14.3 Geometry in Three Dimensions

 

 

 

Simple Closed Surfaces

 

** A simple closed surface has one interior, no holes, and is hollow.**

 

Ex. Sphere                                                                   See Figure

                                                                                               

a-d are simple closed surfaces             e, f are not simple closed surfaces

 

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Def. Sphere—the set of all points at a given distance from a given point, the center.

 

Def. Solid—the set of all points on a simple closed surface with all interior points.

 

Def. Polyhedron—a simple closed surface made up of polygonal regions, or faces.

 

PRISMS

 

Def. Prism—a polyhedron in which two congruent faces lie in parallel planes and the other faces are bounded by parallelograms.

 

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**faces other than the bases are the lateral faces**

 

**if the lateral faces of a prism are all bounded by rectangles, then the prism is a right prism; if not, it is an oblique prism.**

 

 

 

PYRAMIDS

 

Def. Pyramid—a polyhedron determined by a polygon and a point not in the plane of the polygon.

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Base----polygonal region

Point---apex

Faces other than the base---lateral faces

 

 

Figure —triangle, square, pentagonal

 

 

CYLINDERS AND CONES

 

Def. Cylinder—a simple closed surface that is not a polyhedron.

 

Ex’s:    circular cylinder—when the base is a circle

 

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right cylinder—when the line segment forming a cylinder is perpendicular to the base.

       

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Def. Cone—a simple closed surface that is not a polyhedron, with a vertex.

 

*vertex

*altitude

 

Ex’s     right circular cone

 

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            Oblique circular cone