Constructing The Universe



Classes for Adults & Youngsters



Hands-On Learning in Math, Science, Nature and Art



"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



"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






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



** After three great years the Constructing The Universe Classroom has closed.**
With Thanks to all my students and supporters for this wonderful experience.








 255 Sir Francis Drake Blvd.
(in the parking lot at the west end of Bank Street,
and near the "Hub")

San Anselmo, CA 94960






Click on Interactive Map



More precise in Google Earth:
37°58'30.85" N, 122°33'43.50" W









A youngster's interest in the usual school topics is transitory unless it's seen as part of something interesting and meaningful. My approach to teaching is that the seemingly separate topics of learning, especially involving nature, mathematics, science, history and art are all interrelated facets of one whole, and that all topics can be taught through any topic. Many bright youngsters are bored in their classes, or have interests beyond the school curriculum. This Constructing The Universe classroom is for them.


These classes are not "tutoring" sessions for the usual school topics although they often involve the same skills used in the context of a creative investigation. Young people can learn to see and appreciate the excellence of nature and its patterns which teaches many valuable lessons. I approach each subject to promote wonder at the ordinary, the interconnectedness of knowledge and a love of learning in general. There is absolutely no religous teaching involved here.



The Constructing The Universe classroom is a relaxed, learner-friendly creative atmosphere where youngsters (ages 8-12) can participate in the interrelationship of geometry, numbers, art, nature and the natural sciences with fun and confidence. After many years and situations teaching I see that a little intelligent guidance can help ignite a big interest in learning (even if they're not considered good math, science or art students). For the past few years I've been teaching homeschoolers and other groups of children who benefit from these topics and approach to learning. Classes are 1.5 hours in length and are generally limited to ten students. They're offered in 10-week blocks at a cost of $250 (i.e., $25/class). I offer snacks of fresh fruit and Fig Newmans bars. Parents are welcome to stay and observe, and help if you like.


"Come into the light of things.
Let nature be your teacher."
-- Wordsworth



Classes for Adults



Saturdays from September 15 to November 17, 2012:
1:00pm - 2:30



Ten classes for $250
Classes for Adults follow a similar nature-science-art outline as for youngsters (see below) but the topics tend to be more philosophical
and extend into designs beyond nature including Chartres Cathedral Rose Window and other great art and architecture.
Outline of Classes:
9/15      1) Introduction to the class, Triangle and Hexagon constructions
9/22      2) Dodecagon construction, twelve points around a center
9/29      3) Square and Octagon constructions
10/6      4) Heptagon constructions
10/13    5) Square Root Rectangles
10/20    6) Golden Ratio (Phi), Golden Rectangles, Spirals
10/27    7) Pentagon constructions
11/3      8) Fibonacci Numbers
11/10    9) Phyllotaxis (branch & leaf arrangements), 137.5 degree Phi angle
10/17  10) Platonic Solids
Information about classes for Youngsters and Adults



Past Classes and Workshops for Adults
To register please write to Michael

Classes for Youngsters
HomeSchoolers ages 9-13
September 10 - November 12, 2012
10:30am-12:00 (age 9-11) & 1:00pm-2:30 (age 12-13)
Childrens' classes are limited in size (maximum 8 students)

In these "mathematics enrichment" classes, children are shown how to see nature as written in an alphabet of simple shapes like circle, triangle, square, pentagon and sprials.
When we see and understand why nature appears in terms of numbers, shapes and patterns
students learn to use a compass and straightedge to replicate nature's geometry.
The constructions begin with simple and easy ones and develop into others more challenging.
No previous experience with a compass is necessary.





Students then use their imagination to turn their constructions into art of their own design using a variety of media
including various papers, clays, colored pencils, paints, leaves, shells and other materials.





These activities develop eye-hand coordination, teach a need for observation, care and accuracy,
develop mathematical skills and artistic abilities, self-confidence, and offer other benefits.



Here are photos taken at the Constructing The Universe classroom.



We follow a simple outline:
To understand most of the designs seen in nature, technology and throughout the universe,
we really only have to know about the numbers 1 through 12 and their shapes,
which naturally form four groups:



Getting Started: Numbers 1 and 2, represented by the circle and intersecting circles;

Numbers of Structure: (which nature and people build with):
Numbers 3, 4, 6, 8 and 12 (triangle, square, hexagon, octagon and dodecagon);

Numbers of Life: Numbers 5 and 10 (pentagon and decagon, producing spirals);

Numbers of Mystery: Numbers 7, 9 and 11 (heptagon, enneagon and hendecagon).



There are more advanced classes for students who have been through these first classes.





Here Are Some Class Topics:





Turn Geometric Constructions Into Art

All students first go through a series of classes learning to do the geometric constructions associated with the numbers 1 through 12, from point and circle through dodecagon. The goal is for students to become comfortable using a compass and straightedge and get really good at creating geometric constructions! These reveal interesting and beautiful patterns which students turn into art using colored pencils, paint, clay, sequins, feathers and whatever else is around! No experience is necessary. Beginners are especially welcome. This topic is an extensive part of Constructing The Universe classes.

More advanced classes include related topics described below.



Plant Architecture (Learn Math from Plants!)

Learn about the Fibonacci numbers and the Golden Ratio by examining (and building and transforming) nature's excellent plant architecture.


Build Three-Dimensional Geometry

Hands-on experiments building the five Platonic Solids, crystals, bubbles, puzzles, make pop-up books, and more.


The Mathematics of Music

Did you know that musical notes are numbers that we can hear? Students will learn about this topic by investigating vibrating strings (and other objects) and its fractions to produce musical intervals and notes.



 Learn To Draw Tessellation Patterns

... repeating tile patterns that don't leave gaps or overlap, as seen in the art of M.C. Escher.



 Games, Patterns and Puzzles

... mostly from ancient times and those with numerical and geometric strategies.



 Making Magic Number Squares

... whose columns, rows and diagonals always add to the same value.




Learn the basics of polarity and magnetic fields using magnets and electromagnetism to build interesting projects.
No experience necessary.
Advanced projects for advanced students.



 Electricity and Electronics

Learn the basics of electric circuits and build interesting projects using lights, buzzers, motors, switches and electronic "chips".
No experience necessary.
Advanced projects for advanced students.



... and more!






And in the meantime you can always
Purchase Constructing The Universe Activity Books to learn geometric construction through nature and art at home!



Especially recommended for youngsters are Volumes 1, 2, 3 and 6.


Click on any book to see it's Table of Contents







Perhaps you'd like to watch a DVD: "A Journey From 1 to 12"
(corresponds with Volumes 1 and 2)



To the Constructing The Universe Home Page



(c) 2012 Michael S. Schneider