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1. Writing Assignment #4: Technology Applications
that are appropriate for an interactive approach, including applications of Menelaus and Ceva s theorem, Steiner s theorem, Napoleon s theorem, problems with
http://www.math.ilstu.edu/day/courses/old/326/wa04sample.html

Extractions: Technology Applications for the Classroom: A Sample Report Roger Day return to Writing Assignment #4 a) McGehee, Jean J. "Interactive Technology and Classic Geometry Problems." Mathematics Teacher 91 (March 1998): 204-208. b.i) dynamic geometry software Geometer's Sketchpad b.iii) The author compares two approaches, a traditional approach and an interactive approach, for using dynamic geometry software to explore the circle of Appolonius. She provides step-by-step instructions on both approaches that a Sketchpad user can follow. She claims that the differences in approaches focus on whether students are provided any opportunity to investigate, conjecture, and otherwise carry out some of the steps that a mathematician may actually undergo in attempting to solve a problem. The traditional approach results in a successful verification of the constant ratio in the circle of Appolonius, but allows little if any investigation by users as well as fostering little connection between the concepts involved and the construction carried out. The interactive approach allows users to first experiment and carry out many examples of the situation in order to discover the resultthe constant ratioas a result of the construction. This seemingly subtle difference, the author contends, spells the difference between students simply following and completing a procedure to focusing on the concept of the locus and using technology for exploration and discovery. The author provides suggestions of other classical geometry constructions that teachers might consider for similar interactive approaches. In so doing, students and teachers will experience more completely the kind of activities engaged in by mathematicians.

2. Dynamic Geometry Module: Lesson 5
incenters and orthocenters!). Napoleon s theorem states that the centers X, Y, and Z form an equilateral triangle. Join these points
http://mtl.math.uiuc.edu/modules/dynamic/lessons/lesson5.html

Extractions: Lesson 5: The Center of Things The medians of a triangle all intersect in a point (the centroid of the triangle). The same is true of the angle bisectors (the incenter), the altitudes (the orthocenter) and the perpendicular bisectors of the sides (the circumcenter). These are all examples of important "centers" for a triangle. Use Sketchpad to construct each of these centers. This is also referred to as the Toricelli Configuration. It consists of an equilateral triangle drawn outward from each side of a triangle. You can see an example in the accompanying sketch for this lesson ( See file ex5_1.gsp In this sketch, P Q , and R are the vertices of the equilateral triangles and X Y , and Z are their centroids (which also happen to be the circumcenters, incenters and orthocenters!). Napoleon's Theorem states that the centers X Y , and Z form an equilateral triangle. Join these points and measure the sides of the resulting triangle to verify this. Be sure to move the vertices around and see that this property holds in all cases. Now delete those segments and join each center to the vertex of the original triangle that is opposite it. That is, draw the lines

3. FlipCode Message Center - Any Nice Proofs Using Geometric Algebra - Random Bits
I m looking for a nice simple theorem (like Napoleon s theorem or something simple like that) but that can be proved with GA, preferably for any number of

4. Angles Orientés De Vecteurs Dans Le Plan
theorem - the Napoleon s theorem.
http://pauillac.inria.fr/coq/contribs/Angles.html

Extractions: A partir d'une axiomatisation des angles orientés de vecteurs du plan euclidien,on donne des preuves classiques des théorèmes de cocyclicité, de Simson, de Napoléon et de l'orthocentre. Voir le rapport de recherche associé (http://www-sop.inria.fr/lemme/FGRR.ps) et le fichier README. Download (archive compatible with Coq V8.0) Author: Frédérique Guilhot (Frederique.Guilhot@sophia.inria.fr) Institution: INRIA Sophia Antipolis, projet Lemme Date: 15 janvier 2002 Keywords: Pcoq géométrie théorème démonstration angle cercle geometry theorem proof angle circle The README file of the contribution: This page was automatically generated from this description file

5. Australian Mathematics Trust
One notable example of the latter is the DouglasNeumann theorem, an extension of Napoleon s theorem discovered independently by Bernhard and the Fields
http://www.amt.canberra.edu.au/bhnobit.html

Extractions: VALE BERNHARD NEUMANN 1909-2002 Emeritus Professor Bernhard Hermann Neumann, who provided the greatest inspirational influence in mathematics in Australia over a 40-year period, died in Canberra on 21 October 2002 not long after happily celebrating his 93rd birthday. He first visited Australia for three months in 1959, during sabbatical leave, and fell in love with the country. So when, late in 1960, he was invited to found a Department of Mathematics in the research-focussed Australian National University, he was receptive to the idea. Within days of his permanent arrival on 2 October 1962, he also became involved in activities supporting the teaching of mathematics in schools. Bernhard had a great influence in the founding and administration of the Australian Mathematics Trust. He became a mentor and source of inspiration to Peter OHalloran (1931-1994) who, while on the staff of the Canberra College of Advanced Education (later the University of Canberra) during the period of the early 1970s to the early 1990s, is acknowledged as the Founder of the Trust. Peter gained great strength from Bernhards encouragement, not only while Bernhard held his position as head of mathematics in the Institute of Advanced Studies at the Australian National University, but also after Bernhards retirement. Bernhard took an active personal part in the Trusts activities. He was the Inaugural Chairman of the Australian Mathematical Olympiad Committee, a position he held from 1980 to 1986. He was also the representative of the Canberra Mathematical Association (a sponsor of the Australian Mathematics Competition (AMC) for the Westpac Awards) on first the AMC Governing Board, and then on the Advisory Committee of the Trust. He was an active member of the Advisory Committee until his death.

6. Masteringti-92 Contents
117. Exploration 5 Geometry Napoleon s theorem 123. Exploration 6 Precalculus Polynomial Functions of Higher Degree 129. Exploration
http://www.gilmarpublishing.com/contents/masteringti92.html

7. Gov's Web
1. Properties of Parallel Lines 2. Equations of Lines 3. The Burning Tent Problem 4. Angle Bisectors in a Triangle 5. Napoleon s theorem 6. Properties of
http://www.northern.edu/haighw/gov.html

Extractions: Aberdeen Area Workplaces Visited A total of eight Aberdeen area workplaces (Table 1) were visited to observe the computer technology used and, where appropriate, incorporated into university mathematics classes (Table 2) . The computer technology used at these worksites included: (1) spreadsheets; (2) programming in various languages; (3) statistical analysis packages; (4) Internet; (5) software to solve systems of differential equations; (6) topographic map packages; and (7) graphing packages.

8. Center For Technology And Teacher Education: Content Areas: Mathematics
Napoleon s theorem Explorations Draw a triangle. On the edges of the triangle, construct equilateral triangles. Find the centroids