Constructing The Universe
The Universe may be a Mystery, but it's not a 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.
 
He's the author of "A Beginner's Guide to Constructing the Universe," six hands-on Activity Books, and a DVD about the numbers 1 through 12.
 
 
"The central task of education is to implant a will and facility for learning; it should produce not learned but learning people.
The truly human society is a learning society, where grandparents, parents, and children are students together."
-- Eric Hoffer
 

"Education is not the filling of a pail, but the lighting of a fire."
-- William Butler Yeats

 
“The best teacher is not the one who knows most but the one who is most capable of reducing knowledge to that simple compound of the obvious and wonderful.”
-- H.L. Mencken
 
"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
 
 

"One of [the brain's] functions is to make the miraculous seem ordinary, and turn the unusual into the usual.
Otherwise, human beings, forced with the daily wondrousness of everything would go around wearing a stupid grin, saying "WOW" a lot.
Part of the brain exists to stop this happening. It is very efficient and can make people experience boredom in the middle of marvels."

--  SirTerry Pratchett, English author


New!
 
Another original four-hour DVD is now available!
 
Fibonacci Garden: Mathematics in the Plant World
 
Only $29.95
 
 
Click on the disc for more information!
 

 
Yet another view of this marvelous mathematical cosmos can be found in this unique DVD:
 
A Journey From 1 to 12
A Four-Hour Tour
$29.95 On Sale! Now only $26.95
Click on the disc for more information!
 

 
 
A Beginner's Guide To Constructing The Universe
is now available in an eBook edition!
 
Find it here or at your favorite bookstore site.
 

"When we try to pick out anything by itself, we find it hitched to everything else in the universe."
-- John Muir


Which of the following interconnected topics are you interested in?

 

Numbers and Shapes: The Universal Language of Nature and Art

The numbers 1 through 12 and their practical and symbolic 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


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, the Golden Ratio and the Human Body:

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"

 

 

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

 


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).


I was quoted in an article on the KQED website in an article titled

Imagery: A Key to Understanding Math

Click on the title to read it!

 
 

 
 
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.

 

 
How to Draw the Oval of the Oval Office
 
Hint: two Golden Rectangles!

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

 


A prediction from the year 1910 about education in the year 2000 --
 
Click on the picture above for more "predictions" from the same source.
 
“Where all think alike, no one thinks very much.”
-- Walter Lippmann (1889-1974)
 

“[The aim of public education is not] to fill the young of the species with knowledge and awaken their intelligence. . . .
Nothing could be further from the truth. The aim . . . is simply to reduce as many individuals as possible to the same safe level,
to breed and train a standardized citizenry, to put down dissent and originality. That is its aim in the United States…”

-- H. L. Mencken (1880-1956) in 1924

 

 
How children played in 1982 and in 2012:
 

 
 
 
 
 
 
Old, old School:
 
Click on this heading below if you think you can pass an 8th grade test from 1912:
 

 
Math For The Feeling Years
A Curriculum 
by Rachel Van Boven
Download these lesson plans for a dynamic math program centered around symmetry in nature
and creative self-expression designed by a teacher for ages 6-12!
 

 
Question: How many mathematicians does it take to screw in a light bulb?

 Answer: 0.99999999....
 

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 and also this one 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.)

 

What do U.S. paper sizes
have in common with the Earth and Moon?
Click on the picture to find out.

 

 

Want a unique Earth-Moon Squared-Circle T-Shirt?
 
 
Sorry, they're no longer available, but you can  click on the picture for more information about the design.
 
 
A Rare Rectangular Galaxy Was Recently Discovered!

What Rectangle Is It?


 
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!
 
Learn to use a geometric compass!
These workbooks provide step-by-step visual instructions for hands-on, self-paced learning
about the shapes and patterns shared by nature, science, technology and art.


Appreciated by Teachers, Artists, Designers, Architects, Home Schoolers, and Self-Motivated Learners!


730 pages filled with original activities for you to do with a compass and straightedge!
(and colored pencils help too!)
 

Over 7 Pounds of Knowledge!
(regarding traditional interests relevant today)

"An investment in knowledge pays the best interest." - Benjamin Franklin
 
These six volumes, along with "A Beginner's Guide to Constructing The Universe" and  DVD "A Journey From 1 to 12,"
provide a rich education in traditonal knowledge, a 
practical and philosophical approach to the simple numbers, shapes and proportions
displayed throughout this Cosmos and in the great
worldwide traditions of the human arts and other affairs.
The Activity Books have a tape-binding so that they can be easily folded back to do the constructions upon, and are printed in black and white (actually, grayscale).
 
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
 
 
On Sale!
 
Volumes 1, 2, 4, 5 only $22 $20 each
Volume 3 only $25
$22
Volume 6 only $20 $18
or All Six Volumes for only $115 $105!
 
 add to them the DVD and you'll have plenty of opportunity for a rich education
 
Click Here to Purchase any or all of the Activity Books
 
 
 
 
International shipping is available.
 

Constructing The Universe Classroom
in San Anselmo, California


For three years this classroom was 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 growths.
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

 
Scientists finally prove what I wrote about in 1993!

On pages 159-160 in A Beginner's Guide to Constructing the Universe I described the reasons, as I saw them,
that birds often fly in V-formation:

 

 

Now, over 20 years later, scientists have done experiments to prove it:

Science Magazine

National Geographic

USA Today

NPR

 


"How I Came to Write A Beginner's Guide to Constructing the Universe"

I wrote this autobiographical essay and answered questions as Author of the Month (December 2013) at the Graham Hancock website.

