- 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 TI-85 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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- Approaches to High School Mathematics - Martin Cohen
A short essay and examples of ways of teaching high school level mathematics so as to make it more interesting, by a computer programmer. Topics: Use of Slide Rule as a Teaching Tool; Teaching Geometric Series; Rotations and Revolutions; and some problems.
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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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- The Area of a Circle - Jon Basden, Highland Middle School
A one- or two-period lesson plan in which students use work sheets to cut circles into sectors, rearrange them, and derive the formula for the area of a circle.
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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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- Becoming Archimedes - Samir Boulos
Imagine you are living in the era of Archimedes (287-212BC). Calculus (the study of differentiation and integration) has not yet been invented. You want to find the area of a circle of radius 2 meters. You can't use the equation for the area of a circle,
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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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- Bicycles - John P. Crotty - Yale-New Haven Teachers Institute
A unit designed to show how to use bicycles to teach mathematics and science, with applications to program in a computer class, experiments, and an appendix that discusses approximate numbers and significant digits.
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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((s-a)(s-b)(s-c)(s-d)) 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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- Calculating Cones - Monika Schwarze and Bianca Gonterney
A complete lesson plan including all materials, emphasizing a challenging and motivating method for self-guided and co-operative learning.
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- The Catenary - Samir Boulos
An article addressing the questions that arise when describing a suspended chain: the mathematics, physics and applicability of the catenary shape.
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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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- The Chryzodes (Golden Writing on a Circle)
Un voyage en Images dans la science des nombres (Arithmétique) - graphic patterns of phenomena connected to arithmetical congruences. Using circles to represent numbers; an investigation into the grammar of shapes and resonances where simple multiplication
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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
Whole-class 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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- Classic Curves - Paul Bourke
A list of common curves. Each one gives the name, the mathematical formula, and an example showing the general form. Formulas are either described in cartesian coordinates (x,y) or polar coordinates (r,theta). a and b are used to represent constants.
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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 90-degree 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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- Data Analysis and Geometrical Systems - Elaine Young; University of Oklahoma
Illustrated introductions, with vocabulary glossaries, to concepts of probability, statistics, and geometry. Probability covers simple probability, conditional probability, joint probability, odds, and permutations; statistics covers statistical graphs,
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- Defining Geometric Formulas (Ask Dr. Math FAQ) - Math Forum
Definitions of two- and three-dimensional 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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- Discovering Pi (CEC) - Jack Eckley, Sunset Elem., Cody, WY
A geometry lesson plan for grades 5-7: Measure the circumference and diameter of an object to the nearest millimeter; explain how the number 3.14 for pi was determined; demonstrate that by dividing the circumference of an object by its diameter you end
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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 cross-section, 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; L-curves; 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 9-point 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 9-point 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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