Geometry for the Classroom
 Binding: Paperback
 Publisher: Springer Verlag
 Publish date: 05/01/1991
Description:
Intuition. I1: Geometry is about shapes. I2:... and more shapes. I3: Polygons in the plane. I4: Angles in the plane. I5: Walking north, east, south, and west in the plane. I6: Areas of rectangles. I7: What is the area of the shaded triangle?. I8: Adding the angles of a triangle. I9: Pythagorean theorem. I10: Side Side Side (SSS). I11: Parallel lines. I12: Rectangles between parallels and the Zprinciple. I13: Areas: The principle of parallel slices. I14: If two lines in the plane do not intersect, they are parallel. I15: The first magnification principle: preliminary form. I16: The first magnification principle: final form. I17: Area inside a circle of radius one. I18: When are triangles congruent?. I19: Magnifications preserve parallelism and angles. I20: The principle of similarity. I21: Proportionality of segments cut by parallels. I22: Finding the center of a triangle. I23: Concurrence theorem for altitudes of a triangle. I24: Inscribing angles in circles. I25: Fun facts about circles, and limiting cases. I26: Degrees and radians. I27: Trigonometry. I28: Tangent a =(rise)/(run). I29: Everything you always wanted to know about trigonometry but were afraid to ask. I30: The law of sines and the law of cosines. I31: Figuring areas. I32: The second magnification principle. I33: Volume of a pyramid. I34: Of cones and collars. I35: Sphereworld. I36: Segments and angles in sphereworld. I37: Of boxes, cylinders, and spheres. I38: 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?. I39: Excess angle formula for spherical triangles. I40: Hyperbolicland. Construction. C1: Copying triangles. C2: Copying angles. C3: Constructing perpendiculars. C4: Constructing parallels. C5: Constructing numbers as lengths. C6 Given a number, construct its square root. C7: Constructing parallelograms. C8: Constructing a regular 3gon and 4gon. C9: Constructing a regular 5gon. C10: Constructing a regular 6gon. C11: Constructing a regular 7gon (almost). C12: Constructing a regular tetrahedron. C13: Constructing a cube and an octohedron. C14: Constructing a dodecahedron and an icosahedron. C15: Constructing the baricenter of a triangle. C16: Constructing the altitudes of a triangle. C17: Constructing a circle through three points. C18: Bisecting a given angle. C19: Putting circles inside angles. C20: Inscribing circles in polygons. C21: Circumscribing circles about polygons. C22: Drawing triangles on the sphere. C23: Constructing hyperbolic lines. Proof. P1: Distance on the line, motions of the line. P2: Distance in the plane. P3: Motions of the plane. P4: A list of motions of the line. P5: A complete list of motions of the line. P6: Motions of the plane: Translations. P7: Motions of the plane: Rotations. P8: Motions of the plane: Vertical flip. P9: Motions of the plane fixing (0,0) and (a,0). P10: A complete list of motions of the plane. P11: Distance in space. P12: Motions of space. P13: The triangle inequality. P14: Coordinate geometry is about shapes and more shapes. P15: The shortest path between two points.... P16: The unique line through two given points. P17: Proving SSS. Computer Programs. CP1: Information you''ll need about the CPpages. CP2: Given two points, construct the segment, ray, and line that pass through them. CP3: Given a line and a point, construct the perpendicular to the line through the point, or the parallel to the line through the point. CP4: Given a segment, construct its perpendicular bisector. CP5: Given an angle, construct the bisector. CP6: Given three vertices, construct the triangle and its medians. CP7: Given three vertices, construct the triangle and its angle bisectors. CP8: Given three vertices, construct the triangle and its altitudes. CP9: Given a figure in the plane and a positive number R, magnify the figure by a factor of R. CP10: Given a figure in the plane and two positive numbers R and S, magnify the figure by a factor of R in the horizontal direction and by a factor of S in the vertical direction. CP11: Given the center and radius of a circle, and two positive numbers R and S, magnify the circle by a factor of R in the horizontal direction and by a factor of S in the vertical direction. CP12: TRANSLATIONS: Given a figure in the plane and two numbers a and b, show the motion m(x,y) = (x + a, y + b). CP13: ROTATIONS: Given a figure in the plane and two numbers c and s, so that c2 + s2 = 1, show the motion m(x,y) = (cx  sy, sx + cy). CP14: FLIPS: Given a figure in the plane, show the motion m(x,y) = (x, y). CP15: Composing a set of two motions. CP16: Composing a series of motions. CP17: Given a point and a positive number R, construct the circle of radius R about the point. CP18: Given three points in the plane, construct the unique circle that passes through all three points. CP19: Given the center of a circle and a point on the circle, construct the tangent to the circle through the point. CP20: Given a circle and a point outside the circle, construct the two lines tangent to the circle that pass through the point. CP21: Given a point X inside or outside the circle of radius one and center O, construct the reciprocal point X''. CP22: Given two points inside the circle of radius one about (0,0), construct the hyperbolic line containing the two points.
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