Mudd Math Fun Facts: All Fun Facts Method; Multiplication by 11; Music Math Harmony; napoleon's theorem;Nine Points! Odd Numbers in Pascal's Triangle; One Equals Zero! http://www.math.hmc.edu/funfacts/allfacts.shtml
DC MetaData For: Napoleon's Theorem With Weights In N-Space napoleon's theorem with Weights in nSpace by H. Martini, B. Weißbach. Keywordsnapoleon's theorem, Torricelli's configuration. Upload 1998-08-24-08-24. http://www.math.uni-magdeburg.de/preprints/shadows/98-20report.html
Introduction To Shalosh B. Ekhad XIV's Geometry Textbook Hence in order to understand the statement of napoleon's theorem you only needto look up the definitions Ce, Center, CET, Circumcenter, DeSq and http://www.math.rutgers.edu/~zeilberg/PG/Introduction.html
Extractions: Cover Foreword Definitions Theorems Dear Children, Do you know that until fifty years ago most of mathematics was done by humans? Even more strangely, they used human language to state and prove mathematical theorems. Even when they started to use computers to prove theorems, they always translated the proof into the imprecise human language, because, ironically, computer proofs were considered of questionable rigor! Only thirty years ago, when more and more mathematics was getting done by computer, people realized how silly it is to go back-and-forth from the precise programming-language to the imprecise humanese. At the historical ICM 2022, the IMS (International Math Standards) were introduced, and Maple was chosen the official language for mathematical communication. They also realized that once a theorem is stated precisely, in Maple, the proof process can be started right away, by running the program-statement of the theorem. All the theorems that were known to our grandparents, and most of what they called conjectures, can now be proved in a few nano-seconds on any PC. As you probably know, computers have since discovered much deeper theorems for which we only have semi-rigorous proofs, because a complete proof would take too long.
Napoleon's Theorem napoleon's theorem. by Kala Fischbein and Tammy Brooks. Given any triangle,we can construct equilateral triangles on the sides of each leg. http://jwilson.coe.uga.edu/emt725/Class/Fischbein/napoleon.triangle/Napoleon/nap
Extractions: Given any triangle, we can construct equilateral triangles on the sides of each leg. In these equilateral triangles, we can then find the centers: centroid, orthocenter, circumcenter, and incenter. Each of these centers is in the same location because the triangles are equilateral. After the centers have been located, we connect them thus forming Napoleon's Triangle.
Essay 3 Napoleon's Theorem napoleon's theorem goes as follows Given any arbitrary triangle ABC, constructequilateral triangles on the exterior sides of triangle ABC. http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Martin/essays/essay3.html
Extractions: Essay 3: Napoleon's Triangle by Anita Hoskins and Crystal Martin Napoleon's Theorem goes as follows: Given any arbitrary triangle ABC, construct equilateral triangles on the exterior sides of triangle ABC. The segments connecting the centroids of the equilateral triangles form an equilateral triangle. Let's explore this theorem. Construct an equilateral triangle and see if Napoleon's triangle is equilateral. We can see from this construction, that when given an equilateral triangle, the resulting Napoleon triangle is also equilateral. Construct an isosceles triangle. Again, we see that with an isosceles triangle, Napoleon's triangle is still equilateral. Now, let's construct a right triangle. Still, even with a right triangle, Napoelon's triangle is equilateral. Now, we will prove that for any given triangle ABC, Napoleon's triangle is equilateral. We will use the following diagram: A represents vertex A and it's corresponding angle. a denotes the length of BC, c denotes the length of AB, and b denotes the length of AC. G, I, and H are the centroids of the equilateral triangles. x is the length of segment AG and y is the length of segment AI.
Napoleon's Theorem napoleon's theorem. This is a theorem attributed by legend to NapoleonBonaparte. It is Century. Statement of napoleon's theorem. For http://www.math.washington.edu/~king/coursedir/m444a02/class/11-25-napoleon.html
Extractions: This is a theorem attributed by legend to Napoleon Bonaparte. It is rather doubtful that the Emperor actually discovered this theorem, but it is true that he was interested in mathematics. He established such institutions as the Ecole Polytechnique with a view to training military engineers, but these institutions benefited mathematics greatly. French mathematicians made many important discoveries at the turn of the Eighteenth to the Nineteenth Century. For any triangle ABC, build equilateral triangles on the sides. (More precisely, for a side such as AB, construct an equilateral triangle ABC', with C and C' on opposite sides of line AB; do the same for the other two sides.). Then if the centers of the equilateral triangles are X, Y, Z, the triangle XYZ is equilateral.
