81. Triangle Triangles are uniquely determined by specifying three sides (SSS theorem), two anglesand a side (AAS theorem), or two sides with an adjacent angle (SAS theorem http://mathworld.pdox.net/math/t/t285.htm

Triangle A triangle is a 3-sided Polygon sometimes (but not very commonly) called the Trigon . All triangles are convex. An Acute Triangle is a triangle whose three angles are all Acute . A triangle with all sides equal is called Equilateral . A triangle with two sides equal is called Isosceles . A triangle having an Obtuse Angle is called an Obtuse Triangle . A triangle with a Right Angle is called Right . A triangle with all sides a different length is called Scalene The sum of Angles be Parallel to ) in the above diagram, then the angles and satisfy and , as indicated. Adding , it follows that since the sum of angles for the line segment must equal two Right Angles Let stand for a triangle side and for an angle, and let a set of s and s be concatenated such that adjacent letters correspond to adjacent sides and angles in a triangle. Triangles are uniquely determined by specifying three sides ( SSS Theorem ), two angles and a side ( AAS Theorem ), or two sides with an adjacent angle ( SAS Theorem ). In each of these cases, the unknown three quantities (there are three sides and three angles total) can be uniquely determined. Other combinations of sides and angles do not uniquely determine a triangle: three angles specify a triangle only modulo a scale size ( AAA Theorem ), and one angle and two sides not containing it may specify one, two, or no triangles (

82. Geometria JavaScript. Exercises. Projects. First Examples. Varignon's theorem; Napoleon'stheorem; Parabola; Nonaffin Mapping; Pick's Formula; Matrix Multiplication; http://www.joensuu.fi/mathematics/DidMat/Ehmke/seminar-joensuu/first_examples.ht

Home First Examples Resp. Analysis JavaScript ... Projects First Examples Varignon's Theorem Napoleon's Theorem Parabola Non-affin Mapping ... Zeros of Parabola

83. Introduction To Geometry: Course Schedule Assignment Read 5.6. Do Exercises 5.6 4,6,8. Fri. 10/12, Fagnano's theorem; Napoleon'stheorem; Fermat's Point. Assignment Read 5.7. Do Exercises 5.7 2,3,4. Mon. http://campus.northpark.edu/math/courses/Math_3010/schedule.html

Introduction to Geometry: Course Schedule The assignments from each week are due on the Wednesday of the following week. It is preferred that each day's assignment be stapled and labeled separately. Date Content Mon. 8/27 Discussion "What is Geometry?" The problem with Euclid. The use of axioms. The Incidence Axioms. The role of models. Assignment: Read 2.3. Do Exercises Wed. 8/29 Distance and Metrics Betweeness Assignment: Read 2.4. Do Exercises Fri. 8/31 The Angle Axioms and the Protractor Postulate Using Geometer's SketchPad Assignment: Read 2.5. Do Exercises Wed. 9/5 Triangles and Congruence Assignment: Read 3.1. Do Exercises Fri. 9/7 Motivating Theorems Congruence Theorems Methods of Proofs Proof by Contradiction Proof of Set Equality Assignment: Read 3.3. Do Exercises Mon. 9/10 Review of possible Congruence Theorems Hyperbolic and Spherical Triangles Theorems 1 and 2. Assignment: Read 3.4. Do Exercises Wed. 9/12 Corrections: Proof of the Saccheri-Legendre Theorem Ptolemy's Theorem and Orthogonal Circles Corollaries of the Exterior Angle Theorem Assignment: Read 3.5. Do Exercises

84. Site Map These pages contain several examples of a quincunx, and simple explanationsof these concepts. Central Limit theorem Applet R. Todd Ogden; Dept. http://www.mccallie.org/myates/5lessonplansonline.htm

Site Map Home Lesson plans and units on-line Biology: Complete Population Growth and Balance Lesson including a computer model as well as all the biology and mathematics behind it. (installed July 21, 2000) When am I ever going to use that? Applications of Mathematics Lessons linked to specific occupations encourage students to see where applied courses can take them in the real, working world. Over a thousand years ago, artisans in the Islamic world began to develop a system for constructing intricate geometric art based on radially symmetric starlike figures. This site has an applet that lets you create your own, plus descriptions of the various patterns. Visual Geometry Pages are an online geometry book. It is a book illustrating problems from differential geometry and mathematical visualization using applets, images, animations, and Java software. For some really really terrific eye candy on the most complex shapes imaginable: i-Math Investigations are ready-to-use, online, interactive, multimedia math investigations. Complete i-Maths include student investigations, teacher notes, answers, and related professional development activities. (Not every i-Math is currently complete, but they are all ready to be used. To get an idea of what a complete i-Math looks like, see Shedding Light on the Subject: Function Models of Light Decay Interactive Tools for Mathematics Investigations The following tools are available for public use provided that you do not charge for any use of the tools and you include a reference to the NCTM Illuminations web site:

