## GeoGebra Tutorial 29 – Animation, Roses and Radian

This is the 29th GeoGebra tutorial of the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, you might want to read the GeoGebra Essentials Series.

In this tutorial, we learn the concept of radian.  One radian is equal to the subtended angle of the arc with the same length as the circle’s radius. In this tutorial, we rotate radius AB’ about point A, the center of the circle. As the point rotates, point C goes back and forth from A to B’ at the same speed. The path of point C forms petals (see red petals in the figures below). The ratio of the maximum number of petals formed and the number of rotations is a good approximation of $\pi$ Instructions

If you want to follow this tutorial step-by-step, you can open the GeoGebra window in your browser by clicking here. The output applet of this tutorial can be viewed here. » Read more

## GeoGebra Tutorial 26 – Constructing a Cycloid

This is the 26th tutorial of the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, you might want to read the GeoGebra Essentials Series.

A cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line.  In this tutorial, we use GeoGebra to construct a cycloid, the path traced by a rotating circle. In reality, we will not really roll the circle but use mathematics to make it appear is if it is rolling. We will set the amount of rotation to $4 \pi$ but you can choose to increase it later on.

The output of this tutorial is shown above. Move the slider and observe what happens.

## GeoGebra Tutorial 21 – Spreadsheet and Similarity

This is the 21st tutorial of the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, you might want to read the GeoGebra Essentials Series.

In this tutorial, we  investigate what happens if we multiply the coordinates of the vertices of a triangle with a constant.  First, we  plot three points that will be the vertices of a triangle, and then draw the triangle using the Polygon tool. Next, we will construct slider k, and see what happens if we multiply the coordinates (x1,y1), (x2,y2) and (x3,y3) of the vertices of the triangle by k. We also explore the relationship between the original triangle and the triangles  with coordinates (kx1,ky1), (kx2,ky2) and (kx3,ky3).

You can view the output of this tutorial here.

Step-by-Step Instructions