Annual Member
| Author | Clemens, C. Herbert. author |
|---|---|
| Title | Geometry for the Classroom [electronic resource] / by C. Herbert Clemens, Michael A. Clemens |
| Imprint | New York, NY : Springer New York : Imprint: Springer, 1991 |
| Connect to | http://dx.doi.org/10.1007/978-1-4612-0961-4 |
| Descript | 356 p. online resource |
Intuition -- I1: Geometry is about shapes -- I2:โฆ 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 Z-principle -- 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: Hyperbolic-land -- 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 3-gon and 4-gon -- C9: Constructing a regular 5-gon -- C10: Constructing a regular 6-gon -- C11: Constructing a regular 7-gon (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: Co-ordinate geometry is about shapes and more shapes -- P15: The shortest path between two pointsโฆ -- P16: The unique line through two given points -- P17: Proving SSS -- Computer Programs -- CP1: Information youโll need about the CP-pages -- 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 Xโ -- CP22: Given two points inside the circle of radius one about (0,0), construct the hyperbolic line containing the two points
