giving birth, since it was used to generate many other numbers and forms, beginning with three and four, the triangle and the square. In Christian art, the area where the two circles overlap may be taken to represent the Incarnation, the beginning of the union of divine and human natures.

The figure was the subject of intense mystical speculation among the Pythagoreans and their successors. The mathematical ratio of its width to its height is the square root of 3, the ratio 265:153 being the best possible approximation to this square root using small whole numbers. As a result the number 153 was sometimes called “the number of the fish”. It is probably no coincidence that the number 153 also appears in the Gospel of John (21:11) as the number of fish Jesus caused to be caught miraculously after his resurrection. The writer of the Gospel would hardly have recorded the number if it had not been believed to be highly significant, and its occurrence is suggestive of a Pythagorean or Platonist influence.

But why as a Catholic do I speak of “sacred geometry”, a term so associated with the New Age movement? I believe that, as the Pope says in The Spirit of the Liturgy, the “mathematics of the universe… comes from the Logos, in whom, so to speak, the archetypes of the world’s order are contained.” And I agree with Michael S. Schneider that children miss out if they are exposed to numbers merely as quantities instead of qualities, each with a distinct character, connected with all others in endlessly fascinating patterns. Such patterns can awaken us to a world of wonder and beauty, and point to the underlying harmony between science, art, and religion.

As you might see from the Comments, Charlotte Ostermann and others are adapting some of these ideas for Catholic homseschoolers. If you are interested to find out more, add a comment of your own, or get in touch directly. In the sidebar you'll find a section where I plan to collect useful ideas for what to do with younger kids to get them interested in all this - not just in geometry, but in the whole process of learning and the development of a vision of how everything connects together.


  1. Charlotte Ostermann7 August 2009 at 03:08

    I love the vesica piscis! Truly, it is matter for intense contemplation. I just wanted to let you know I figured out how to get to these discussions, and will be watching for developments. I just had to figure out how to do lettering around a 'sphere', to make it look like a sphere tho' 2-D, and had to think about the shapes of the ellipses on the surface as the viewer sees it. Look what shape is in the center...the vp...and as we move away from that widest, most open point we narrow to nothing at the 'edges'. In my mind's eye, I 'see' the two-point perspective between mine and God's 'eyes' and my heart breaks because the closer someone stands to one of the 'extremes', the more distorted his view of God, of Self would be. I am constantly advising that we must stay before the face of God to retain the fullness of our humanity, and I love this visual, elegant image of the same concept. Also, one can imagine the Spirit, circling between the Father and the Son, who of course has come to stand firm in the one point of perfect perspective to show us the way, beautiful.

  2. The first Proposition in Euclid's Elements uses this figure:

  3. I agree that we ALL "miss out" when we relate to numbers as mere quantities. The same is true for letters, also symbols, which used to represent entire concepts in and of themselves. We can find the archetypal shapes and forms of numbers and letters in nature and within our bodies (also nature). I have found a fascinating book for awakening to the qualities you speak of: A Beginners Guide to Constructing the Universe by Michael S. Schneider. I continue to return to this text for reference and have used it as a guide for home-school math for my 2 children.

  4. Quite informative information on your post.looking forward for some futher information.
    keep posting