 About Ellipses  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about ellipses, such as calculating their areas and perimeters, graphing them, and determining equations for them.
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 About Rainbows  Beverly T. Lynds
A tutorial on the physical nature of the rainbow, with graphics and text references. The traditional rainbow is sunlight spread out into its spectrum of colors and diverted to the eye of the observer by water droplets. The "bow" part of the word describes
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 Algebra (Seeing is Believing)  De Silva, D'Andreti; ThinkQuest 1997
An algebra tutorial, comprising: mathematical numbers; real number system; numerical representations in algebra (algebraic expressions); algebraic techniques (factoring); quadratic equations and inequalities; graphing (coordinate systems, conic sections,
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 Andy Norton's Web Page  Dept. of Mathematics Education, Univ. of Georgia
Illustrated essays and explorations of algebra and geometry using various technology, including TI85 calculators, CBL's and computer software such as Geometer's Sketchpad (with sketches to download), Algebra Expressor, and Excel, by a grad student in
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 Approximating the area of a unit circle with regular polygons  Lisa Markus; Furman University, Greenville, SC
A Java applet for the area of a circle of radius 1. Enter the number of sides, from 3 to 1000, draw the polygon, and see the corresponding area.
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 Area and Diameter  NASA Lewis Learning Technologies Project
Mrs. Bosley wants a big round piece of plastic to throw over her little boy's round sandbox to keep the sand clean. The sandbox has a diameter of 3 meters. Approximately how big will the round piece of plastic need to be? A detailed answer is provided.
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 Area and perimeter  Mark Motyka, Math League Multimedia
Definitions and illustrations: Area; Area of a square; Area of a rectangle; Area of a parallelogram; Area of a trapezoid; Area of a triangle; Area of a circle; Perimeter; Circumference of a circle.
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 Area of a Circle  Jon Seaton
Enter a radius, diameter, circumference, or area of a circle, and this simple JavaScript calculator returns all of those measures.
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 Area Of A Circle  Kuldeep Kaur
Lessons and worksheets to find the area of a circle. Kaur has posted stepbystep instructions through this blog, which dates back to December, 2011.
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 The Area of a Circle (SMILE)  Edwina R. Justice, Gunsaulus Academy
A grade 8 lesson designed to teach the relation between circumference and diameter and how that relation, called pi, is used in the formula for the area of a circle. From the Geometry and Measurement section of a collection of almost 200 single concept
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 The Area of a Circle (Version 2.0) (SMILE)  Edwina R. Justice, Gunsaulus Academy
A grade 8 lesson designed to review areas of plane figures; determine the relation between the circumference and diameter of a circle; show the geometric representation of the area of a circle as the shape of a parallelogram; and use the formula for computing
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 Beyond the Ellipse  Ivars Peterson (MathLand)
There's a simple trick one can use to draw an ellipse. Tie the ends of a length of string to two pins (or thumbtacks) stuck in a sheet of paper on a drawing board. Then, keeping the string taut with the point of a pencil, allow the pencil to trace a path
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 Bob's Pages  Bob Allanson
A collection of geometry applets. Generate and modify polyhedra, investigate the Mandelbrot and Julia sets, or experiment with Pappus's arbelos, the porisms of Poncelet and Steiner, and a logarithmic spiral.
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 The brachistochrone problem
 MacTutor Math History Archives
Linked essay on the brachistochrone problem, posed by Johann Bernoulli in Acta Eruditorum in June, 1696. With references and other related web sites.
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 Brahmagupta's Formula  Jim Wilson, Dept. of Mathematics Education, Univ. of Georgia
Problem: Develop a proof for Brahmagupta's Formula, which provides the area A of a cyclic quadrilateral (i.e., a simple quadrilateral inscribed in a circle) with sides of length a, b, c, and d as A = sqrt((sa)(sb)(sc)(sd)) where s is the semiperimeter
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 Cabri Conic Macros  Jim King, University of Washington
Nine Cabri Geometry II macros for constructing conics from various givens and for constructing certain features of given conics. Contains a documentation file.
