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, science and culture.
He's the author of "A Beginner's Guide to Constructing the Universe
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
"This book makes available in the most direct and disarming way the sometimes difficult ideas of the ancient Platonic Quadrivium.
The author has a background in primary education and the book is presented with the clarity of a teacher’s lesson plan.
Each section is integrated with analysis of architectural and art objects across the historical and cultural spectrum."
--  Institute of Classical Architecture and Art bookstore review
And a great bargain of 5,120 words per ounce!
(You'll have to purchase A Beginner's Guide To Constructing The Universe (HarperPerennial paperback or Kindle ebook) at your favorite book store or website!
(I don't sell them since I can't get them any cheaper than you can!)
If you'd like to hear A Beginner's Guide to Constructing the Universe read to you,
you might enjoy this audio book!
 Click on the picture for more information 
Would you like to see the geometry underlying great art?
Click on the cover ...
(or go to your local bookstore or regional online book seller)
And now an eBook pdf download version too!


DVD: A Journey From 1 to 12
DVD: Fibonacci Garden: Mathematics in the Plant World
and any or all of the six
Constructing The Universe Activity Books

by Michael S. Schneider
B.S. Mathematics
M.Ed. Mathematics and Science Education
Available only through this website.
Click on a DVD or Activity Book cover for more information about it.
4 hours each!


Very limited supplies of the Activity Books available.
No more will be printed.

730 pages total!
Click Here to Purchase 


"All who have meditated on the art of governing mankind have been convinced
that the fate of empires depends on the education of youth."
-- Aristotle

"Don't let schooling interfere with your education."
-- Mark Twain 

"Education is the kindling of a flame, not the filling of a vessel."
— Socrates, "On Personal Service," 469-399 BCE.

"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
"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


"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


Interview with Michael Schneider in the Temenos Academy Review:

A Beginner’s Guide to Symbolic Geometry:
An Interview with
Professor Michael S. Schneider
Christine Rhone (Co-author with John Michell of "Twelve-Tribe Nations: Sacred Number and the Golden Age")

YouTube lecture by Christine Rhone about Twelve-Tribe Nations here.


The Geometry of Rose Windows:

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


         Chartres Cathedral, France

         Grace Cathedral (San Francisco, California)



          Horoscope of the Iskandar Sultan 
         Geometry of a Shakyamuni Buddha thangka painting 

    Golden Rectangle geometry of the Babylonian Shamash Tablet



        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.


           Click on the coin to read an article where I contributed some geometric analyses:

             by David F. Phillips SHA
        Geometry of A Pectoral of Princess Sit-hathor-yunet
          Geometry of a pectoral of Princess Mereret


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

Sacred Geometry of Egyptian Art, an illustrated talk given at a conference about ancient knowledge in 2009.

"Composing in the Round: Polygons in Traditional Art" at the The Prince's Foundation School of Traditional Arts in London 19 June 2019

"The Geometer's Breakfast: Cosmic Proportions in a Humble Meal" at the Fourth John Michell Symposium in London 22 June 2019



Julie Motz of KWMR Radio (Point Reyes Station, CA) interviews Michael about numbers and more March 19, 2015 (53 minutes)

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).

Bruce Rawles interviews Michael in 1997, Grass Valley, CA



Michael presented an illustrated lecture at The Prince's Foundation School of Traditional Arts in London, England, on June 19, 2019
showing how geometry has been used around the world in a variety of cultures over fifty centuries:

Composing in the Round: Polygons in Traditional Art

Greek, Egyptian, Mayan applications of pentagonal symmetry

Mathematics is rarely associated with art these days, and their connection is almost never taught to art students. Yet, the greatest works of art, crafts, design and architecture of many cultures and times most certainly used these ideas. And while geometry — aka spatial relationships -– is included in every definition of artistic composition, its application and psychological impact on the viewer are poorly understood. It's quite simple yet quite profound in its effects for feelings of harmony and rhythm.  

