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Math 310

Math 310. Section 9.4 3-Dimensional Geometry. Simple Closed Surface. Def A simple closed surface is a surface with exactly one interior, no holes, and is hollow. A Solid. Def A solid is the set of all points on a simple closed surface along with all its interior points. Polyhedrons.

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Math 310

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  1. Math 310 Section 9.4 3-Dimensional Geometry

  2. Simple Closed Surface Def A simple closed surface is a surface with exactly one interior, no holes, and is hollow.

  3. A Solid Def A solid is the set of all points on a simple closed surface along with all its interior points.

  4. Polyhedrons Def A polyhedron is a simple closed surface made up of polygonal regions, or faces. The vertices of the polygonal regions are the vertices and the sides of each polygonal region are the edges of the polyhedron.

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

  6. Lateral Faces Def For a prism, the faces other than the bases are the lateral faces of a prism.

  7. Right Prism Def A right prism is a prism in which the lateral faces are all rectangles.

  8. Oblique Prism Def An oblique prism is a prism in which at least one of the lateral faces is not a rectangle.

  9. Pyramid Def A pyramid is a polyhedron determined by a polygon and a point not in the plane of the polygon. The pyramid consists of the triangular regions determined by the point and each pair of consecutive vertices of the polygon and the polygonal region determined by the polygon. The polygonal region is the base, and the point is the apex. The triangles comprise the lateral faces of the pyramid.

  10. Right Pyramid Def A right pyramid is a pyramid whose lateral faces are congruent isosceles triangles.

  11. Convex Polyhedron Def A convex polyhedron is a polyhedron in which any two points in the interior of the polyhedron can be connected by a segment that lies entirely within the polyhedron.

  12. Regular Polyhedron (Platonic Solids) A regular polyhedron is a convex polyhedron whose faces are congruent regular polygonal regions such that the number of edges that meet at each vertex is the same for all the vertices of the polyhedron.

  13. Cylinder Given a line AB, allow the line to move in 3 dimensions such that it always remains parallel to some given line l. If the points A and B trace out simple closed curves other than polygons, then the surface traced out by segment AB and the simple closed curves along with their interiors form a cylinder. The simple closed curves and their interiors form the bases of the cylinder while the surface created by segment AB is the lateral surface.

  14. Circular Cylinder If the base of a cylinder is a circular region then the cylinder is a circular cylinder.

  15. Right Cylinder If the segments forming the lateral surface of the cylinder are perpendicular to the base, then the cylinder is a right cylinder. All other cylinders are oblique cylinders.

  16. Cones Read page 622, last paragraph.

  17. Sketches

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