This is a great exercise for Common Core Geometry instruction in the area of transformations.

HINT: highlight a slider’s button, then use your cursor keys for fine adjustment; play around with the numbers to get pleasing shapes.

Use slider n for number of iterations

Use slider r for rotation in 0.001 increments

Use slider d for dilation in 0.001 increments

Build command structure in 3 steps:

Enter Dilate[poly1, d^i], where i = 1, 2, 3 to find pattern

Enter Rotate[Dilate[poly1, d^i], i r π], where i = 1, 2, 3 to find pattern

Enter Sequence[Rotate[Dilate[poly1, d^i], i r π], i, 1, n, 1]

This Sequence command should work for all polygons.

The downloadable file can be found here.

My other GeoGebraTube apps **can be found here**.

## Polygons and Diagonals

Number of diagonals in a polygon:

If n = number of vertex points, then D = number of diagonals = n(n-3)/2.

Slider n controls the number as well as the color. In the Advanced tab,

Red = n / 36, Green = 1 – n / 36, and Blue = 0, so the color changes from Green

to Red as the number of sides moves from 3 to 36.

reference: I modified sonom’s idea from http://tube.geogebra.org/material/show/id/137056

The downloadable file can be found here.

My other GeoGebraTube apps **can be found here**.

An epitrochoid is the path traced by a point on a circle (M)

that travels on the outside of another circle (E).

This can be used to model the path of the Moon (M) in orbit around the Earth (E).

There are about 13.3 revolutions(n) of the Moon about the Earth in one year.

-credit-Malin Christersson-http://www.geogebratube.org/material/show/id/87141

The downloadable file can be found here.

My other GeoGebraTube apps **can be found here**.

## Polar Vector Clock

Polar definitions: Sec=90°-(6a)°, Min=90°-(a/10)°, Hour=90°-(a/120)°

NOTE 1: when using polar coordinates a semicolon is needed

NOTE 2: “Alt-o” (letter O, not number 0) gives degree symbol

Vectors are used for clock hands.

-from wikimedia commons: the clock face background,

and set at Layer=0; other graphics are at Layer=1

-Animation speed = 0.00023148 to move second hand accurately

-credit: Malin Christersson-http://www.malinc.se/math/geogebra/slideren.php

The downloadable file can be found here.

My other GeoGebraTube apps **can be found here**.