Math 444 Aut 2002 Week 9 Assignment 9 Due Monday 12/02; Statement of napoleon's theorem for Assignment 9.Wallpaper Groups concepts of transformation group, symmetry group, basic unit http://www.math.washington.edu/~king/coursedir/m444a02/wk09.html
Extractions: Math 444/487 Geometry Week 9 Monday 11/25 - Friday 11/29 444 Home Page Week 9/30-10/04 Week 10/07-11 Week 10/14-18 ... Week 12/09-13 Monday 11/25 444 Web Resources : Some very good material on symmetry in general and wallpaper groups in particulat is on the web. Wednesday 11/27 444 Relations among tetrahedra, cubes and octahedra Cube decomposes into 3 congruent pyramids. From this and a bit more it follows that the volume of any pyramid is (1/3) * base area * height. Symmetries of tetrahedra, cubes and octahedra
Extractions: Bernard's Bag(P) - solutions(P) Penta Probs(P) - solutions(P) Let Me Try(P) - solutions(P) Kid's Mag(P) Play Games(P) Staff Room(P) 6 Problems - solutions 15+Challenges - solutions Articles Games LOGOland Editorial News Geometry-Euclidean Properties of Shapes Polygons Problem Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR? Click here for an interactive version of this problem. This week's interactive Java problem uses JavaSketchpad . Users may find that they need to update their browser. This applet works with or Microsoft Internet Explorer 4 Triangle ABC has equilateral triagles drawn on its edges. Points
Extractions: Geometry-Euclidean Properties of Shapes Polygons Problem Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR? Click here for an interactive version of this problem. This week's interactive Java problem uses JavaSketchpad . Users may find that they need to update their browser. This applet works with or Microsoft Internet Explorer 4 Triangle ABC has equilateral triagles drawn on its edges. Points P Q and R are the centres of the equilateral triangles. Experimentation with the interactive diagram leads to the conjecture that PQR is an equilateral triangle. This can be proved using vectors or complex numbers. In the following w e p i so that 1 + w w = 0. Also multiplying a complex number by w rotates it by 60 degrees. Referring to the given diagram let A B be represented by the complex numbers a b . The third vertex of the triangle with base AB is represented by the complex number b w a b ). Therefore
Glossary Of Mathematical Terms point; Napier Bones; napoleon's theorem napoleon's theorem, a generalization;napoleon's theorem by Plane Tesselation; napoleon's theorem http://www.cut-the-knot.org/glossary/ntop.shtml
Napoleon's Propeller (2), Of course, (2) could be used to derive napoleon's theorem. napoleon's theoremis equivalent to the Asymmetric Propeller's theorem! How small is the world! http://www.cut-the-knot.org/ctk/NapoleonPropeller.shtml
Extractions: by Alex Bogomolny July 2002 As the two most recent columns have been devoted to synthetic proofs of a curious result , I've been looking for an example or two of an illuminating analytic proof. I found quite a few. Two such appear below. In the process I made a small, but surprising, discovery that is reflected in the title of the present column. Three altitudes of a triangle meet at a point known as the orthocenter of the triangle. There are many proofs of that result. Here's one that uses complex numbers. Given ABC, we may assume its vertices lie on a circle centered at the origin of a Cartesian coordinate system. Let's think of points in the plane as complex numbers. Define H = A + B + C, a simple symmetric function of all the vertices. In fact, H is the common point of the three altitudes of the triangle. Indeed, for AH and BC to be orthogonal, the ratio (H - A)/(B - C) must be purely imaginary. But
Crocodile Clips Lesson Plan Crocodile Clips Homepage Mathematics products. Lesson Plan napoleon's theorem(LP0148). Author John Buckley. Learn and explore napoleon's theorem. Resources. http://www.crocodile-clips.com/gpv70/LP/mathematics/LP0148/LP0148.htm
Extractions: Mathematics products Author: John Buckley Published: th September 2002 Age group: Student activity: Simulation files: Learning objectives Allow investigation of the relationship between equilateral triangles constructed on the sides of an arbitrary triangle. Learn and explore Napoleon's theorem. Resources Procedure Ensure Crocodile Mathematics 1.2 (or later) is installed and the simulation files and are accessible Introduce and explain the learning objectives listed above. Complete lesson activity Discuss the activity and the related points listed below. Classroom discussion points Assessment lessons@crocodile-clips.com
Crocodile Clips Lesson Activity Student Activity napoleon's theorem (LA0148). Author John Buckley. In this lessonwe will investigate this theorem. Constructing napoleon's theorem (LF0148a). http://www.crocodile-clips.com/gpv70/LP/mathematics/LP0148/LA0148.htm
Extractions: Mathematics products Author: John Buckley Published: th September 2002 Lesson plan: Introduction The French emperor Napoleon (1769 - 1821) is attributed with the discovery of a theorem relating equilateral triangles constructed on the sides of an arbitrary triangle. In this lesson we will investigate this theorem. Constructing Napoleon's theorem (LF0148a) Open the Crocodile Mathematics simulation file Arrange each of the three equilateral triangles so that one edge is coincident with one edge of the blue triangle (put a different triangle on each edge of the blue triangle). Now drag on a scalene triangle and arrange it so that each point is coincident with the centre (pivot) of the three equilateral triangles. What do you notice about the scalene triangle, is there anything special about it? You can check the side lengths by hovering over them with the mouse. Drag on another equilateral. Is it possible to make it exactly coincident with the scalene you dragged on in step 2? Rivet the three coincident lines together and then resize the blue triangle. If you repeat step 2 does the relation you found still hold?
