Geometry for the Classroom: Exercises and Solutions
Published on 1. May 1991
Book
Paperback/Softback
VI, 180 pages
978-0-387-97565-8 (ISBN)
Description
This workbook is intended for college courses for prospective or in-service secondary school teachers of geometry. It contains solutions and commentary to the numerous exercises in the accompanying workbook.
More details
Edition
1991 ed.
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Professional/practitioner
Illustrations
VI, 180 p.
Dimensions
Height: 279 mm
Width: 210 mm
Thickness: 10 mm
Weight
445 gr
ISBN-13
978-0-387-97565-8 (9780387975658)
DOI
10.1007/978-1-4612-0969-0
Schweitzer Classification
Content
Intuition.- I1e: Geometry is about shapes..- I2e: . and more shapes..- I3e: Polygons in the plane.- I4e: Angles in the plane.- I5e: Walking north, east, south, and west in the plane.- I6e: Areas of rectangles.- I7e: What is the area of the shaded triangle?.- I8e: Adding the angles of a triangle.- I9e: Pythagorean theorem.- Il0e: Side Side Side (SSS).- I12e: Rectangles between parallels and the Z-principle.- I13e: Areas: The principle of parallel slices.- I14e: If two lines in the plane do not intersect, they are parallel.- I15e: The first magnification principle: preliminary form.- I16e: The first magnification principle: final form.- I17e: Area inside a circle of radius one.- I18e: When are triangles congruent?.- I19e: Magnifications preserve parallelism and angles.- I20e: The principle of similarity.- I21e: Proportionality of segments cut by parallels.- I22e: Finding the center of a triangle.- I23e: Concurrence theorem for altitudes of a triangle.- I24e: Inscribing angles in circles.- I25e: Fun facts about circles, and limiting cases.- I26e: Degrees and radians.- I27e: Trigonometry.- I28e: Tangent ? =(rise)/(run).- I29e: Everything you always wanted to know about trigonometry but were afraid to ask.- I30e: The law of sines and the law of cosines.- I31e: Figuring areas.- I32e: The second magnification principle.- I33e: Volume of a pyramid.- I34e: Of cones and collars.- I35e: Sphereworld.- I36e: Segments and angles in sphereworld.- I37e: Of boxes, cylinders, and spheres.- I38e: If it takes one can of paint to paint a square one widget on a side, how many cans does it take to paint a sphere with radius r widgets?.- I39e: Excess angle formula for spherical triangles.- I40e: Hyperbolic-land.- Construction.- C1e: Copying triangles.- C2e: Copying angles.- C3e:Constructing perpendiculars.- C4e: Constructing parallels.- C5e: Constructing numbers as lengths.- C6e: Given a number, construct its square root.- C7e: Constructing parallelograms.- C8e: Constructing a regular 3-gon and 4-gon.- C9e: Constructing a regular 5-gon.- C10e: Constructing a regular 6-gon.- C11e: Constructing a regular 7-gon (almost).- C12e: Constructing a regular tetrahedron.- C13e: Constructing a cube and an octohedron.- C14e: Constructing a dodecahedron and an icosahedron.- C15e: Constructing the baricenter of a triangle.- C16e: Constructing the altitudes of a triangle.- C17e: Constructing a circle through three points.- C18e: Bisecting a given angle.- C19e: Putting circles inside angles.- C20e: Inscribing circles in polygons.- C21e: Circumscribing circles about polygons.- C22e: Drawing triangles on the sphere.- C23e: Constructing hyperbolic lines.- Proof.- P1e: Distance on the line, motions of the line.- P2e: Distance in the plane.- P3e: Motions of the plane.- P4e: A list of motions of the line.- P5e: A complete list of motions of the line.- P6e: Motions of the plane: Translations.- P7e: Motions of the plane: Rotations.- P8e: Motions of the plane: Vertical flip.- P9e: Motions of the plane fixing (0,0) and (a,0).- P10e: A complete list of motions of the plane.- P11e: Distance in space.- P12e: Motions of space.- P13e: The triangle inequality.- P14e: Co-ordinate geometry is about shapes and more shapes.- P15e: The shortest path between two points..- P16e: The unique line through two given points.- P17e: Proving SSS.