 Virtual Optima  Tony Hürlimann, Chris Hürlimann
A company offering consultancy, software (a linear programming language for mathematical optimization and modeling), and sport league schedules. It also offers a book of optimization problems, with sample problems available online.
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 Virtual Paper Cut & Fold  Mike Sokolov
A Java applet and a Flash tool for folding paper online. Make snowflake patterns; learn how to create a fivepointed star with a single cut. With a gallery of folded paper creations.
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 Virtual Polyhedra  George W. Hart
A growing collection of over 1000 virtual reality polyhedra to explore, complementing Hart's Pavilion of Polyhedreality. Includes instructions for building paper models of polyhedra including modular origami, with ideas for classroom use. Each of the
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 Virtual Skies  NASA Ames Education Division
Tutorials, interactive illustrations, career explorations, decisionmaking scenarios, and selftests in each of the following areas: weather, aviation research, airport design, air traffic management, navigation, communication, and aeronautics. A "Teacher's
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 A Virtual SpaceTime Travel Machine  JeanFrançois Colonna, École Polytechnique
Still Pictures and MPEG Animations (Images Fixes et Animations MPEG): Art and Science, Artistic Creation, Astrophysics, Celestial Mechanics, Deterministic Chaos, Deterministic Fractal Geometry, Fluid Mechanics, From the Infinitely Small to the Infinitely
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 Virtual Training Suite: Mathematics  TutorPro
A stepbystep tutorial covering information skills for the mathematics Internet environment. Learn how to use the Internet to help with coursework, literature searching, teaching, or research.
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 Virtual Trips to Black Holes and Neutron Stars  Robert Nemiroff
A published paper understandable to undergraduates: "Visual Distortions Near a Black Hole and Neutron Star," Nemiroff, R. J. 1993, American Journal of Physics, 61, 619. Gravitational Principles and Mathematics; General Description of Visual Distortion
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 Virtual Tutor  Calculus
An Internet service that delivers a tutor containing over 700 calculus problems and their solutions. Topics covered match those presented in most first year calculus textbooks. Each solution contains solution hints and hyperlinks to the relevant theory
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 Virtual University (VU)  Stephan Nicolas
Math lessons: Introduction to Topology; Arithmetic; Introduction to Probability; Mathematical Approach to Probability; Random Variables, Expected Value, Variance.
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 Visible Euclidean Algorithm: finding greatest common divisors  Paul Garrett
Enter two positive integers, and click the button to see the operations of the Euclidean Algorithm.
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 Vision Props of Signed Numbers (SMILE)  Mable McMiller, South Shore High School
A lesson designed to teach students about the number line and signed numbers by working with acid and alkaline solutions. From the Algebra and Trigonometry section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative
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 Visions Of Chaos  Jason
A Windows application that generates fractals, cellular automata, attractors and other chaos simulations. Supports 2D images, 3D images and AVI movie creation. With galleries of fractals and Mandelbulbs; cellular automata and Lsystems music; and chaos
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 Visiting Artlandia  Ivars Peterson (MathTrek)
Have you ever admired any of the bold, colorful designs splashed across a variety of fabrics used for scarves, neckties, shirts, and other apparel? There's a chance that you may come across the work of a physicist. Igor Bakshee got into fabric design
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 A visit to James Clerk Maxwell's House  MacTutor Math History Archives
Linked essay outlining the life and work of Edinburghborn mathematician James Clerk Maxwell, with an outline of his childhood, pictures of his home, some mathematical poetry, and references (books/articles).
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 ViSta: the Visual Statistics System  Forrest W. Young
ViSta features visual tools for revealing structure in data; for showing the results of statistical analyses; for guiding the analyst through an analysis; and for structuring the analyst's data analysis process. ViSta is designed for a wide range of users,
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 Visual Calculus (Mathematics Archives)  Larry Husch; University of Tennessee, Knoxville (UTK)
A collection of notes that give some ideas how technology, in particular computers, can be used in the teaching of calculus. Detailed instructions on implementing these ideas with various public domain, shareware and commercial software packages are provided.