"And since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art..."
-- Albrecht Dürer (1471 - 1528, Course in the Art of Measurement 1525)


See Michael's presentation here 



Michael was a presenter at

The Fourth John Michell Symposium

London, 22 June 2019

"The Geometer's Breakfast"
Cosmic Proportions in a Humble Meal


Sponsored by the Temenos Academy

The Temenos Academy is an educational charity which aims to offer
education in philosophy and the arts
in the light of the sacred traditions of east and West.

 Click on the painting to see Michael's presentation.


The Geometer's Breakfast is the name of a watercolor painting by John Michell. Depicting a humble meal, an egg on toast, it actually contains profound cosmic proportions.

It models the Cosmological Circle diagram (see workshop below) which represents the order of the universe and the numerical code that underlies it.

It contains all the relevant numbers, measures, shapes, proportions and musical harmonies found in nature.

It reconciles all opposites and the disparate elements that comprise it.

It is an image of paradise, a symbol of Divine Wisdom restored to Earth.

It's found in ancient monuments, worldwide architectural designs, and city planning.

It served as the pattern and instrument of statecraft in stable civilizations which sought to attract happiness, blessings, justice and prosperity.

In this presentation, Michael will reveal the geometry behind the painting and the significance of the numbers within it.


Click on the above picture to see these presentations

London, June 23, 2019

The Cosmological Circle Diagram contains all the relevant numbers, measures, shapes, proportions and musical harmonies found in nature.
Described as an image of paradise, of universal harmony, a symbol of Divine Wisdom restored to Earth, the diagram appeared as a revelation, as it traditionally does, to Michael’s friend,

In this workshop, Michael Schneider, ably assisted by master geometer Adam Tetlow,taught participants the steps of its geometric construction using compass and straightedge.



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


In the late 1980s I wrote many articles and created posters and teacher's editions for many educational magazines for children, including Super Science.

Click on the picture below to see an article I had fun writing and designing called The Secret Powers of Seeds.


Welcome to modern ..




A prediction from the year 1910 about education in the year 2000 --
"Education means to bring out wisdom. Indoctrination means to push in knowledge."
-- Dick Gregory (1932-2017)
“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+:

Too bad. Why? Read on ...

 8 Sept 2018
"Children are less inquisitive and ask fewer questions because their minds have been dulled by iPads before they even enter primary school, according to the head of Britain’s biggest head teachers’ association. Andrew Mellor, the president of the National Association of Head Teachers (NAHT), said children were coming into school as passive rather than active learners because parents were using iPads as “soothers” to keep them quiet. He said it prevented them developing their imagination and an inquisitive mind which came from reading picture books with their parents." Read more...
Click headlines to read...
Children are better off doing activities which use their hands to develop small finger muscles and their imaginations!

Try handwriting with pencils (bring back cursive!), drawing, sewing, weaving, model building, stringing beads, playing with clay, sorting small objects, using scissors, crumple paper, pop bubble-wrap, build with blocks, button shirts, use a geometric compass, or a thousand other traditional activities! Read this --
Reaching and grasping: Learning fine motor coordination changes the brain

 Click headlines to read... 
 Click headlines to read...
 Is it really worth it?
It's much better for youngsters to use their hands, read actual books, build things, use a geometric compass, socialize in person (when possible).
Click on these headlines for more information
Here and Here
Doing geometric constructions with a compass, straightedge and pencil is a traditional approach to achieving this, and more...!


“Knowledge is knowing that a tomato is a fruit; wisdom is not putting it in a fruit salad.”
-- Miles Kington 

Has it ever occurred to you that the plural of "half" is "whole"?
-- Allan Sherman
"A circle is a round straight line with a hole in the middle."
-- Mark Twain, quoting a schoolchild in "English as She Is Taught", Century Magazine, May 1887
"Infinity is a floorless room without walls or ceiling."
~Author unknown


“[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 has Common Core worked out so far?
 "Common sense is so rare these days, it should be classified as a superpower."
-- Unknown
Old, old School:
Click on this heading below if you think you can pass an 8th grade test from 1912:
Rules for Teachers 1901:

Mathematical Ideas for Artists
A Curriculum 
by Michael S. Schneider


For 17 years, from 2001 to 2018, I created, developed and taught an original course called “Mathematical Ideas for Artists” at the California College of the Arts in San Francisco and Oakland, California.

