Constructing The Universe
The Universe may be a Mystery, but it's no Secret!

This website is a look at some interests of
Michael S. Schneider
 offered for your enjoyment and education

 

Michael S. Schneider is an educator and writer who encourages a love of learning through an appreciation of
the intersections of mathematics, nature, art and science.


"There is a geometry of art as there is a geometry of life,
and, as the Greeks had guessed,
they happen to be the same."
-- Matila Ghyka




Observe Geometry Within A Flower

 
 

What do U.S. paper sizes
have in common with the Earth and Moon?

Want a unique Earth-Moon Squared-Circle T-Shirt?
Now available!
Click on the picture for more information

A Rare Rectangular Galaxy Was Recently Discovered!

What Rectangle Is It?




How to Draw the Oval of the Oval Office





The Golden Ratio at your Dinner Table

If you're sitting around the kitchen or waiting for your meal at a restaurant (and you're mathematically minded)
you might marvel at this unexpected appearance of the famous Golden Ratio first discovered and expressed in marvelous ways by the artist Jo Niemeyer.





Here's something interesting to ponder:

 Geometry within a painting about
the geometric creation of the universe!

What is the interesting geometric relationship between the two important circles?
Click on the picture to find out...


"When He prepared the heavens, I was there:
        when He set a compass upon the face of the depth..."
Proverbs 8:27 

Which of these interconnected topics are you interested in?

Numbers and Shapes: The Universal Language of Nature and Art

The numbers 1 through 12 and the language of geometric patterns in nature, art and culture.

One and Two: Unity and Polarity
Three: Tri-Unity
Four: Fair and Square
Five: The Flag of Life (Pentagram, Fibonacci Numbers and Golden Section)
Six: The Joy of Six
Seven: The Virgin Number
Eight: Periodic Renewal
Nine: The Horizon
Ten: New Unity
Eleven: The PassageWay
Twelve: Cosmic Dozens

Beautiful Proportions in Sacred Arts, Crafts and Architecture

Worldwide traditions looked to the archetypal patterns of mathematics and nature for their compelling designs.

Natural Design and Sacred Art
The Art of Root-Rectangles
The Art of Polygons
Worldwide Healing Art
Sacred Windows
Principles of Sacred Architecture
Design A Cathedral
Design Sacred Pottery
Design Egyptian Jewelry
Golden Section Design
Islamic Patterns and Escher's Art

Constructing The Universe: Traditions of Mathematical Wisdom

The Geometer's Creation Myth
The Geometry of Fruits & Vegetables
Pythagorean Arithmetic: Figurate Numbers
The Tetraktys
Magic Squares
Knotted-Rope Geometry
The Five Platonic Solids
The Cosmological Circle
Music of the Spheres
The Spiral Path of Conflict Resolution
The Solar System Mandala
Ancient Metrology: Straightening Out Sacred Measure

Traditional Wisdom Survey

An appreciation of sacred traditions and related topics.

Egyptian Mysteries
The Eleusinian Mysteries
The School of Pythagoras
Savitri by Sri Aurobindo
Chakra Symbolism Around the World
Geometric Construction as Meditation

Click on this picture to see some geometric watercolors I've painted.

Here are some large public mandalas in Ireland influenced by my books. They're each made of natural materials and objects.

Essays on the Web

The Geometry of Rose Windows:

Cathedral of St. John The Divine (New York City)

Chartres Cathedral, France

Grace Cathedral (San Francisco, California)

The Amen Break and the Golden Ratio

Geometry of a Kangra Painting

The Geometry of a Herter Brothers Cabinet

"Cosmic Dozens: Twelve-Fold Designs of Society and Art "

"Orienting From The Center"

See Michael on YouTube:

Egyptian Mathematics: See how the ancient Egyptians multiplied without a "times-table" the way modern computers do.

Fibonacci Numbers: See how the plant world is structured mathematically. (Introduction starts at about 2:00 minutes, Michael @ 3:00).

LISTEN!

Red Ice Radio of Gothenburg, Sweden, an interview with Michael by Henrik Palmgren July 11, 2010

Eric Tomb of Booktown on KVMR radio interviews Michael about numbers (May 25, 2010)

Walter Cruttenden and Geoff Patino of the Binary Research Institute interview Michael about numbers, nature, art and ancient philosophy here. (March 2008)

Hear an interview with Michael on the Voice Of America program "Our World" (27 December 2003, 5.4 Mb .mp3 audio file)

Click here to hear a review of "A Beginner's Guide To Constructing The Universe" regarding mathematics education.

