include "../../include.php"; ?>
Webpage of GeoGebra.
Euclid's Proposition 1 on constructing equilateral triangles. Construction of regular quadrilaterals (squares).
Discussion of Homework 1; presentation of tube-at-an-angle problem; Tom's GeoGebra worksheet.
Discussion of Homework 2 (circumference and radius of circles on spheres, and bug on box problem).
Continued discussion of spherical geometry.
Continued discussion of lowest point of tilted square between two unit squares. Solution of two-dimensional problem. Modeling in GeoGebra. Posed problem of path of other corners of the square, and the three-dimensional cubes version.
Discussed definition of triangle in the plane. Checked definition against a menagerie of triangles. Made a Venn diagram categorizing types of triangles. Discussed spherical triangles.
Spherical Easel, a Java applet that models spherical geometry.
Discussion of Homework 3 (GeoGebra construction of triangle centers, and cake cutting problem).
More discussion of the definition of triangles on the sphere.
Minimizing distance carrying a bucket from the car to the river to the campfire.
Discussion of Homework 4 (range of angle sums of spherical triangles, and area of star).
Area of a spherical triangle.
Construction of quadrilaterals on the sphere; properties of angles.
Motion in GeoGebra of other points on the rotating square.
The Vanishing Leprechaun, created by Pat Lyons and published in 1968 by the W. A. Ellott Co. in Toronto.
Discussion of Homework 5 (wine bottles in GeoGebra and angle sums).
The spherical law of cosines and application to calculating distance on the Earth.
Discussion of Homework 6 (moving sofa around corner, conveying card hand, height of right pyramid). Further discussion of the dropped cube problem.
Discussion of Homework 7 (central angle theorem and circles at right angles).
Showing that the angle sum of triangles in the Euclidean plane is 180 degrees.
Discussion of Homework 8 (Legendre's false proof of the parallel postulate, and Playfair's Axiom). Writeup for Problem 1.
Finished the worksheet on angle sum of triangles in the hyperbolic plane. Discussion of the critical angle for parallel lines.
GeoGebra model of the sofa problem. Discussion of the truck problem.
Empirically determined a relationship between area of triangles on the hyperbolic plane and their angle sums.
Discussion of Homework 9 (testing whether space is Euclidean or hyperbolic). Discussion of relativity and the types of 3-dimensional spaces.
Derived the formula for area of triangles on the hyperbolic plane in terms of the angle sum defect.
Discussion of The Vanishing Leprechaun.
Regular shapes in 3-dimensional Euclidean space: Platonic and Archimedean solids.
|Back||This page last modified echo date("D, F j, Y \\a\\t g:ia",getlastmod()); ?>.|