When You Do the Art, Math Happens

Native American Geometry

A Creation Math by the Dots

NATIVE AMERICAN GEOMETRY is a free online workshop

Welcome to NATIVE AMERICAN GEOMETRY, brought to you by EarthMeasure Research. This website is now heading into its 12th Year and enjoys thousand of hits a week.

There is not much text, but please at least skim the material and your experience will be more enjoyable. This is a SKILL CENTERED APPROACH. You will find all emphasis on actually doing it: making the circles and drawing the lines, and connecting the natural dots that occur along the way. These are the dots of Creation. Two intersecting circles united by the same radius: this is the door. The perfect polygons soon follow, each filled with far ranging mathematical discoveries in the midst of artistic beauty.

Since you begin with artistic designs and geometric constructs, think about purchasing this book:
    Geometric Design by Seymour D. Palo Alto: Dale Seymour Publications 1988

See REFERENCES for other books tailored to various grade levels. They will definitely expand your mind and your appreciation for why all of our ancestors -- going back 10,000 years -- were all enthusiastic by these perfect shapes. You find it in every major civilization, whether they knew about the math or not.

There are many wonderful designs that will amaze your students, young or old, from simple to challenging. And they will be making them. Inside or outside: your choice. Everything you construct on paper can be taken outside on a much larger scale. The angles and the proportional constants learned about in class will be exactly the same at larger scales. Draw a huge geometric mural on a wall or actually design, layout and plant a huge Renaissance-like garden in the schoolyard. Again, your choice. Whatever you decide, all of your art designs will be full of dormant math lessons.

Above all, the emphasis is on accurate designs to begin with. Once you have "protractor ready" designs - generally in a week or two - then you are also ready for introducing the Square Root Number Line. Or not. Each mathematical component of this online workshop is based on the design component. That means, don't sweat the math. Leave it alone if you want. DESIGN lessons are completely separate from MATH lessons, if you want.

FOR THE BEST RESULTS, students should utilize the protractor in order to make their designs as precise and perfect as possible. The protractor should be put to work immediately to measure your first hexagon or triangle. All angles are easy to remember: 30, 60, 90, 120. It is why the ancestors invented the 360-degree circle: it is highly divisible into simple whole-number angles, and that is why the polygons are such perfect learning tools. Again, this might take anywhere from a couple days to a week or so. Kids pick up the idea real quick. Wait until you see their snowflakes!

The protractor takes on a different functional role, more intimate. It gauges your precision. You do not construct the shapes with the protractor. Instead, you apply the protractor to see how close you are to perfection. It provides direct and immediate feedback as you acquiring your new skills.

Nature's dots are exactly spaced, and Precision Generates Excellence, and this fuels Self-Esteem. Just give your hand a chance to get used to the compass; tips are provided during the online workshop. All of your actions will cultivate a behavioural intimacy between hand and eye. That alone wakes up the entire brain and its numerous "intelligences." The protractor checks your work. Precision is paramount, but incredibly easy to attain. If 2nd graders can master the perfect hexagon in an hour, so can you.

Precision begets proportional constants -- generally regarded as evil spirits with nonsensical, impossible numbers: Pi, phi, and an abundance of square roots. In a single hour's workshop, you can be shown how to look for these mathematical artifacts of Creation. The words, harmonious and holistic, only scratch the surface.

Welcome to The Natural History of Shapes. Even the shapes of Molecules. Once molecules were idealized in geometric forms. The world's first photo of a molecule shows that the Ideal turns out to be Real!

Enjoy your stay, and come back often. New wonders are around the corner.

E-mail Chris Hardaker


Native American Geometry Workshop

World's First Photo Of A Single Molecule

Above, finally pictured for the first time, a single molecule, of pentacene.
Below, a typical graphic representation of this molecule.