Geogebra Stuff

After clicking on one of the links below, click on the big "Go to Student Worksheet" button in the new window. Be patient -- the Geogebra file can take a little while to load within the web browser.
If you really want to explore in depth, click the download link in the new window to save the file to your computer. Install Geogebra and then open the file. You'll have access to all the Geogebra tools, be able to zoom in and out with the scroll wheel on your mouse, and probably have better computer performance this way.



Other Miscellaneous

Function Transformations

Explore how changing parameters in a function equation result in transformations of the graph. Choose from among 13 "basic" functions.

Parabola Parameters


An exploration of how each parameter of the parabola y=ax^2 + bx + c ("standard form") or y = a(x-h)^2 + k ("vertex form") affects the graph.

Exponential Functions


A brief introductory exploration of exponential functions.

Exponential Function through two given points


Visualize the exponential function that passes through two points, which may be dragged within the x-y plane.
Also see the resulting equation.

Discontinuities of Rational Functions

Make visual connections between the algebraic and graphical representations of a rational function.

Inverses of Functions

Explore the graphical and numerical relationship between a function and its inverse. Adjust a slider to watch the original function flipping over the line y=x.

Unit Circle - Trig functions vs. Geometry definitions

See deeper connections between Trigonometry concepts and their Geometric counterparts. For example, see the relationship between the "tangent" of an angle and a line segment being "tangent" to a circle.

Formation of a Sinusoid (Sine/Cosine Wave)

Based on your knowledge of the unit circle, see how sinusoids (sine and cosine waves) get their shapes.

Stadium Screen Viewing Angle

Explore the "viewing angle" of a stadium screen as a function of distance from the screen and other physical dimensions.
This is ideally part of either a PreCalculus lesson on inverse trig functions, or a Calculus lesson on Optimization (after learning how to derive inverse trig functions).

Simple Harmonic Motion

Ferris Wheel Simple Harmonic Motion
Pendulum Simple Harmonic Motion
Skyscraper Simple Harmonic Motion
Piston Simple Harmonic Motion
Mass hanging from a spring Simple Harmonic Motion

SSA triangle - The Ambiguous Case


Illustrates the SSA case for triangles, in which two sides and one of their opposite angles are given. Intended for use in a PreCalculus or Trigonometry class while studying the Law of Sines.

Rectangular to Polar Wrapping/Unwrapping


How does the function y = f(x) in rectangular coordinates relate graphically to the curve r = f(theta) in polar coordinates?
I recall trying to explain to my Calculus class last year how one may envision taking the rectangular function (or more specifically, its inverse) and wrapping it around a pole at the origin. Clearly my explanation fell short on many students.
This Geogebra construction is intended to demonstrate that concept.

Fourier Plaything


Imagine: Around the sun rotates the earth (Let's pretend a circular path with sun at the center). Around the earth rotates the moon (Again let's pretend...). Around the moon rotates a... house (We're allowed to imagine, right?). Around that house rotates a space dog. Around that dog rotates a cosmic flea. And so on.
From the fixed perspective of the sun, what's the shape of the path traced out by the smallest rotating object? Find out by playing with the sliders in this construction.

Definite Integral Approximations


Compare and contrast the various methods for approximating or calculating definite integrals:
Left/Middle/Right sums, Upper sums, Lower sums, Trapezoidal sums, and the Definite Integral itself.

Volumes of Revolution -- Disk/Washer Method


Demonstrates the concepts behind the disk/washer method for calculating Volumes of Revolution.

Dashboard Calculus


It would be a shame for Calculus students to get behind the wheel of a car and not even realize that their favorite subject is being displayed right there on the dashboard. The speedometer represents your velocity function while the odometer represents your "distance traveled" function.
In this construction, press "start," drag the speedometer needle, and examine how distance traveled may be viewed as the "area under the velocity curve."

Parallel Parking

Parallel Parking visualization, U.S. customary units [feet]
Parallel Parking visualization, metric units [meters]
Go here for more background and Geogebra visualizations, including my brief moments of nerd fame in the New York Times and Times Picayune.

General Conic Section

general conic section

For any general conic section defined by Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, this applet gives you a cone and a plane whose intersection gives the same curve. For non-degenerate cases, the type of conic curve is identified (ellipse, parabola, hyperbola). Admittedly, degenerate cases (points, parallel lines, intersecting lines) are not detected, yet the world keeps turning!



A Geogebra version of the ancient Chinese puzzle. Instructions included within the worksheet.

Fourier Series


With Fourier Series, see how adding many sinusoids of different amplitudes and frequencies can result in interesting shapes.

Rotating Cube


Hold a cube (e.g. Rubik's cube) by its diagonally-opposite corners between your thumb and forefinger. Spin the cube as fast as you can about the diagonal. Even though the cube is composed of flat surfaces and straight edges, can you see the curved profile it carves out in 3D space? This worksheet presents a mathematical model of the illusion.

Rubber Pencil


An attempt to model the famous "Rubber Pencil Illusion" mathematically. Plenty of content is available on the Internet describing how to perform this simple illusion, but I've found little else out there to explore the math/physics behind it.

Binary Spring Clock


This Geogebra simulation demonstrates how a series of springs could theoretically be used to construct a "binary clock."
Inspired by the some students telling me that the AP Physics teacher had suggested a "binary pendulum" could theoretically be constructed as a time measurement device for an upcoming Science Olympiad competition.

Ball Rolling On Incline


How fast does a ball have to be traveling at the edge of a ramp in order to not re-contact the corner of the ramp?
In terms of ball radius r, gravitational acceleration g, incline angle theta, what is the minimal speed v that the ball must have at the edge of the ramp?