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Applets

This is an applet that allows you to move the vertices of polyhedra around and view what they look like in 3D.

An applet that lets you choose which polyhedra you want to view, in which there are 74 out of the 80 possible polyhedra. It is a three dimensional image that rotates.

This applet lets you type in the number of sides the shape has and tells you the name of the polyhedron.

This applet uses Geogebra and allows you to visualize what truncating polyhedrons does.

An applet that lets you visualize how polyhedra and spheres are related. You can change the opacity of the different features in the applet.

Applet Collections

A collection of applets that illustrate math concepts related to statistics. The topics the applets cover are data analysis, sampling distributions, probability, statistical inference, and multiple variables.

A collection of applets that illustrate math concepts related to AP Calculus using Geogebra. The topics the applets cover are limits, sampling derivatives, integrals, differential equations, area and volume, and the fundamental theorem of calculus.

This is a collection of applets that illustrate descriptive statistics. There is a standard deviation applet, a statiscope applet, etc.

A collection of applets that illustrate math concepts relevant to K-12 curriculum. Topics include area, fractions, graphing, geometry, and calculus.

This is a collection of applets all about geometry. It covers a lot about Euclidean geometry and a little about Hyperbolic and Spherical geometry. The applets cover the basic geometric constructions and theorems.

Resources

Website

This website provides information about unfolding polyhedra and Euler's formula. There are graphics that allow you to visualize where the information comes from.

Video Lesson

A video lesson about what polyhedrons are composed of. The lesson then goes over Euler's Theorem and how it is relevant.

Slideshow

A slideshow that goes over what semi-regular and regular polyhedra are. It also explains how you are able to tile space with both types of polyhedra.

Example Video

This video uses Magformers, which are magnets that are different shapes. They use the Magformers to be shaped like the regular polyhedra and transform them from regular to semi-regular polyhedra.

Info Page

This is an information page that goes over the history of polyhedra in mathematics. It is a timeline that shows how our knowledge of polyhedra has grown overtime.

Pascals Triangle and the Binomial Theorem

Introduction to Polyhedra video

Applet 1: Sine Function Transformation

Questions to Consider:
  1. What is the role of "a" in the graph of this function?
  2. What is the role of "b" in the graph of this function?
  3. How does g(x) compare to f(x)?

Applet 2: Riemann Sums

Use the checkboxes to toggle between the different types of Riemann Sums.
You can type in whatever function you want to look at.
You can also type in the endpoints and change the number of divisions by using the slider.

Applet 3: 3d Solids

Use the checkboxes to toggle between the different solids.
You can use the slider to change the radius of the solids.
Questions to Consider:
  1. When you adjust r and h what happens to the volume of the cone?
  2. When you adjust r and h what happens to the volume of the cylinder?
  3. When you adjust r and h what happens to the volume of the sphere?
  4. What is the relationship between the volume of the cone, cylinder and sphere?

Original Geogebra Applet: Regular Polyhedra Nets

Use the sliders to view the nets of each different polyhedron.
Press the Animation! button to see all of the nets unfold at the same time.
Questions to Consider:
  1. How does seeing the nets of the Regular Polyhedra help you understand them?
  2. How many of the polyhedra are composed of triangles and why can there be multiple composed of triangles?
  3. Does seeing the net make it easier or harder to compute Euler's Formula (Faces+Vertices-Edges=2) and why?
Here is a link to view the applet in Geogebra: Regular Polyhedra Nets Applet

Tower of Hanoi

The goal is to move all the disks from the leftmost peg to the rightmost peg while following these rules:
  1. Move only one disk at a time
  2. A larger disk can not be placed on top of a smaller disk
  3. All disks, except the one being moved, must be on a peg