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 CalculateWhat  Colin Fagras
Free online calculators. In addition to covering math topics such as algebra, geometry, and statistics, CalculateWhat crunches numbers on topics financial, scientific, and  under a category called "miscellaneous"  more whimsical and topical in nature.
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 Calculating Cones  Monika Schwarze and Bianca Gonterney
A complete lesson plan including all materials, emphasizing a challenging and motivating method for selfguided and cooperative learning.
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 Center for Technology and Teacher Education  Curry School of Education, University of Virginia
An interdisciplinary group that develops materials to prepare teachers to use technology to enhance and extend students' learning of mathematics. This site offers activities using graphing calculators, The Geometer's Sketchpad, Microsoft Excel, the ExploreMath.com
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 Chase Four Sketches  Bill Finzer, Key Curriculum Press
A sketch and a script to answer the question: if there are four ants in the plane and each crawls continuously toward the next ant, what do their paths look like?
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 Circle Drawing Experiment  Thomas Denney
Draw a figure on the grid by clicking and dragging. Upon release of the mouse button, this JavaScript calculates a "perfect circle" accuracy score by using the sketch's perimeter as the circumference of a perfect circle, and comparing its area to the
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 Circle Formulas  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about circle formulas, including how to find their circumferences and areas.
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 Circles  360 Degrees  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about why a circle has 360 degrees, and the origin of that degree measurement.
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 Circles and Spheres (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on circles and spheres.
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 Circles  Diameter, Circumference, Radius and the Discovery of Pi (SMILE)  Kathleen Ryan, Randolph Magnet School
A 7th grade lesson designed to help students identify and measure the diameter, circumference, and radius of a circle. The students discover the approximate value of pi through the relation between the diameter and circumference. From the Geometry and
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 Circles in Geometry  Lesson Ideas: Math: Geometry; Teachnet.Com
Wholeclass and group activities for teaching circle concepts, pi, circumference, etc.
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 Circumference of an Ellipse (Ask Dr. Math FAQ)  Math Forum
A discussion of the derivation of the formula for the circumference of an ellipse. Also discussions of the evaluation of the formula, and approximating the circumference.
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 Circumferences, Diameters, and Radii (SMILE)  Dwayne Belle, Fuller School
A lesson designed to teach students to measure circumferences in inches, and compute radii and diameters, given different circumferences. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and
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 The Coffeecup Caustic  Roy Williams
You are drinking from a cylindrical cup in the sunshine. Sometimes, when the sun shines into the cup, you can see a crescent of light as the sunshine reflects from the inside of the cup onto the surface of the drink. This Java applet illustrates the optics
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 Cone, Cylinder Edges?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about whether cones or cylinders have edges, such as "Does a cone have an edge? A vertex?"
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 Cone Layout  Jock Dempsey, Dempsey's Forge
A flat layout showing that the ratio or percentage of the layout circle is also the sine of half the angle of the top of the cone. If you want a cone with a 90degree point, the ratio is the sine of half the angle of the point.
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 The Conic Sections in Polar Coordinates  David Arnold; Mathematics Dept., College of the Redwoods, CA
An interactive study of the polar form of the equation for a conic section, for readers familiar with polar coordinates and triangle trigonometry. This activity is also a vehicle for the introduction of the Geometer's Sketchpad, though no prior experience
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 Conics (Manipula Math)  International Education Software (IES)
Java applets to investigate the conic sections, including different ways to draw them, their reflective properties, and the shapes traced by shadows at different latitudes.