Click here to hear a review (podcast or .mp3) by Jeffrey Millburn at Omni Art Salon about using the book for developing awareness.

Click here to listen to Documentary Film Maker Elizabeth Upton speak about Michael's work in an interview about "Sacred Geometry" on Mike Hagen's Radio Show (10.5 Mb .mp3 audio file).

Constructing The Universe Classroom
in San Anselmo, California


For the past three years this classroom has been dedicated to teaching adults and homeschoolers age 8 - 13 about nature's mathematical wonders.
We emphasized traditional geometric construction with a compass and straightedge to explore nature's many marvelous shape and number patterns.
And then the students transformed their learning into art. I love seeing the same idea manifest in as many unique expressions as there are students.
I'm extremely proud of their accomplishments and of having a part in sharing this uplifting vision which teaching mathematics can be
when free of textbooks and time constraints.             


Recently I taught a series of classes about the Fibonacci Numbers and how to draw flowers, leaves,
branches and berries using the ideal Golden Ratio angle of 137.5 degrees between consecutive expressions.
Here are a few of the results:



     

But now, after 3 great years, the Constructing The Universe Classroom has closed,
             having appeared for a while and then faded back into the mist of time, a Brigadoon of mathematical education.
With Immense Thanks! to all my students, adults and children (and their dedicated parents)
            and the many friends and supporters of the Classroom and this positive approach to mathematics education. 

What next? The contents of the classroom are going into storage, like a seed pod awaiting the proper conditions for another bursting forth.
In the meantime I'll be working on making available the educational materials I've developed here for others to use
                  for teaching and learning the many topics this classroom gave me the time and enthusiastic students to create. 

November 2012

A prediction from the year 1910 about education in the year 2000 --           
 


“Where all think alike, no one thinks 
very much.”-- Walter Lippmann (1889-1974)
 
Click on the picture above for more "predictions" from the same source.

How children played in 1982 and in 2012:

Michael is the author of
A Beginner's Guide To Constructing The Universe:
The Mathematical Archetypes Of Nature, Art and Science
(HarperPerennial paperback 1995)
Dutch  Korean

"In this book you will find something that cannot be obtained elsewhere,
a complete introduction to the geometric code of nature,
written and illustrated by the most perceptive of its modern investigators."
-- From the Preface by John Michell
And a great bargain of 5,120 words per ounce!
Michael is also the author of six accompanying workbooks
Constructing The Universe Activity Books
Available Only Through This Website!
Step-by-step visual instructions for hands-on self-paced learning
about the shapes and patterns shared by nature, science and art.

Ideal for Teachers, Artists, Designers, Architects, Home Schoolers, and Self-Motivated Learners!

730 pages filled with original activities!
Over 7 Pounds of Knowledge!
For a general description of the series, click here, or...
Click on any cover to read its Table Of Contents
  
Read what people are saying about these unique Constructing The Universe Activity Books
   Volumes 1, 2, 4, 5 only $22 each
Volume 3 only $25Volume 6 only $20All Six Volumes for only $115! 
Click Here to Purchase any or all of the Activity Books
International shipping is available.
(Please be aware that your country might charge a VAT (Value Added Tax)
in addition to the US Post Office shipping charge.
Some countries do, others don't. Please check with your post office.)

A  DVD is now available! -- A Journey From 1 to 12 



Click on the disk for a description and how to purchase!

---

Golden Ratio Geometry & Egyptian Art DVD

I presented my findings about Golden Ratio geometric composition in ancient Egyptian arts, crafts and architecture at the CPAK conference on Saturday October 10th, 2009 at the National Academy of Sciences' Beckman Center at UC Irvine, California.

A Golden Rectangle surrounds this Udjat eye pectoral.
Any Golden Rectangle may be divided into a square and another Golden Rectangle
by swinging an arc from the middle of a square,
as the vulture goddess Mut does here with her wing.
Similar "movements" place each element of it's design into harmonious arrangement.

To purchase the DVD of my presentation, please click on this banner:

---

Does 5x5=25 or 14? Are you sure?
Ma and Pa Kettle mix mathematical principles in this amusing old movie clip on YouTube.

Can 7x13=28? It doesn't seem likely, but perhaps you'll be convinced!
Abbott and Costello also mix mathematical principles in this amusing old movie clip on YouTube.

---

When asked, most people get this question wrong:
What do the 50 stars on the flag of the United States represent?

Most people will say that the 50 stars stand for the 50 states, but that's incorrect !

The quantity 50 does indeed represent the number of states, but the 5-pointed star itself is a symbol of life and humanity:
thus, the 50 stars represent the people of the 50 states, not the states themselves.

