What Is Euclidean Geometry?

Euclidean Geometry is the study of plane and solid figures based on the axioms and theorems outlined by the Greek mathematician Euclid (c. 300 B.C.E.). It is this type of geometry that is widely taught in secondary schools. For much of modern history the word geometry was in fact synonymous with Euclidean geometry, as it was not until the late 19th century when mathematicians were attracted to the idea of non-Euclidean geometries. Euclid’s geometry embodies the most typical expression of general mathematical thinking. Rather than simply memorizing basic algorithms to solve equations by rote, it demands true insight into the subject, cleaver ideas for applying theorems in special situations, an ability to generalize from known facts, and an

Not far removed from the information given above, a geodesic is simply the shortest distance between two points. This is a concept we should all be familiar with. In R2 a geodesic is just a straight line. In spherical geometry a geodesic is a great circle. Unlike hyperbolic geometry, which may appear to have a more abstract beginning, the idea of a geodesic has a more concrete relation to the real world. The word geodesic itself comes from geodesy, which is the science of measuring the shape of the earth. Shifting focus to perhaps a more interesting topic, we can begin the discussion on the mathematics of geodesics. The geodesic dome presented by this group is what is known as a 2V Icosa Alternate or more broadly a Class I Dome. It is created by fitting 4 triangles inside each triangular surface of an icosahedron; which is one of the five solids created by the ancient Greeks. When considering a icosahedron, or any regular polyhedral for that matter, we have the following formulas to consider:

1. V = 10υ2 + 2

2. F = 20υ2

3. E =

They also gain strength from the triangular rigidity of the dome which greatly helps to prevent crushing and falling. The shape of a triangle makes it very strong and able to withstand heavy loads. The triangle is in actuality the strongest shape known to man. Box structures, which are the typical conventional homes, on the other hand are easily distorted by heavy loads. When many triangles are connected to form the shell of a dome, they translate to tremendous strength which makes them self-supporting. This in turn eliminates the need for supporting structures. The tremendous strength is a result of triangles distributing strength evenly across the entire structure. Rectangular or box structures for that matter distribute loads at right angles making them considerably