Index A Generalization of napoleon's theorem, napoleon's theorem Explorations.napoleon's theorem (Jessica D. Dwy), Interactive Geometry Problem. http://poncelet.math.nthu.edu.tw/chuan/99s/
Mathematisches Seminar: Geometrie Translate this page Galerie - Bildersammlung. Satz und Beweis napoleon's theorem with 2 Proofs.Geschichte Napoléon Ier, Empereur des Français / Napoleon Bonaparte. http://www.gris.uni-tuebingen.de/gris/grdev/java/geometry/doc/html/MainPage.html
Extractions: mit oder ohne Frames Frank Hanisch G leichseitige Dreiecke - Der Satz von Napoleon hnliche Dreiecke PQR - Verallgemeinerung Fall 1 hnliche Dreiecke LMN - Verallgemeinerung Fall 2 P flasterung - Auspflasterung der Ebene G alerie - Bildersammlung Satz und Beweis: Napoleon's Theorem with 2 Proofs Geschichte: Napoleon Bonaparte Geometrie: Triangle Centers Mathematik: Math Forum Programm: JavaSketchpad
Extractions: Geometry Problems Poncelet's Theorem Napoleon's Theorem Eyeball Theorem Steiner's Theorem ... Sangaku Problem (An Old Japanese Theorem) Sangaku Problem 2 Sangaku Problem 3 Butterfly Theorem Langley Problem: 20° Isosceles Triangle ... Morley's Theorem 1. Poncelet's Theorem. Proof Home Top 2. Napoleon's Theorem. Proof Home Top 3. Eyeball Theorem. Proof Given two circles A and B, draw the tangents from the center of each circle to the sides of the other. Then the line segments MN and PQ are of equal length. Home Top 4. Steiner's Theorem. Proof Home Top 5. Carnot's Theorem. Proof In any triangle ABC the algebraic sum of the distances from the circumcenter O to the sides , is R+r , the sum of circumradius and the inradius Home Top 6. Sangaku Problem (An Old Japanese Theorem) Let a convex inscribed polygon be triangulated in any manner, and draw the incircle to each triangle so constructed. Then the sum of the inradii is a constant independent of the triangulation chosen.
Geometry Problems Index Geometry Problems. Poncelet's Theorem. napoleon's theorem. Eyeball Theorem.Steiner's Theorem. Carnot's Theorem. Sangaku Problem 1 An Old Japanese Theorem. http://agutie.homestead.com/files/Geoproblem_A.htm
Napthm napoleon's theorem is the name popularly given to a theorem which states that ifequilateral triangles are constructed on the three legs of any triangle, the http://www.pballew.net/napthm.html
Extractions: and the Napoleon Points Napoleon's Theorem is the name popularly given to a theorem which states that if equilateral triangles are constructed on the three legs of any triangle, the centers of the three new triangles will also form an equilateral triangle. In the figure the original triangle is labeled A, B, C, and the centers of the three equilateral triangles are A', B', C'. If the segments from A to A', B to B', and C to C' are drawn they always intersect in a single point, called the First Napoleon Point. If the three equilateral triangles are drawn interior to the original triangle, the centers will still form an equilateral triangle, but the segments connecting the centers with the opposite vertices of the original triangle meet in a (usually) different point, called the 2nd Napoleon Point.
MATH WORDS, AND SOME OTHER WORDS OF INTEREST If you have suggestions or comments Email to Pat Ballew A B C D E F G H IJ K L M N O P Q R S T U V W X Y Z N Napoleon's Point; napoleon's theorem; http://www.pballew.net/etyind2.html