Follow my journey of learning through its links.

To read the essay, click on the book cover...


 
Yet Another DVD!

This is the video of a presentation I gave concerning my take on the apparent

Golden Ratio Geometry in Egyptian Art

In modern orthodox Egyptology, recognizing the consistent, intentional application of the Golden Ratio
in the designs of their arts, crafts and architecture is controversial, even denied,
but to me there is no doubt about it!

It is consistent with their philosophy of Ma'a, of maintaining eternal Truth, Justice, Uprightness and Right Order
in symbolic and mythological alignment with the eternal Truths found in mathematics, in simple numbers, shapes and their proportions.

This DVD is a visual presentation of my findings of apparent applications of Golden Rectangles
in the
geometric composition and symbolism of ancient Egyptian arts, crafts and architecture.
It was presented at the CPAK conference on Saturday October 10th, 2009,
at the National Academy of Sciences' Beckman Center at UC Irvine, California.

If you're interested in Egyptian art and/or the Golden Ratio then you might enjoy its interesting examples. 


For example, a Golden Rectangle surrounds this Udjat (eye) pectoral.

It's divided into a large red square (right) and vertical Golden Rectangle (left, split into square and smaller Golden Rectangle) containing the vulture goddess Mut.

Mut simply swings her wing and divides the Golden Rectangle into a square above a smaller Golden Rectangle (yellow).

This is part of the alignment of it's elements into harmonious arrangement
of the parts with each other and the whole,
the essential idea of Golden Ratio mathematics.
 

To purchase (from CPAK) this DVD of my presentation, please click on this banner:
 
 

For those of you interested in the great Golden Ratio and art 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.

 



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...
 

A (Kindle) Book of JM essays! (November 2012)
If you don't have a Kindle, you can get a free Kindle Reader app for your computer, phone or tablet 
here.

Rules and Revelations


Rules and Revelations contains more than fifty essays from The Oldie not previously anthologised in 'Confessions of a Radical Traditionalist.'
A lovely reminder of John's view of things. He's present again in these short, delicious and brilliant essays.

Click on the book to order it!

For information about upcoming and past conferences, talks, links, videos, DVDs and more about John Michell visit

 

 The John Michell Network
 


Highly recommended books written by friends... 

Infinite Measure by Rachel Fletcher

 

 

How the World Is Made: The Story of Creation according to Sacred Geometry by John Michell and Allan Brown

 

 All Done With Mirrors by John Neal

IMO, the most important book about metrology ever written.

 

Beauty for Truth's Sake: On the Re-enchantment of Education by Stratford Caldecott

 

Drawing Geometry: A Primer of Basic Forms for Artists, Designers, and Architects
by Jon Allen (Compiler) , Keith Critchlow (Foreword)

 and

  

 

The Hidden Geometry of Flowers: Living Rhythms, Form and Number by Keith Critchlow

 

 

KAIROS NEWSLETTERS 1990-2010

Very valuable geometry/philosophy newsletters published by Keith Critchlow's KAIROS Foundation are available through the Temenos Academy.

 

 

Sacred Geometry by Miranda Lundy

 

Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology
by
Miranda Lundy, Anthony Ashton, Dr. Jason Martineau, Daud Sutton, John Martineau

 

The Golden Section: Nature's Greatest Secret by Scott Olsen

 

Sacred Geometry Design Sourcebook by Bruce Rawles

 

SNAP:  Scaffolding for Numerical Synapses by Sheryl Nichols Morris
(Awakening Curiosity in the Numbers One to Ten)

 

The Mandala Book: Patterns of the Universe by Lori Bailey Cunningham

 

The Book of Symbols: Reflections on Archetypal Images

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'm honored to have contributed 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.)

 

And other books of value...

 

Count Like An Egyptian by David Reimer

 
 
Beautiful Geometry by Eli Maor and Eugen Jost
 
 
 
The Art of Compostion: A Simple Application of Dynamic Symmetry (1926) by Michel Jacobs (downloadable pdf)
 
 
This volume is a useful supplement to Volume 4 ("Dynamic Rectangles") of my Constructing The Universe series of Activity Books.
 

 
 
 

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


Here is the work of my friend
the Danish artist Kirsten Høst who develops geometric constructions into wonderful oil paintings.
 

 
And Don't forget!
 
 
You can only purchase Constructing the Universe Activity Books and the DVDs "A Journey From 1 to 12" and "Fibonacci Garden" here!
 
 
 
(But you'll have to purchase A Beginner's Guide To Constructing The Universe (HarperPerennial paperback)
at your favorite book store or website!
(I don't sell them since I can't get them any cheaper than you can!)
 
The best way to use the full range of these materials is in conjunction with one another:
 
Since all the chapter numbers of the books and DVD correspond with each other as the simple number they concern,
it's easy to learn by combining their different approaches.
 
For example, after you read Chapter 5 in A Beginner's Guide about the number 5 and its shapes and symbolism,
then watch the DVD chapter about the number 5,
and then get your hands and compass moving
by delving into Activity Book Volume 1 Chapter 5 to learn about and do
the corresponding geometric constructions themselves
and upon images from nature and art.
 
The Fibonacci Garden: Mathematics in the Plant World goes along with Activity Book Volume 3: The Fibonacci Numbers and Golden Mean.
 
 
Only available at this website.
 


About Michael ... Photo by Karen Koshgarian

Michael S. Schneider has been an educator for 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.

 

 

© Michael S. Schneider 2000-2014