85. NRICH | December 1998 | 15+ Problems | Napoleon's Theorem (Dec 98) The Nrich Maths Project Cambridge, England. Mathematics resources for children, parents and teachers to enrich learning. Published on the 1st of each month. Problems, children's solutions, interactivities, games, articles, news http://nrich.maths.org/mathsf/journalf/dec98/just_mcprob5.html

Problems See solution NRICH Prime NRICH ... Get Printable Page March 03 Magazine Site Update News Events Problems Solutions ... Games Archive Problems Solutions Articles Inspirations ... Interactivities Web board Ask NRICH Asked NRICH NRICH Club Register Tough Nuts About Help! ... Where is NRICH? Associated Projects Maths Thesaurus MOTIVATE EuroMaths Millennium Maths ... Project Display maths using fonts images Help Back Issues Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 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 Napoleon's Theorem (Dec 98) 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 Similar Problems: Geometry-Euclidean Properties of Shapes Polygons Return to top

86. Preprints 1998 Schwerkraftwirkung MSC 76B10. 9820 Martini, H.; Weißbach, B. Napoleon'sTheorem with Weights in n-Space MSC 51N10, 51N20. 98-19 http://www.math.uni-magdeburg.de/preprints/98.html

Preprints 1998 Preprints Preprints 1998 V. John; L. Tobiska Smoothers in Coupled Multigrid Methods for the Parallel Solution of the Incompressible NavierStokes Equations MSC: 65M55, 65N22, 65N55, 65Y05 published in : Int. J. Num. Meth. Fluids 33, 453 - 473, 2000 with the title 'Numerical Performance of Smoothers in Coupled Multigrid Methods for the Parallel Solution of the Incompressible NavierStokes Equations' ) Sofiane Gasmi; Ernie Love; Waltraud Kahle A general repair/proportional hazards framework to model complex repairable systems MSC: 60K10, 60K05, 62F10 Sotskov, Y.N.; Tanaev, V.S.; Werner, F. Scheduling problems and mixed graph colorings MSC: 90B35, 05C15 published in : Optimization, Vol. 51 (3), 2002, 597 - 624.) Juhnke, F.; Sarges, O. Minimal spherical shells and linear semi-infinite Optimization MSC: 52A40, 90C34 Christoph, G.; Schreiber, K. Rates of convergence to stable and discrete stable laws MSC: 60E05, 60F05, 60E07 published in : Probability Theory and Mathematical Statistics, Proceedings of the 7th Vilnius Conference (1998), Grigelionis, B. (ed.) et al., S. 147-156. ) Knobloch, Petr; Tobiska, Lutz

87. ´X¦ó§@¹Ï¥Ø¿ý The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://140.114.32.3/summer99/18/page2.html

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88. Www.math.temple.edu/~zeilberg/mamarim/mamarimTeX/Gtext Don't worry, none of the definitions are circular. Example Look up Napoleon'sTheorem. It involves two definitions ItIsEqui and CET. Look up ItIsEqui. http://www.math.temple.edu/~zeilberg/mamarim/mamarimTeX/Gtext

" (without the quotes); once inside Maple, #type: "read text; <2 then ERROR(`Need at least two Pts`): fi: for i from 3 to nargs do if AREA(args[1],args[2],args[i])

89. Circle Centres Using SketchPad Notes (1). All of these filenames in this page are LONG! Therefore,if you want to preserve these (Because Version 3.* of SketchPad http://www.mfdabbs.pwp.blueyonder.co.uk/Maths_Pages/SketchPad_Files/Triangles/In

Circle Centres: SketchPad Files Home Maths Excel About Me ... Triangles Notes: (1). All of these filenames in this page are LONG! - Therefore, if you want to preserve these (Because Version 3.* of SketchPad does not use long filenames) you must either RIGHT-CLICK on the file links within the above directories and then choose "Save Target As...". This allows you to save the file directly to a disk/drive or after using a LEFT-CLICK select the "Save this file to disk" Option Box rather than selecting the "Open this file from its current location". If you choose this last option then Geometer's SketchPad will automatically open - if you have it! - but then after viewing the file if you then try to save it you will not be able to use a long filename. Sketches D - Centroid Sketch.gsp D - Circumcentre with Radius.gsp D - Fermat Point.gsp D - Incentre and Excircles.gsp ... Triangles

90. Geometries A Survey on Geometries. Euclidean Geometry, Spherical Geometry, Hyperbolic Geometry,Projective Geometry, Transformation, Symmetry. Instructor Dr. Z. Shen. http://www.math.iupui.edu/~zshen/teaching/m463spring2002/

A Survey on Geometries Euclidean Geometry, Spherical Geometry, Hyperbolic Geometry, Projective Geometry, Transformation, Symmetry Instructor : Dr. Z. Shen Office : LD 224Q Classroom : SL 137 : MW 4:00P-5:15P Email zshen@math.iupui.edu Phone Office Hour : MW 1:30P-2:30P Syllabus Homework Updated Scores Euclidean Plane Geometry (an outline by Z.Shen) ... Napoleon's Theorem Other links: Euclidean Plane Geometry Non-Euclidean Geometries Transformations

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