Nature, Number, and Geometry


In this fascinating study the student learns of the intrinsic geometrical structure in many of nature’s forms. Throughout the centuries this discipline has been known as the study of sacred geometry. The student will gain facility with compass, triangle, and straight edge as he/she learns the structure and properties of the snowflake, honeycomb, nautilus shell, and human skeleton. This book, like the astronomy book, is divided into two sections. The first section contains lessons for the sixth-grade, while section two is useful for carrying on this study into the seventh grade.

Six-Fold Symmetry of the Snow Crystal

Lesson 8

Construct the six-divisions of the circle [with a radius of at least 2 inches] to find points a, b, c, d, e, and f around the circumference. Connect these six points to the center of the circle to form the six “spokes of the wheel” which are the six structural axes of the snowflake. Now draw several more (at least two) concentric circles within this original circle. Refer to the next page to see some field samples of snowflakes.

Use one of these as a model to form the six-fold symmetry of the snow crystal. Figure 10 describes one way to proceed. Notice that the student has created a beginning form in the most outer zone at point a, and then repeats this same figure again in the outer zone at point e. This same little figure will be repeated exactly in the outer zone at the remaining four points around the circle. Now the student proceeds to the middle zone and creates a hexagonal figure that you see again on the axis in line with point a. Notice that this figure is repeated on the axis connected to point c , and again in the middle zone. This little hexagon will be repeated on the remaining four axes and in the middle zone. Finally the last figure was created in the inner zone on the axis connected to point a . This form will be repeated five more times on the remaining axes.

Use the examples on the accompanying page to create more geometrically constructed snowflakes. Figure 11 shows a design created in this manner.

Snowflake by Kristelle Monterrosa age 13
  • Introduction: How to Proceed with These Lessons
  • Materials Needed
  • Recommended Sources
  • Six-Fold and Twelve-Fold Symmetry in Nature’s Plants and Crystals
  • 14 Lessons
  • Pentagonal Symmetry in Nature’s Forms
  • 6 Lessons
  • The Golden Triangle and the Star Ladder
  • 2 Lessons
  • Exploring the Golden Proportion
  • 2 Lessons
  • Three Kinds of Number Progressions
  • Arithmetic Progressions and the Archimedean Spiral
  • 4 Lessons
  • Geometric Progressions in Nature’s Spirals
  • 3 Lessons
  • The Golden Rectangle and Fibonacci Numbers
  • Man the Measure: The Golden Proportion in the Human Being
  • 2 Lessons