 Some Solid (Threedimensional) Geometrical Facts about the Golden Section  Ron Knott
Phi and threedimensional geometry  Dice Shapes; Coordinates and other statistics of the 5 Platonic Solids; The Greeks and the platonic solids; Quasicrystals and Phi; Footnotes on Plato and Euclid, and on shapes for fair dice.
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 sonata mathematique  Rachel Kernodle
Blog by a high school math and learning specialist. Posts, which date back to June, 2011, have included "twitter math camp," "mathematical art," "i also want you to learn…," and "rational functions take two."
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 SpaceBric
Tetrahedral linking blocks and design software using that shape. Download trial versions of the software or get the fullyfeatured versions with a registration key. Blocks may be purchased on line as well. SpaceBric also offers school fundraising and
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 SpaceShape  Matt Storz
SpaceShape is a Windows95 program that allows various 3D shapes to be created and then flattened so that a pattern can be printed to make a model of the 3D shape. Various 3D shapes are supplied with the program (octahedron, dodecahedron, icosahedron,
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 Spidron System  Daniel Erdely
Erdely calls a planar, planefilling object a Spidron. Upon threedimensional deformation subject to specific constraints, the planar system generates a regular, dynamic, geometrical construction. Erdely's experiments have led to the idea of creating
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 Stella: Polyhedron Navigator  Robert Webb
"Small Stella" is a program for viewing polyhedra and printing their nets so you can build your own. It has over 150 builtin models, plus their duals. Models include Platonic solids, Archimedean, KeplerPoinsot, Johnson solids, "Near Misses," and Stewart
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 Stellated Icosahedra  Roman Maeder
An excerpt of an article published in Mathematica in Education. There are 59 stellations of the icosahedron; these pages contain various images of them, ordered by increasing circumradius, and some background information. The metric properties and graphics
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 studio:ludens  Wouter Walmink and Alexander Rulkens
Free online tools that "let you play with your own creativity," designed by two Dutch industrial and interaction designers in Eindhoven. Create your own patterns with Repper; your own tessellating coasters with Epa:kato; your own fractals and other complex
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 studymaths.co.uk  Jonathan Hall
Free help on your maths questions. See also the bank of autoscoring GCSE maths questions, games, and resources such as revision notes, interactive formulae, and glossary of terms.
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 Surface Area of a Rectangular Solid  NASA Lewis Learning Technologies Project
What is the surface area of a rectangular solid whose length is 6 centimeters, depth is 5 centimeters, and height is 4 centimeters? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Symmetry  Rick Engel
A lesson on the symmetry of the Platonic and Archimedean solids using Polymorf, a math manipulative product. Demonstrates inscription, truncation, sectioning, and space filling with polyhedra.
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 Synergetics on the Web  Kirby Urner, 4D Solutions
R. Buckminster Fuller's "explorations in the geometry of thinking" is detailed in two thick volumes, Synergetics and Synergetics 2. Synergetics thoroughly permeates the rest of Fuller's writings as well. The invention for which Fuller is most famous,
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 Tap Into Teen Minds  Kyle Pearce
"Transforming mathematics education in an iPad paperless classroom." Posts, which date back to September, 2011, have included "Apple TV In The Classroom – The New Smart Board," "OAME Tap Into Teen Minds Educational Technology Presentation," "Problem Solving
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 Termesphere Gallery  Dick Termes
Spherical paintings that use a six point perspective. View images of the paintings and read about the artist. Products and services include workshops, lectures, books, and models of the Platonic solids, as well as the painted spheres.
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 Tessellated Polyhedra  Jill Britton
Fullpage printable nets of each of the regular polyhedra, decorated with individual surface tessellations in full color. A higherresolution blackandwhite version of each tessellated net appears in Polyhedra Pastimes, by Jill Britton, published by
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 Tetrakys
Interlooping equilateral, isosceles, and scalene triangles for building two and threedimensional geometric objects, exploring area and volume, and visualizing fractions and arithmetic operations. The foam composition of these colorful manipulatives
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 Think3d!  Allyson Hutton, Director
Inspired by an architect's visit to a 4th grade classroom, this elementary school curriculum develops spatial reasoning and visuospatial thinking through 2D to 3D transformation challenges in origami and popup paper engineering. Collaboration with
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 Thinking Fountain  Science Museum of Minnesota
Thinking Fountain offers surprising and personal connections to science. It's a living card file full of ideas and activities. Includes the opportunity to add your own projects. See Shapes Cluster: Shapes & Math: Shape Walk, I C Shapes, Bubble Geometry,
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 TI89 Calculus Calculator Programs
TI89 calculator programs for sale. Enter your variables and see answers worked out step by step: a and b vectors, acceleration, area of parallelogram, component of a direction u, cos(a and b), cross product, curl, derivative, divergence of vector field,
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 Tilings (Graphics Archive, Special Topics)  The Geometry Center
Regular subdivisions of the plane or space.
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 Timothy Kasper
Screencast geometry lessons, most less than five minutes long, narrated by a seventh grade teacher in Indiana.