They're there to remind us that the ultimate power in the United States resides in the hands of free people who consent to be governed, not in any government that the people have elected to protect and serve them.
Fifty stars represent free citizens ruling themselves, having inalienable rights, not subjects of any government deciding which rights to grant or deny them.
It's important to remember this, and that the blue field should never be replaced with any other symbol than 5-pointed stars, representing We The People.

(Although dozens of countries' flags display the five-pointed star, a few employ it this way as an archetypal symbol of humanity and others interpret it culturally in different ways.)

---

Is there anything interesting about the geometry of the face of the pyramid
seen on The Great Seal of the United States?

Click on the picture to find out...

---

My dear friend and teacher, the philosopher, antiquarian, artist and writer John Michell, passed into the Light peacefully on April 24, 2009.
The influence of this gentle, generous and brilliant man upon me and many others is incalculable.
Click on his picture for more...

I'm very pleased to let you know that The Book of Symbols: Reflections on Archetypal Images has been published.

(Congratulations to Ami Ronnberg and her staff for years of careful work!)

I mention it here partly because I contributed to the entry on Spirals.


Published by the Archive for Research in Archetypal Symbolism (ARAS), it's based on Carl Jung's work on the archetype and the collective unconscious.
 It's an astounding pictorial and written archive of mythological, ritualistic, and symbolic images from all over the world and from all epochs of human experience.
It contains over 800 beautiful color images, all perfectly chosen.

The book is great, an instant classic, and I highly recommend it.

If you're ever in New York City and need to research archetypal symbolism, be sure to visit ARAS at 28 East 39th Street during visiting hours and at their interesting events.

(I once gave a slide presentation and talk about spirals at one of their monthly Lunchtime Lectures.
My favorite moment at it was when I pointed out that the words "matter" and "pattern" derive from mater and pater, "mother" and "father," and the audience gasped in a collective relevation.)




For those of you interested in the great Golden 
Ratio I suggest you visit the       
Museum of the Golden Ratio

"dedicated to collecting and preserving individual expressions in art of the myriad aspects of the Golden Ratio...."       
         
You'll find links to mathematics, nature, science, art, videos, interviews and more, but         
   
it's especially fresh with links to the works of 
contemporary artists who make intentional use of the Golden 
Ratio. 

About Michael ... Photo by Karen Koshgarian

Michael S. Schneider has been an educator for nearly four decades. He delights in exploring the intersections of nature, science, mathematics and art.

Michael has a Bachelor of Science degree in Mathematics from the Polytechnic Institute of Brooklyn, (now The Polytechnic Institute of NYU) and a Master's Degree in Mathematics Education from the University of Florida (Gainesville). He taught youngsters for twelve years in public and private schools at the Middle School and Elementary school levels. In 1977, Michael was a Fulbright-Hayes Scholar in India studying ancient mathematics and sciences. He has been a computer consultant at the United Nations, Nickelodeon, MTV, NYTimes and many other corporations. He has worked for the New York Academy of Sciences, and wrote articles, posters and teachers' editions for various Scholastic magazines including Science World, SuperScience, DynaMath, and Teaching and Computers magazines. Michael was the creator and writer of the weekly "Mother Nature" segment at WNYC-FM radio on the popular live broadcast "Kids America" program (1986-87). He's also held workshops for educators at The Metropolitan Museum of Art in New York through their Education Department including "Science in the Art Museum", "The Mathematics of Islamic Art" and "Showing Children Harmony".In 1993 Michael worked with master stonecarver Simon Verity to design the geometry harmonizing the statues on the south side of the "Portal of Paradise" (central entrance) to the Cathedral of St. John the Divine in New York City. During 1996-97 Michael was the Dean of Mathematics and Dean of Science at The Ross School in East Hampton, NY. He presently lives in northern California.

Michael is the author of "A Beginner's Guide To Constructing The Universe: The Mathematical Archetypes Of Nature, Art and Science" (HarperPerennial paperback 1995), six "Constructing The Universe Activity Books" and numerous articles concerning mathematics and teaching mathematics through nature, art science and philosophy.

Although the back of A Beginner's Guide... says that Michael lives in New York City, he actually resides in Marin County, California. He's a Senior Adjunct Professor at the California College Of The Arts (San Francisco) teaching art students "Mathematical Ideas For Artists" as Durer might have. He's also taught at the Ex'pression College For Digital Media in Emeryville and the Sophia Center For Graduate Studies in Culture and Spirituality at Holy Names University in Oakland.