Section a polyhedra Section b flag Construction Section C
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- Number 76 Geometry Junkyard
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Social elementsIn the book, men are portrayed as polygons whose social class is directly proportional to the number of sides they have; therefore, triangles, having only three sides, are at the bottom of the social ladder and are considered generally unintelligent, while the Priests are composed of multisided polygons whose shapes approximate a circle, which is considered to be the "perfect" shape. On the other hand, the female population is comprised only of lines, who are required by law to sway back and forth and sound a "peace-cry" as they walk, due to the fact that when a line is coming towards an observer in a 2-D world, it appears merely as a point. A. Square talks of accounts where men have been killed (both by accident and on purpose) by being stabbed by women. This explains the need for separate doors for women and men in buildings. In the world of Flatland, classes are distinguished using the "Art of Feeling" and the "Art of Sight Recognition". Feeling, practiced by the lower classes and women, determines the configuration of a person by feeling one of their angles. The "Art of Sight Recognition", practiced by the upper classes, is aided by "Fog", which allows an observer to determine the depth of an object. With this, polygons with sharp angles relative to the observer will fade out more rapidly than polygons with more gradual angles. The population of Flatland can "evolve" through the Law of Nature, which states: "a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on." This rule is not the case when dealing with isosceles triangles (Soldiers and Workmen), for their evolution occurs through eventually achieving the status of an equilateral triangle, removing them from serfdom. The most acute angle of an isosceles triangle gains thirty minutes (half a degree) each generation. Additionally, the rule does not seem to apply to many-sided polygons; often the sons of several hundred-sided polygons will often develop fifty or more sides than their parents. The book poses several interesting thoughts, including the idea that higher dimensional beings have god-like powers over lesser dimensions. In the book, the three-dimensional Sphere has the ability to stand inches away from a Flatlander and observe them without being seen, can remove flatland objects from closed containers and "teleport" them via the third dimension apparently without traversing the space in between, and is capable of seeing and touching the inside and outside of everything in the two dimensional universe; at one point, the Sphere gently pokes the narrator's intestines and launches him into three dimensions as proof of his powers. The book implies the possibility that higher dimensions than three exist, implies a satirical description of Victorian life, and teaches a lesson about ignorance, closed-mindedness, and self-satisfaction. Number 74 Coordination Polyhedra http://www.hull.ac.uk/php/chsajb/general/shapes.html A simple site still under construction. Number 75 Fractal Polyhedra
An interesting idea of models made of many polyhedra diminishing in size. Number 76 Geometry Junkyardhttp://www.ics.uci.edu/~eppstein/junkyard/polytope.html An absolute must. There is so much on this site to satisfy all geometers. It is continuously being updated. Number 77 Arts, Mathematics and Architecture http://www.isama.org/polyh/ A list of very good links. Each one of the links is worth a visit. Number 78 Crystallographic Polyhedra http://www.jcrystal.com/steffenweber/POLYHEDRA/p_00.html An interactive site illustrating 29 polyhedra in wireform in Applets. Number 79 Sandor Karbai (Hungary) http://www.kabai.hu/ This site has a lot of gifs that would make good classroom posters. Unfortunately they are not in English but this is offset by the clarity of the illustrations. There are some excellent ‘colouring in’ books and some interesting lessons in Polyhedra. Number 80 Korthals Altes Paper Models of Polyhedrahttp://www.korthalsaltes.com/ This site has so many nets for polyhedra. A site well worth visiting time and time again. Number 81 Playing to Win http://www.learner.org/exhibits/dailymath/placebets.html A statistics site that may be useful. Number 82 Polyhedra by Peter Cromwell http://www.liv.ac.uk/~spmr02/book/ This is a book review Number 83 Origami Polyhedrahttp://www.math.lsu.edu/~verrill/origami/ A very good site with very clear explanations of method. There are a lot of models to create using this module technique. Number 84 Euler’s Formula http://www.math.ohio-state.edu/~fiedorow/math655/Euler.html This is a simple site with a few illustrations. Number 85 Tetrahedral Puzzleshttp://www.math.ucdavis.edu/~deloera/CURRENT_INTERESTS/tetrapuzz.html Dissection puzzles that would make good classroom activities. Number 86 The Platonic Solids http://www.math.utah.edu/~pa/math/polyhedra/polyhedra.html Here is a good little treatise on the Platonics. Number 87 - 88 Uniform Polyhedra 2 PDF http://www.math.washington.edu/~grunbaum/Newuniformpolyhedra.paper.pdf http://www.math.washington.edu/~grunbaum/Your polyhedra-my polyhedra.pdf Here is a rather technical approach to the subject of Polyhedra. Number 89 Polyhedral Links and Reviews http://www.math.washington.edu/~king/coursedir/m444a03/as/polyhedra-links.html Some reviews worth reading. Directory: advisor advisor -> Virginia polytechnic institute and state university advisor -> Rick Scott Governor Celeste Philip, md, mph advisor -> Mission: To protect, promote & improve the health of all people in Florida through integrated state, county & community efforts. Rick Scott advisor -> Of Transportation Federal Aviation Administration advisor -> U. S. Department of Transportation advisor -> Original: English advisor -> United Nations A/hrc/AC/16/2 advisor -> Theme: Real World Connections, Social Responsibility and Leadership Lesson: Internet Shopping Business Idea 2 Learning Outcomes Download 258.25 Kb. Share with your friends:
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