Once upon a time, there was a beautiful little boy who could always smell the ocean air through his window.
One day when the sun was high in the sky, he went for a walk on the moist, smooth sand. Suddenly an enormous sea serpent, as wide around as a tree trunk slithered up out of the ocean and approached the boy. The boy looked around quickly, and grabbed a long piece of driftwood to try to protect himself from the oncoming serpent. The serpent slithered up the beach, and stopped where the wet sand meets the dry, leaving the boy nowhere to run but into the ocean. The snake opened up it’s enormous mouth, and showed off it’s venomous fangs, big and sharp as sabers. It’s eyes glowed with purpose, and it stared directly into the boy. “Hello, boy” hissed the snake. “What... what do you want?” stammered the boy. “Ah, you sssee...you belong to meee now, boy”. “I belong to no-one!” “Ah but you have always belonged to the sea, you see? And now the sea has come to claim you” “But I want to stay on the land. I don’t want to be claimed by the sea!” “It looks to meee that you belong in the sssea boy. You stand on that wet sand there... almost as much sea as it is earth. There is no line between them.”
This gave the boy an idea. He reached out the end of his stick, and rotated slowly around drawing a circle in the sand. “You see?” He said to the snake, mocking it, “I’m now inside, and you can’t get me!” “Ah, how ingeeenioussss, boy. You are right. I cannot claim you now, but you are trapped insssside.”
The boy went to the very edge of his circle, toward the serpent, and drew another circle from where he was standing. This expanded his enclosed space. He boldly moved toward the edge of his second circle, and drew another. This brought him right to the enormous body of the snake. “How will you pass me now, boy?” The boy wondered about this for a moment. “I can prove to you that I am of the earth.” He said. If I can create three precious diamonds from only this sand, will you accept those as an adequate gift, and let me return to my home?” “Ah yesss.... that would be ssssufficient. But only the depthsssss can produssse diamonds from ssssand. I think you will ssstill be coming with meeee”
The boy took up his stick, and walked to where the edge of one circle crossed another. He drew another circle there. He repeated this for each of the four points where one circle crossed another.
The serpent looked on curiously, but the boy wasn’t done. He then took his stick, and connected the six intersection points along the edge of the inner circle. The serpent’s eyes started to darken, as he suspected a trick, but he kept watching. As his last move, the boy drew three lines into the center of his shape, creating three diamonds.
The serpent bowed his gigantic head to the boy, the boy bowed back, and the serpent disappeared back into the ocean.
The word “shape” is both a noun and a verb. When we draw a shape, we are defining a space. We are giving shape to space. The roots of the word “geometry” are often translated as “to measure earth”, but it could also mean “to define the land”, or “to shape a space”. Humans have been defining spaces for as long as they have been making dwellings. A round tent has an inside and an outside. It says “this is my space, separate from you, and from the rest of the world.” This is much like the boy’s initial circle in the story. However, at some point in human history, we discovered that if you take a shape, and repeat it in a pattern, it can define an infinite space.
Many cultures have infused their lives with these infinitely repeating geometric patterns. In Islamic practice, these repeating patterns display the infinite complexity of the divine. In some religious traditions, such as the Greek, Egyptian, or Christian traditions, the Divine is shown embodied in human or animal form. In the Muslim tradition, the Divine is shown embodied in geometric pattern. Many of these patterns are based on a grid of interlocking circles, as seen in the story. This grid is often called “the flower of life”. By connecting the points where the circles intersect, many shapes and patterns can be defined without the need for numeric calculations. While many intricate patterns can be created by connecting these points in different ways, the simplest pattern is a grid of equilateral triangles, which can themselves yield a surprising amount of complexity.
Many cultures have infused their lives with these infinitely repeating geometric patterns. In Islamic practice, these repeating patterns display the infinite complexity of the divine. In some religious traditions, such as the Greek, Egyptian, or Christian traditions, the Divine is shown embodied in human or animal form. In the Muslim tradition, the Divine is shown embodied in geometric pattern. Many of these patterns are based on a grid of interlocking circles, as seen in the story. This grid is often called “the flower of life”. By connecting the points where the circles intersect, many shapes and patterns can be defined without the need for numeric calculations. While many intricate patterns can be created by connecting these points in different ways, the simplest pattern is a grid of equilateral triangles, which can themselves yield a surprising amount of complexity.
December 15, 2009
An introduction to a 4/5th grade geometry unit I wrote as a final project for my graduate work at Antioch University.
