 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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 Volume of Water in an Aquarium  NASA Lewis Learning Technologies Project
How much water will fit in an aquarium that is shaped like a box and is 10 inches high, 6 inches wide, and 14 inches long? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Voronoi Art  Scott Sona Snibbe
Using a retroreflective floor to display the Voronoi diagram of people walking on it, exploring notions of personal space and individualgroup relations. See also Scott's other projects.
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 Voronoi Diagrams of Points, Segments and Arcs in 2D  Martin Held
VRONI is a software package for computing Voronoi diagrams of points and line segments in the Euclidean plane. Based on the Voronoi diagram, VRONI can also compute offset patterns or perform buffering. Since VRONI computes a Voronoi diagram of points
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 The Voronoi Web Site  Christopher Gold; Université Laval
A site established to encourage communication between workers (academic or commercial, users or developers), using Voronoi or Delaunay methods of spatial analysis, in the hope that the exchange of ideas in this field among a wide variety of users will
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 Vortex Leapfrogging Interactive Pages  Amanda Johns, The University of Surrey, England
Interactive experiments in fluid dynamics, in particular, the motion of vortices: "A vortex is a spinning energy wheel. When you take the plug out of a bathtub, you will see that the water creates a vortex as it runs down the drain. In common usage, by
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 Voyager Learning Math Solutions  Cambium Learning, Inc.
Math curricula and programs from "your comprehensive intervention partner": Inside Algebra, Voyager Online Algebra, Vmath Summer Adventure, VmathLive, Showtime! Math, Vmath, TeachingBOT, and TransMath.
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 Voyager Sopris Learning  Voyager Sopris Learning, Inc.
Researchbased curricula, targeted interventions, assessments for Dynamic Indicators of Basic Early Literacy Skills (DIBELS), positive school climate resources, and professional services to educators working with preK12 students who have special needs
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 vrml.calculus.net (calculus@internet)  Curtis, Davis, Wayand
The visual study of threedimensional calculus using the power of VRML  Virtual Reality Modeling Language. The next generation of calculus course materials. Text in progress: Virtual Reality & 3D Calculus  addressing the question how virtual reality
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 VRML Gallery of Electromagnetism  Rob Salgado
A collection of VRML worlds that visualize the vector fields of electromagnetism. Subcategories: addition; wedge product; raising and lowering of indices; unit vectors; charged point (Coulomb); two charged points; charged dipole; charged sphere; charged
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 VulcanSoft
Win95/NT4 software. Includes a measurement converter with 15 categories and over 270 different measurement units, a financial calculator with 14 different financial calculations and table output, and a city distance calculator with over 1900 cities, which
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 Vygotsky  Cristina Guerra
A brief description of Vygotsky's theories about thought, language, and intellectual development.
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 Vygotsky's Distinction Between Lower and Higher Mental Functions and Recent Studies on Infant Cognitive Development  Eugene Subbotsky; Psychology Department, University of Lancaster, UK
One of the major theoretical advances of Vygotsky's approach to cognitive development was his thesis that human mental functions are social in origin. In making this claim, Vygotsky was confronted with the difficulty of reconciling it with the fact that
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 Vygotsky  Trish Nicholl
This paper includes sections entitled Higher and lower mental functions; Intramental vs intermental abilities; The zone of proximal development (ZPD); Psychological tools; and Semiotic potential and the decontextualisation of mediational means. With references.
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 Waldomaths  Ron Barrow
Original applets on number, algebra and graphs; shape, space and measure; probability and data handling, including histograms; investigative tools (quadratic and cubic sequences); core (pure) mathematics; decision mathematics (network graphs and linear
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 Walking Randomly  Michael Croucher
Croucher's blog, which dates back to August of 2007, has included posts such as "Logo Programming on the pocket PC," "Christmas gifts for math geeks (like me!)," "Martial Mathematics," "R Compared to MATLAB (or 'learning a thing or two from your students'),"
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 WallaceBolyaiGerwien Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
According to the WallaceBolyaiGerwien theorem, all simple polygons of equal area are equidecomposable by dissection. The site offers a proof of the theorem and several dynamic illustrations of equidecomposition in special cases.
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 Wallpaper Groups (Plane Symmetry Groups)  David Joyce; Dept. of Mathematics & Computer Science, Clark University
Mathematicians classify plane patterns such as wallpaper patterns by means of symmetry groups  groups of transformations of the plane that leave the pattern invariant. A transformation slides, rotates, and reflects the plane into another position. Such
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 Wallpaper Groups: The Discontinuous Groups of Rotation and Translation in the Plane  Xah Lee
An undergraduate tutorial on wallpaper groups, with illustrations of the 17 wallpapers groups and a wallpaper gallery. Technically, the derivation of all discontinuous groups of rotation and translation in the plane. Contents include: Some Theorems on
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 Walpha Wiki  Derek Bruff and others
As collaborative site to record how secondary and undergraduate math educators use WolframAlpha, or Walpha as it's called here, in the classroom. In particular, the authors are interested in how students might use Walpha themselves, as well as how teachers
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 Wanted: A New Mix  Keith Devlin (Devlin's Angle)
An essay on the insularity of mathematicians. "...mathematics as a whole should be prepared to embrace as a useful and bona fide part of the enterprise, collaborative investigations involving mathematicians together with experts in other disciplines."
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 Waring Experiments  Ivars Peterson (MathLand)
You might suspect that, at some point, four squares would no longer be enough to express a given whole number. This reasonable supposition was overturned in seventeenth century, when Pierre de Fermat proved that every positive whole number can be expressed
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 Washington MESA
Washington MESA (Mathematics, Engineering and Science Achievement) is developing middle and high school curriculum units and middle school modules/books available through Cuisenaire Dale Seymour Publications that integrate concepts within mathematics
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 WASL Math Prompts  Port Angeles School District, Washington state
Sample questions for the WASL, Washington State Assessment of Student Learning. Most questions have answers printed above the questions. Sample questions are offered for kindergarten through high school levels, organized by mathematical content, and accompanied
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 Was Math Invented or Discovered?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about whether math was invented or discovered.
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 WatchKnowLearn  Community Foundation of Northwest Mississippi
Thousands of free online math educational videos, categorized into topics such as mathematics for young learners, number operations, math in the real world, precalculus, math study skills and test prep, and history of math.
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 Waterloo Fractal Compression Project  Edward R. Vrscay
A research project dedicated to the study of fractal analysis and Iterated
Function Systems/Fractal Transforms from theoretical and practical perspectives, focussing on image and signal compression. Both mathematical and nonmathematical introductions
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 Waterman Polyhedra and Maps  Steve Waterman
World maps based on close packing of spheres that resemble B.J.S. Cahill's octahedral butterfly world map, but with only five degree graticule. With links to the mathematics behind the cartography, polyhedra applications, and other original findings.
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 The Water Puzzle  Doug Ensley, Shippensburg University
Starting with a pail of water holding some unknown quantity greater than 8 quarts, and small (3 quarts) and large (5 quarts) vases as measuring devices, explore how to split 8 quarts of water from the pail equally between two people.
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 Water Puzzle  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
There are three glasses  3, 5, and 8 oz. The first two are empty, the last contains 8 oz of water. By pouring water from one glass to another make at least one of them contain exactly 4 oz of water. Investigation into this puzzle by experimentation,
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 Water Tidbits: Questions and Answers  U.S. Geological Survey (USGS)
Topics covered include: Water use in the United States, USGS water data and measurements; Water use in your home; Chemistry and water. Links to other sites about water.
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