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 Toys from Trash  Arvind Gupta
Stepbystep photographic instructions for building elegantly simple, colorful "Math Magic" doityourself manipulatives: Abacus, Flexagon, Triangle Grid, Flat Flexagon, Slipper Insets, Folding Pentagon, Tangram, Paper Octagon, Cylinder and Cone, Area
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 Transformulas  Jedidiah Butler
Blog about transformational geometry, subtitled "picture = 100 formulas." Posts, which feature Butler's original GeoGebra applets and teaching notes, date back to March, 2014: "One Formula ... to Rule them All," "Circles Part 2: Angle Relationships,"
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 Triangles and Pyramids: Playing Math!  Hollis Easter
A "teachable" on the construction of freestanding pyramids made "by folding a single piece of paper, with only a single piece of tape to hold them together...." This blog post goes on to include photos of a net, diagrams, and "things to investigate":
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 Triangles and Simplices (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on triangles and their higherdimensional generalizations (simplices), with a particular interest in partitioning regions into triangles, tetrahedra, or higher dimensional simplices, for various applications
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 triangular prism  Manjit Singh Atwal
Download lessons and worksheets about triangular prisms, including finding surface areas and volumes.
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 Understanding Mathematics: A study guide  Peter Alfeld, University of Utah
A resource and source of encouragement, with questions and Alfeld's comments (Are you frustrated working through heaps of meaningless problems that are all alike? Does the thought "I can look it up if I have to" occur to you frequently? Do you feel that
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 Une Balade dans le Monde des Polyèdres  Maurice Starck
Les polyèdres convexes, non convexes, et intéressants: les polyèdres uniformes, les stellations de l'icosaèdre, des tétraèdres remarquables, le découpage d'un tétraèdre par un plan, les deltaèdres
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 Utah Elementary Mathematics  David A. Smith
Blog of conceptual frameworks and other classroom resources for Utah educators implementing the Utah Core State Standards. Smith, the Elementary Mathematics Specialist at the Utah State Office of Education (USOE), has posted since October, 2013; and also
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 Videodiscovery
A publisher and distributor of innovative multimedia products for educators and families. Laserdiscs and CDROMs for the K12 and college market. Product offerings now include laserdiscs with accompanying software, as well as CDROMs for both the school
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 Vi Hart  Vi Hart
Blog, videos of math "doodling," instructions for slicing food mathematically, and more from the selfdescribed recreational mathemusician who considers math a hobby, with "special interests in symmetry, polyhedra, and surreal complexity. This usually
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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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 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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 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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 Weekend Projects—Picnic Geometry  Make Podcast
This video shows how to build an icosahedron out of paper plates, cups, or plastic sheeting—and pack some geometry into your next picnic! MAKE's accompanying post provides stepbystep instructions for assembling icosahedra from picnic supplies.
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 Whistler Alley Mathematics  Paul Kunkel
Kunkel's Geometer's Sketchpad lessons convey a conceptual understanding, usually without rigorous proof, with questions and suggestions for extensions: Buffon's Needle (an old probability exercise); Chinese Handcuffs (questions with applications for geometry,
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 Wholemovement  Bradford HansenSmith
Bradford HansenSmith presents the art and geometry of folding circles. As he explains, "Everything we know about geometry, mathematics, and all spatial arrangement and organization of matter is demonstrated by cutting into the wholeness of the sphere.
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 Wild About Math!  Sol Lederman
Math posts, which date back to October, 2007, have included "10 ways to get wild about Math," "How to square large numbers quickly (part 1)," "26 tips for using learning styles to help your kids with Math," "The algebra of crossmultiplication," "Flexagon
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 window into a math classroom  Sadie Estrella
A snapshotdriven blog subtitled "a glimpse into a math classroom once a day." Estrella's posts, enlivened with pictures of her students and of their work on classroom dryerase whiteboards, have included "Trying Math MetaCognition," "More Arguing about
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 Worksheet Works  WorksheetWorks.com
This site generates high quality PDFs of worksheets with the flick of a few checkboxes. Just specify level of difficulty, range of numbers, font size, or other parameters.
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 The World of Geometric Toy  Akira Nishihara
Play with animations and applets of Buckminster Fuller's Tensegrity and the Indian Ball (also known as the flexisphere), as well as wireframe renderings of the torus, the magic ring, the toroflux, the reversible polyhedron, and other objects. Nishihira
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 YMath Mathematical Models  Jan de Koning
Models and building boxes for education include magnetically connectable "mathmaker" and "polylinks," and tetrahedron puzzles. Other polyhedral furniture and housewares include cube moneyboxes of plywood, copper, and brass; dodecahedron bottle openers;
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 You Can Do The Rubik's Cube  Rubik's, Seven Towns Ltd.
The You CAN Do the Rubik's Cube Solution Kit offers teachers lesson plans, homework sheets, and answer keys aligned to national standards as well as 19 state frameworks, anchors and 21st Century Skills. Lessons and activities support Geometry, Algebra
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 Zome: Truncated 120cell  PCMI @ Math Forum: SSTP 2007
One of the activities at the 2007 Secondary School Teachers Program in the Park City Mathematics Institute was the construction of a truncated 120cell using Zometool. View both an explanation of the mathematics and photos of the construction.
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