## What is Geogebra and Where Do I Get It?

GeoGebra is a free interactive math program: geometry, algebra, and calculus. One of the things I like about it is the ability to easily export things to interactive html pages. For information about GeoGebra, visit the GeoGebra home page.. Go to Learning Materials (item 3 under first steps last time I looked at the page). There you will find downloads and lots of examples various people have created.

Below are a few things I have created. At the moment I haven't gotten around to loading them on the GeoGebra wiki. The Creative Commons license applies to them. The interactive worksheets are web pages. You're powers to change things are somewhat limited but they are instantly available. The GeoGebra files (.ggb) you may download and edit with the full power of GeoGebra.

### Derivatives

This is a bit of exploration of the derivatives of simply polynomials. It's also one of the first things I wrote as I began learning GeoGebra.

Playing with derivatives of polynomials: what is a derivative - interactive worksheet
Playing with derivatives of polynomials: what is a derivative - GeoGebra file

### Cycloid

This is a bit of exploration of rolling circles and the cycloid.

cycloid - interactive worksheet
cycloid - GeoGebra file

### Superposition of waves

In many, though by no means all or even all interesting, cases, two or more waves overlapping in space and time combine according to the principle of superposition.

We speak of interference when the waves have the same frequency but travel different paths (different distances) before being detected by eye or ear or some mechanical device.

interference - interactive worksheet
inteference - GeoGebra file

In music, the superposition of waves of similar but not identical frequencies is very important. It tells musicians whether or not they are in tune. When frequencies differ more, intervals arise - some pleasant and some less so.

beats - interactive worksheet
beats - GeoGebra file

### LRC Series circuit

These two sets of files show the behavior as a function of time of voltages and other quantities in a circuit consisting of a sinusoidal applied voltage connected to a resister, a capacitor, and an inductor in series. The first set shows the behavior as a function of time illustrating how the phases change as inductance, capacitance, and driving frequency are varied.

LRC as a function of time - interactive worksheet
LRC as a function of time - GeoGebra file

The second set show the impedance and the peak voltages as functions of frequency. This set makes it easier to see resonance and the simple filtering aspects of inductor and capacitor behavior.

LRC as a function of frequency - interactive worksheet
LRC as a function of frequency - GeoGebra file

### Geometric Optics

These are intended for use after basic ray-tracing has been covered. In each the object can be moved and its height changed by dragging the dot at the top of the arrow labeled object. In addition, the focal point f can be dragged along the axis. In the case of the mirror, the object can be dragged through the mirror so that the connections between concave and convex mirrors may be easily explored. In the case of the lens, the focal point can be dragged through the lens which will cause the lens to switch between converging and diverging.

Concave and convex mirror ray tracing - interactive worksheet
Concave and convex mirror ray tracing - GeoGebra file
Converging and diverging lens ray-tracing - interactive worksheet
Converging and diverging lens ray-tracing - GeoGebra file

The prism files show how a beam of light passes through an equilateral prism depending on the apex angle, the incident angle, and the indices of refraction.

### Waves

This is a basic demonstration of describing a wave in terms of amplitude and frequency.

Amplitude and frequency of a wave - interactive worksheet
Amplitude and frequency of a wave - GeoGebra file

### Fundamental Theorem of Calculus

This illustrates why the value of the lower limit doesn't show up when taking the derivative of a definite integral

Illustration of role lower limit doesn't play - interactive worksheet
Illustration of role lower limit doesn't play - GeoGebra file

### Calculating Path Lengths with Calculus

This illustrates the path length calculation and shows the values of two approximations to the path length.

Illustration of path-length calculation - interactive worksheet
Illustration of path-length calculation - GeoGebra file

### Inverse Functions

This illustrates inverse functions as reflections in the line y=x.

Illustration of path-length calculation - interactive worksheet
Illustration of path-length calculation - GeoGebra file