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 A Visual Dictionary of Special Plane Curves  Xah Lee
Materials that demonstrate interesting properties of plane curves visually. Many concepts or properties of plane curves, such as cusp, tangent, evolute,
involute, or envelope, are more readily explained by an illustration or animation. The mathematics
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 Visual Fractions  Richard E. Rand
A site with 19 Java programs that provide instruction and practice in identifying, renaming, adding, subtracting, multiplying, and dividing fractions. Number lines are drawn to demonstrate each example. Programs include: Identify Fractions; Identify Mixed
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 Visual Insight  American Mathematical Society
A "place to share striking images that help explain advanced topics in mathematics," as edited by John Baez. Twice monthly posts, which date back to August, 2013, have included "Atomic Singular Inner Function," "Catacaustic of a Cardioid {6,3,3}," "Honeycomb
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 Visual Intelligence: How We Create What We See  Donald D. Hoffman
Visual intelligence, cognitive scientist Donald Hoffman writes, is the power that people use to "construct an experience of objects out of colors, lines, and motions." The site includes: places to buy the book; the text of the preface; and animations
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 Visualization Laboratory of Geometric Objects  Mathematics Dept., Universidad Autónoma de México
An electronic journal and works from professors, researchers and students from the Mathematics department of the School of Science of the Universidad Autonoma de Mexico, with a gallery of geometric objects (fractals), and links to other Web pages. Versions
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 Visualization of Complex Dynamical Systems  Visualization and Animation Group, Institute of Computer Graphics, Vienna University of Technology
Software or technical reports to download (in gzipped PostScript format) related to the graphical representation of complex dynamical systems.
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 Visualizing An Infinite Series  Cynthia Lanius
This lesson uses a trapezoid successively divided in 4ths as a visual representation of an infinite geometric series, a mathematical concept that is often only treated symbolically. Explorations are outlined for investigating a number of series, and links
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 Visualizing complex analytic functions using domain coloring  Hans Lundmark; Linköping University, Sweden
An article that illustrates graphically some properties of complex analytic functions (also known as holomorphic functions), explaining how complexvalued functions can be visualized using domain coloring.
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 Visualizing Math
Tumblr of mathematical images begun June, 2013, by two high school students from Minnesota. Images have included "A panorama on a Möbius strip," "Fractal Trees by Robert Fathauer," "elegantly constructed proofs through visual inspection," "animation
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 Visualizing Mathematics  Yerushalmy, Shternberg, Cohen, Talmon
A computeroriented inquiry curriculum for secondary mathematics. Visual Mathematics software programs include Calculus Unlimited; The Geometric Supposer; Modeling: MoveOn, The Function Sketcher & and Escalator. With descriptions, screen shots, ordering
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 Visualizing the Behavior of Functions  Cuoco
Cabri Geometry II figures and a macro accompanying the article "Visualizing the Behavior of Functions" by Albert A. Cuoco in the Technology Tips column of Mathematics Teacher magazine.
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 Visual Mathematics (VisMath): Art and Science Electronic Journal of ISISSymmetry  Nagy, Jablan
The electronic journal of ISISSymmetry (International Society for Interdisciplinary Studies of Symmetry), published by the Mathematical Institute, Belgrade, Yugoslavia. Papers, conferences, the Nexus Network Journal of Architecture and Mathematics Online,
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 Visual Math for Java  Dr. Weiguang Huang
The Java applet Visual Math is an online symbolic math and computer algebra system powered by SymbMath. SymbMath (an abbreviation for Symbolic Mathematics) is a symbolic, numeric and graphic computing environment that performs exact numeric, symbolic
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 Visual Math: Functions  Centre for Educational Technology (CET)
Activities, tools, and tasks for learning about linear and quadratic functions.
Contents: Linear Functions  Functions Defined on Intervals  Equivalent Expressions of Functions  Addition and Subtraction of Linear Functions  Transformations of Graphs
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 VisualMath  G. Fonthal, VisualPhysics
Math shareware programs that feature visual and interactive techniques under Windows 95 may be downloaded from this site: for numbers (real, complex, binary); set theory (Venn diagrams); geometry (shapes and areas, 3D Geometry); algebra (equations, polynomials,
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 Visual Math Institute  Ralph Abraham, Director
Created in 1975 to administer grants from the State of California and the NSF. The "Visual Math Project" was created at UCSC for the development of computergraphic based materials for teaching university math: precalculus, calculus, linear algebra, and
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 Visual Math Learning: An interactive multimedia tutorial  Wayne Allen Bateman
An online tutorial, intended to teach students basic math concepts using interactive multimedia for aid in visualization. Proceed through the text (more sections are planned), or work with the individual exercises separately.