My intent for the course was to introduce young, creative art students to the similarly recurring patterns and proportions found throughout nature and which were intentionally applied to worldwide arts, crafts and architecture in great and small creations since the dawn of civilization.

I’ve decided to make the course’s PowerPoint (.pptx) presentations (and one .pdf Workbook document) available for educators and others to view or download for your own classes, or for your personal study. It also includes exams and their answers. They are presented here free and may not be used for any commercial or financial purposes.

Click the headline for more information

Imparnumerophobia is the fear of odd numbers.
Omalonumerophobia is the fear of even numbers.
Decadisophobia is the fear of decimals.
Oudenophobia is the fear of zero.





Name each angle:






Be careful never to divide by zero!




There's a fine line between a numerator and a denominator.
(Only a fraction of people will find this funny.)

Parallel lines have so much in common.
It's too bad they'll never meet.

Did you hear about the mathematician who’s afraid of negative numbers (Neganumerophobia)?
He'll stop at nothing to avoid them.

I got into a fight with 1, 3, 5, 7 and 9. The odds were against me.

Can 2 + 2 = 5 ?
Only for very large values of 2.

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

 Answer: 0.99999999....

To understand recursion, you must first understand recursion.

Don't ever mention the number 288.

It’s two gross!

What did 0 say to 8?

Nice belt!

What did 8 say to B?

Nice posture!

I, for one, like Roman Numerals.

I can't remember how to write the numbers 51, 6 and 500 in Roman Numerals and I'm LIVID!

How many times can you subtract 10 from 100?

Once. The next time you would be subtracting 10 from 90.

Happy Birthday!

Who won the argument between 19 and 20?




The most dangerous kind of canoes are volcanoes

I skipped third grade.

Really? How did you do that?

I went directly from fourth to second.

Question: How many seconds are in a year?

Answer: Twelve
January 2nd, February 2nd, March 2nd

How many milliseconds are in a day?

Obviously, 1000 milliseconds/second x 60 seconds/minute x 60 minutes/hour x 24 hours/day

= 86,400,000

or, more neatly

= 55 x 44 x 33 x 22 x 11

There are more hydrogen atoms in a single molecule of water
than there are stars in our entire solar system!


A local example of cosmic harmony

The Moon’s Synodic (Lunation) Period is the time between two full moons as seen from Earth (29.53059028 days),
and its Rotation Period is the time it takes to actually turn once upon its axis (
27.3215835 days).

    When their product
is divided by their difference,
we see the precise number of solar days in one Earth year:

       (Lunation x Rotation) / (Lunation - Rotation) = 365.2421964 days

365, the rounded number of days in one Earth year, is itself an interesting number:

365 = 10² + 11² + 12² = 13² + 14²

2024 is a "Leap Year"

(366 calendar days -- Happy Birthday to February 29 people!)


2024 = 2 x 2 x 2 x 11 x 23

Or, in fewer terms: 2024 = (45 x 45) - 1


2024 has 16 divisors:   1, 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, 1012, 2024

The sum of the divisors of 2024 = 4320


This number 4320  (= 12 x 360) is canonical, so its fractions and multiples show up in a wide range of classic measures:

432 grains = 1 ounce

432 vibrations per second = the Perfect Fifth of Pythagorean tuning of the musical scale

432,000 miles = the sun's radius 

432,000 syllables comprise the Indian sacred mythological poem Rg Veda ("Praise Knowledge")

... and quite a bit more ...



