MTH 232 Section 9.3 Figures in Space

From 2-D to 3-D In the previous section we examined curves and polygons in the plane (all the points in the plane and its interior and exterior were coplanar). These figures had only two dimensions (for example, a rectangle has length and width). In this section we expand our discussion to curves and figures that cannot be contained within a flat surface. In the absence of having actual models, these three-dimensional figures are often drawn on a two dimensional surface.

The Sphere

The Cylinder

The Cone

The Polyhedron A polyhedron is a simple closed surface formed from planar polygonal regions. The polyhedron is to space what the polygon is to the plane. Polyhedra have faces, vertices, and edges.

The Pyramid

The Prism

Euler’s Formula In 1752, Leonhard Euler discovered that the number of faces (F), the number of vertices (V), and the number of edges (E) are related to one another:

Revised Homework 2 a, b, d,e, f; 3; 12 a, b; 13; 17 ( them to me); 21; 23; 36; 37; 38