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 Covering Up (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
Have you ever wondered why the cover of a manhole is nearly always round? Why couldn't it be oval or square? The usual answer is that a circular lid, unlike a square or an oval cover, won't fall through the opening, but the circle isn't the only shape
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 Cuisenaire Math  ETA/Cuisenaire
From the makers of Cuisenaire Rods: Connecting Cuisenaire Rods, Cuisenaire Roddles (board games and puzzles that emphasize spatial reasoning skills), Cuisenaire Rods for the Overhead, Magnetic Cuisenaire Rods, and other manipulatives. Publications include
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 Curves on Baseballs  Ivars Peterson (MathTrek)
It's that time of year again (at least in North America), when the thoughts of many sports fans turn to baseball. Over the years, the game has also attracted the attention of mathematicians and statisticians intrigued by the rules, geometric considerations,
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 Defining Geometric Formulas (Ask Dr. Math FAQ)  Math Forum
Definitions of two and threedimensional figures in general, and a note on dimensions.
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 Designs with Circles  Suzanne Alejandre
A Math Forum Web Unit. Includes some background on circles in Islamic cultures, and an activity exploring the geometry involved in some circle designs.
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 Dirichlet Sketches  Jim King, Key Curriculum Press; Math Forum
Three sketches showing the Dirichlet or Voronoi regions corresponding to configurations of 3, 4, or 5 points.
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 EggMath  Bradlow, Sullivan, Levy, UIUC
A collection of modules (including many interactive applets) for K12 classrooms, based on the theme of eggs. Topics include: the shape of an egg (addressing symmetry and crosssection, surfaces of revolution, pin and string construction of ellipses, Cartesian
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 Elliptic Curves  Stéfane Fermigier
A collection of links on research articles on elliptic curves and related topics (applications, modular forms, Fermat's Last Theorem). Algorithmic applications; Modular forms aspects; Lcurves; High rank curves; Heights. Bibliographies. Some papers in
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 Elliptic Functions and Integrals  MacTutor Math History Archives
Linked essay covering 1655 through 1694, with accompanying description of the subject and 8 references (books/ articles).
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 Erich's Packing Center  Erich Friedman
A huge collection of packing problems, each explained with graphics. 2D examples include Triangles in Squares, Circles in Squares, Squares in Squares, Triangles in Triangles, Circles in Triangles, Squares in Triangles, Triangles in Circles, Circles in
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 Essay Ideas  Jim Wilson, Dept. of Mathematics Education, Univ. of Georgia
For a course on Using Computers in Mathematics Instruction. Friday the 13th (show there are at most three and at least one Friday the 13th in each year, consider when two consecutive months can be have Friday the 13th); Gingerbread Man (a Microsoft Excel
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 The Euler Line and the 9point Circle  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A geometric explanation of the Euler Line  how complex numbers give us a broader outlook on the geometric configuration  and the 9point circle of a triangle ABC, which passes through the feet of the three altitudes, the midside points of ABC, and the
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 Examples of Essays  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Extended Concurrencies of the Triangle, J. Wilson; Parabolas Inscribed in a Triangle, G. Giddings; Polygonal Spirals, L. Shook and M. Callinan; Roots 2 and 5, J. Wilson; Those Amazing Palindromes, Shareef Bacchus; Tangrams, Greg Huberty; Phi: That Golden
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 Exercises in Math Readiness for University (EMR)  Dept. of Mathematics and Statistics, University of Saskatchewan
A collection of exercises with solutions/tutorials for high school mathematics topics important for university study in mathematics, sciences, engineering and commerce. Exercises at three degrees of difficulty, covering graphing, solving inequalities,
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 ExploreMath.com  Third Millennium Press
Shockwave activities illustrating realtime correlations between equations and graphs to help students visualize and experiment with concepts from elementary algebra through precalculus: experiment with the graphs of functions, systems, and complex numbers.
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 Exploring Parabolas (JavaSketchpad) (MSTE)  James P. Dildine; University of Illinois at UrbanaChampaign (UIUC)
Directions and descriptions for creating and simulating the creation of a parabola. The creation takes place within a Java Window in the browser and allows the user to interact with the sketch of a parabola he or she creates. The page includes tips and
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 Families of Conics  L. J. Dickey, U. of Waterloo
Seven Cabri Geometry II figures illustrating families of conics associated with the configurations of Pappus and Pascal.
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