This program will enable students to respond to a series of sequential assignments that culminate and terminate in one or more definitions of a geodesic dome and its components. These definitions will be in Algebra, Calculus, Geometry, Trigonometry, or some combination thereof.
A geodesic dome is an almost spherical structure based on a network of struts arranged on great circles (geodesics) lying on the surface of a sphere. The geodesics intersect to form triangular elements that create local triangular rigidity and distribute the stress. It is the only man made structure that gets proportionally stronger as it increases in size.
Of all known structures made from linear elements, a geodesic dome has the highest ratio of enclosed volume to weight. Geodesic domes are far stronger as units than the individual struts would suggest. It is common for a new dome to reach a "critical mass" during construction, shift slightly, and lift any attached scaffolding from the ground.
Geodesic domes are designed by taking a Platonic solid, such as an icosahedron, and then filling each face with a regular pattern of triangles bulged out so that their vertices lie in the surface of a sphere. The trick is that the sub-pattern of triangles should create "geodesics", great circles to distribute stress across the structure.
There is reason to believe that geodesic construction can be effectively extended to any shape, although it works best in shapes that lack corners to concentrate stress.