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 VisualMath  Software And Engineering Co.
A graphic language for solving all types of problems, providing over 80 components, all of which are capable of using matrix input. Many dialogs are used to define properties. A special 3D plotter and table viewer show the results of the solution. VisualMath
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 Visual Modelling Group  University of Brighton
This research group focuses on giving formal semantics to existing notations, developing new visual notations, and reasoning with them. The Visual Modelling Group has developed a constraint diagram notation that visually expresses mathematical constraints
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 Visual Numerics  Visual Numerics, Inc.
Provider of powerful numerics, graphics, data analysis, and charting solutions. IMSL C and C++ Numerical Libraries; Exponent Graphics Home Page and Exponent Graphics Plot Types; IMSL FORTRAN Libraries.
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 Visual Patterns  Fawn Nguyen
Visual patterns to extend and express algebraically, following the prompts on an accompanying handout. Nguyen, who teaches middle school math in California, has posted graphic arrays since December, 2012.
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 Visual Plane Geometry  Edu2000 America Inc.
A full curriculum on CDROM for Windows and Mac, combining hypertext and QuickTime animations to illustrate basic plane geometry concepts, triangles, polygons, circles, and the threedimensional world. Familiar real world examples help students visualize
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 Visual Solid Geometry  Edu2000 America Inc.
A full curriculum on CDROM for Windows and Mac, combining hypertext, graphics, and QuickTime animations to illustrate solid geometry concepts, polyhedra and solids of revolution, and surface areas and volumes of solid figures. Typical "experiments"
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 Visuals Patterns in Pascal's Triangle (SMILE)  Ulysses Harrison, Dunbar Vocational High School
A lesson for grades 5 and up that uses a phenomenological approach to show students the many visual and number patterns present in the sequence of numbers in Pascal's Triangle, and to encourage them to explore the patterns on their own. From the Patterns
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 Visual Structure of Postulates and Axioms in Algebraic Operations
(SMILE)  Sanford Olshan, Roosevelt High School
A lesson designed to reinforce and retain the use of axioms and postulates in various proofs and linear transformations of equations; and to have student build a physical model of the game of "PRUFF" either as a card game or as a board game. From the
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 Visual Thought
A crossplatform diagramming & flowcharting tool running on Windows 95/NT and UNIX. Visual Thought moves ideas onto the screen quickly by making it easy for the user to draganddrop shapes and make rubberbanding connections between objects. It is
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 Vizual Statistix  Seth Kadish
Blog of statistics graphed by a Geoscience PhD who describes data visualization as his passion. Posts, which date back to January, 2012, have included "A Summation of Square Usage over 432 Chess Games"; a tiled plot showing the number of unique configurations
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 Vladimir Trifonov's Research Page  Vladimir Trifonov
The site includes papers "Natural geometry of nonzero quaternions" (International Journal of Theoretical Physics 46 (2) (2007) 251257) and “GRfriendly description of quantum systems” (IJTP, DOI 10.1007/s1077300794743).
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 Vladimir Voevodsky
Lectures, publications, a library of Coq files, and more by the mathematician developing univalent foundations, which start with a view of mathematics where sets parametrize collections of objects without "internal structure" while more general homotopy
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 Vocabulary PuzzleMaker  Glencoe Online
Make the following types of puzzles to go along with your Glencoe text in prealgebra through geometry: crossword, word search with words, word search with clues, or jumble. Available for free download in both Windows and Macintosh formats.
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 Voce Viva ScriviFacile  Danieli Alessandro, SLD Software (Scribit&Legit&Dicit)
Interactive software for the four basic operations and algebraic expressions, primarily in Italian. "Dimostrazione del software Voce Viva ScriviFacile, con sintesi vocale e con comunicazioni vocali interattive che guidano nello svolgimento delle divisioni
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 Volume and Surface Area (SMILE)  Charlotte Goldwater, Kenwood Academy
A lesson for grades K12 designed to teach students to understand the difference between surface area and volume. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative
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 Volume of a Tank  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about finding the volume of cylinders, cones, oblate spheroids, and other tanks, such as "How can I calculate volume of liquid in a cylinder that's not full and lying horizontally?"
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 Volume of a Torus  Paul Kunkel
An investigation into and explanation of the volume of a torus.
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