2020 is a "Leap Year" (366 calendar days)

2020 = 2x2x5x101

2020 has 12 divisors: 1 2 4 5 10 20 101 202 404 505 1010 2020

(There's a lot of doubling among those divisors!)

2,020 seconds= 33 minutes, 40 seconds

And don't forget 20/20 vision!

2019 is simply the product of 3 x 673.
It's also the smallest number that can be written in 6 ways as the sum of the squares of 3 prime numbers.
(Hint: you can do it using only these primes: 7, 11, 13, 17, 19, 23, 31, 37, 41, 43)
Here's one way:

7² + 11² + 43² = 2019 
What are the other five ways?
Find the other ways and read more about the number 2019 here...

What a year!
2017 is the first prime number year since 2011, and the last until 2027.
13 + 23 + 43 + 63 + 123 = 2017
 23 + 43 + 63 + 93 + 103= 2017
or simply
 92 + 442 = 2017

Remember 2016?
(10x9x8x7x6) / (5+4+3+2+1) = 2016
Can you find other ways to combine the first ten numbers for a total of 2016?
To see some, click here.


Happy Holiday!



What is half of 


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.


The Great Math Mystery
Is math invented by humans, or is it the language of the universe?

(My opinion: mathematics comes with the universe but humans invent the numerals and symbols to describe it.)

Watch this NOVA TV program about the appearance of math in the cosmos.


When asked, most people get this question only partly right:

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 not completely correct!

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?

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

"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...

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




Observe Geometry Within A Flower
"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

"We have to admire in humility the beautiful harmony of the structure of this world — as far as we can grasp it..."
-- Albert Einstein


"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."

--  Sir Terry Pratchett, English author

I enjoy building
Mathematical models of plants
Click on the picture to find out more

"You’ve travelled up ten thousand steps in search of the Dharma.
So many long days in the archives, copying, copying.
The gravity of the Tang and the profundity of the Sung make heavy baggage.
Here! I’ve picked you a bunch of wildflowers.
Their meaning is the same but they’re much easier to carry."

-- Empty Cloud (Zen Master 1840-1959)

"Outbursts of Truth"
The July 2015 edition of Science To Sage magazine has a 20-page spread (pages 74 - 93)
of images and information from my Fibonacci Garden DVD.
Click on the cover above to explore the magazine.


Here is the website of the Norwegian painter Siv Moa Lonning who has used these books and DVDs in planning her beautiful "Symphonies of Geometry".


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 video 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.
Click on the picture above to see the video.

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...


Do you live in the UK? Lucky you!

You can easily attend classes at the extraordinary

Sacred Art of Geometry:

"Short courses and symposia in the practice and philosophy of Sacred Geometry and the arts of the Quadrivium."



Can you get to Spain?

You'll be pleased to visit the Flores del Camino Retreat Centre on the Camino de Santiago

for Sacred Geometry, Art and Sacred Crafts Retreats and Workshops!


Highly recommended books written by friends... 


The Cosmos In Stone
Sacred Geometry of a Master Mason
by Tom Bree


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" and the "Ancient Metrology" series by John Neal

IMO, the most important books about metrology ever written.



A Defence of Sacred Measures

Anonymous -- Likely by John Michell



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)




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

May we be guided by Truth
May we have Beauty revealed to us
& May it result in good. 

Pythagorean invocation by Professor Keith Critchlow (1933-2020)





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
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


Books by Matthew Cross



 Math Stories by Howard Schrager



John Anthony West  















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 Polyhedrists: Art and Geometry in the Long Sixteenth Century" by Noam Andrews
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, as is this:

The Diagonal -- edited by Jay Hambidge 1919 -- all 12 volumes together (downloadable pdf and for other media).
A great classic in Dynamic Symmetry studies!



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.


About Michael ... Photo by Karen Koshgarian

Michael S. Schneider has been an educator for over four decades (since 1974). 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, IBM, 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. From 2001 to 2018 he was a Senior Adjunct Professor at the California College Of The Arts (San Francisco & Oakland) 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 2000-2024