Thoughts from a 21st century educator.

## Showing the ratio of any two sides in a triangle is the same, given the shape of the triangle is invariant

If you drag point C, you can change the size of the triangle below dragging the entire triangle can be used to rotate it (around a point "near" B). Notice that the ratio of the three sides, shown on the right, does not change.

[geogebra]ratio_of_triangle_sides_edit.ggb[/geogebra]

## Conic section constructions using Geogebra

The following constructions are all conic sections (as I was teaching this section to my 10th grade students) and are 'quick and dirty' constructions of conic sections. All you need to do in the examples is drag the point C left and right to see the shapes show up.

Parabola:

[geogebra]locus_of_parabola_0.ggb[/geogebra]

Ellipse:

[geogebra]ellipse_construction.ggb[/geogebra]

Hyperbola:

[geogebra]hyperbola_construction.ggb[/geogebra]

## Geogebra on Ubuntu

I got it working on Ubuntu. Turns out the problem was my version of Java, I had 5, Geogebra says it wants 4, but apparently on Ubuntu it actually needs 6.

Whatever, it works, cheer! I love Geogebra, I'm not ready to give it up.

## Geogebra: Weird problem in Ubuntu

So I just started using Ubuntu, and decided that I needed to set up my Ubuntu installation with all of the cool cross-platform programs I've been using in Windows. I swapped Wamp5 for Lampp, and am using Eclipse successfully instead of Programmer'as Notepad. It's only been a couple of days, but so far I am pretty happy. Apt-get is my new favourite command.

## Cubic polynomial with sliders

You can use this applet to show your students how to examine cubic polynomials and determine the effect of changing the 4 coefficients of the equation [tex]f(x)=ax^3+bx^2+cx+d[/tex].

[geogebra]cubic_polynomial.ggb[/geogebra]

## Complex multiplication using vectors

In this applet, we can see visually what happens when we multiply two complex numbers (each of which has a length of 1). Vector u, and vector v are multiplied to give vector w.

Try dragging B and C, the endpoints of v and u respectively to try and see what the result of the multiplication of two complex numbers is.

[geogebra]complex_multiplication.ggb[/geogebra]

## Triangle Angle Bisectors

This applets allows the user to see the complete construction of all 3 angle bisectors of a triangle.

Notice anything about the three bisectors? Where do they intersect?

[geogebra]triangle_bisector.ggb[/geogebra]

## Perpendicular Bisector

This applet allows users to see a quick animation of how to construct a perpendicular bisector.

[geogebra]perpendicular_bisector.ggb[/geogebra]

## Bisecting an Angle

Below is a short step by step animation that shows the steps in constructing an angle bisector.

If you press play, you can see the steps animated one at a time.

[geogebra]bisecting_angle.ggb[/geogebra]

## Distance formula using Geogebra

This applet shows you how the distance formula varies as you change the position of the points.

Drag A or B and see the effect on the distance formula.

[geogebra]distance_formula.ggb[/geogebra]

Created by David Wees on August 30th, 2007 using GeoGebra - Dynamic Mathematics for Schools