Constructing The Universe



Schedule of Classes




Michael S. Schneider
M.Ed. Mathematics and Science Education
Author of
"A Beginner's Guide To Constructing The Universe
The Mathematical Archetypes of Nature, Science and Art"
(HarperPerennial 1995)
six Constructing The Universe Activity Books





Saturday Afternoon Workshops ~ 1:00 pm to 3:30 ~ $25 each, or $125 for all six classes.
If you'd like to attend please send an email (that's michael -at- with your name, the class title(s) and how many people. You'll receive an email reply confirmation.

Next course: April 17 through June 26:

The Geometry of Nature and Art -- A Voyage From 1 To 12
The shapes represented by the numbers 1 through 12 are responsible for the all designs we see in nature and traditional designs of art and architecture. Come join this journey around the world and through the universe looking at numbers and shapes in a new way, as the language in which The Book of Nature is written. Numbers representing archetypal principles also played roles in the creation myths, cosmologies and the structures of societies of the great civilizations. Each class begins with an illustrated presentation followed by hands-on practice doing nature's own geometric constructions with a compass, straightedge and art materials, all supplied. The course builds to encompass the proportions found in universal design, culminating in the appreciation and construction of the Cosmological Circle diagram which harmonizes the twelve numbers and and served as a microcosmic model for the designs of traditional societies.

While these classes together form a complete whole, each class is also a stand-alone event and so you're invited to attend all or any that interest you.

* The First Principles: 1 and 2
* The Numbers of Structure: 3, 4, 6, 8 and 12
* The Numbers of Life: 5 and 10
* The Numbers of Mystery: 7, 9 and 11
* The Marriage of Seven and Twelve
* The Cosmological Circle

Further description for each class can be found below.


Spring 2010





Ongoing Tuesday Afternoons

"How The World Is Made"

Join a geometric exploration of this magnificent new book "How The World Is Made -- The Story Of Creation According To Sacred Geometry" by John Michell and Allan Brown.

Compasses and art materials supplied.


(c) 2010 Michael Schneider

The Geometry of Nature and Art -- A Voyage From 1 To 12

Saturday April 17

The First Principles: 1 and 2

The number One, represented by the point and circle, is the source of all numbers, shapes and forms of nature. Geometric tradition considers the central point as the "Pole of the Universe" symbolizing the unchanging Laws of creation around which the entire universe (literally "turn around one") revolves. The circle introduces the Pi ratio, the most basic relationship between curved and straight, into the universe. Unity is really all there is, but through polarity and other principles represented by the number Two, Unity generates all the remaining numbers. Two, the principle of polarity and paradox is symbolized by the marriage of two circles called the Vesica Piscis or Mandorla, giving birth to the geometric forms which can be constructed with a compass and straightedge (but not all of them). We'll begin our exploration by using a compass and straightedge, metaphors for the tools neded to construct the proportions found in this harmoniously embroidered cosmos.

(c) 2010 Michael Schneider

The Geometry of Nature and Art -- A Voyage From 1 To 12

Saturday May 1

The Numbers of Structure: 3, 4, 6, 8 and 12

The numbers 3, 4, 6, 8 and 12 (and their shapes triangle, square, hexagon, octagon and dodecagon) are those underlying the physical, crystalline structures of nature. They introduce two important ratios into the universal construction: the square roots of two and three. We encounter these ratios in the triangles, squares and other shapes of nature's non-living structures. In this class we'll learn about the unique properties and principles of these six "numbers of structure" and especially the foundational, all-encompassing, majestic, celestial number twelve. Participants will learn how to construct and develop these forms with a compass and straightedge, turning their geometry into art.


(c) 2010 Michael Schneider

The Geometry of Nature and Art -- A Voyage From 1 To 12

Saturday May 15

The Numbers of Life: 5 and 10

With the appearance of the number five into the cosmic construction, new ratios are introduced: the square root of five and it's blossoming into the beautiful Golden Mean ratio. These underlie the proportions found in life, appearing in the living forms of nature from microscopic diatoms to the worlds of plants, animals and humans. Five and the square root of five allows for self-similar regeneration in nature, seen in plants and starfish and the countless fractal forms of universal design. Yet five by itself is limited in it's design possibilities and must mate with another like itself, making Ten, to develop it's pentagonal patterns completely. In this workshop learn how to construct the pentagon and decagon, five and tenfold symmetries, and explore their patterns in geometry and life.


The Geometry of Nature and Art -- A Voyage From 1 To 12

Saturday May 29

The Numbers of Mystery: 7, 9 and 11

Not all numbers can be converted into shapes through the Vesica Piscis as the others have done. The numbers 7, 9 and 11 are not born in the ordinary manner and so cannot be constructed perfectly with a compass and straightedge like them. These are the Numbers of Mystery, associated with that which is beyond earthly life. Seven is the number of spirit and imagination, the virgin number which doesn't relate to the others within the twelve. Nine, the trinity of trinities, symbolizing the "ultimate" ("Dressed to the nines, the whole nine yards," etc.) is associated with mysteries and sacred sciences. Unsubstantial Eleven serves as a passageway between two complete systems, the sublunary Ten and celestial Twelve, and plays a key role in important ratios which construct the universe. In this workshop you'll learn how to construct good approximations of these mysterious principles and turn them into art.

The Geometry of Nature and Art -- A Voyage From 1 To 12

Saturday June 12

The Marriage of Seven and Twelve

"Twelve and Seven, symbolic opposites, standing respectively for rational order and transcendental imagination, have a natural inclination towards each other. The depiction of their sacred marriage is one of the principle attainments of cosmological geometry." -- John Michell

This workshop will introduce you to the significance of these numbers and will show you what happens when they meet: they spontaneously weave into a harmony of lovely proportions. Step-by-step you'll construct their marriage with a compass and straightedge (detail, left) to develop into your own a work of art.


(c) 2010 Michael Schneider

The Geometry of Nature and Art -- A Voyage From 1 To 12

Saturday June 26

The Cosmological Circle

This geometric diagram displays the harmony naturally inherent in the archetypal numbers 1 through 12, encoding the ideal patterns and proportions toward which nature's forms strive. As a symbol of universal harmony it represents the complete order of the universe and thus is a microcosm appearing in the designs of cosmic temples and sacred spaces worldwide. It was an eternal standard of reference in the sacred arts and crafts, an intelligent model for weights and measures, and for sanctifying the Earth with sacred architecture. It served as a pattern and instrument of statecraft for civilizations which sought to attract happiness, blessings, justice and prosperity. At its center is the squared-circle "New Jerusalem diagram" symbolizing the marriage of Heaven and Earth and is based on the dimensions of the Heavenly City described in Revelation. Its twelve circles in the four directions are the "gates like pearls". In this final workshop, the culminations of the series, you'll learn about this remarkable diagram and how to construct it, turning your construction into a work of art.

You may wish to purchase Constructing The Cosmological Circle (Constructing The Universe Activity Book Volume 5) for further background and many hands-on activities on this topic.


 Also available: a four-hour DVD taking you on a journey through the landscape of the numbers 1 through 12.

Click on the disk for more information

And you can always
Purchase Constructing The Universe Activity Books to use at home!


 Click on a book to see it's Table of Contents.




Learn geometric construction through nature, art and technology in a hands-on way.


730 pages filled with original activities!
Nearly 10 Pounds of Knowledge!


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(c) 2010 Michael S. Schneider