Here is a creation by Markus Hohenwarter, the CEO of GeoGebra. (see his page here.) Below I have shown a "doctored" version, where I have shown all the hidden parts of his creation.

Quite often mathematics is what goes on behind the scenes. The math-phobics actually hate that which makes their lifestyle possible!

Thoughts, opinions, and ideas about Mathematics and other things from a retired teacher.

## Wednesday, November 19, 2014

## Monday, November 17, 2014

### A quick GeoGebra-based illusion

This sketch was created to show how easily our eyes and brain can mislead us.

A simple rotation is perceived differently if key anchor segments are removed.

The complete file is here.

A simple rotation is perceived differently if key anchor segments are removed.

The complete file is here.

## Friday, November 14, 2014

### Polar Roses

This is a continuation of my investigations which I have called "floating midpoints". Enjoy

## Saturday, November 8, 2014

### Limacons and cardiods without trig!!!

You have control over the location of point E along the x-axis from 1 TO 4. Point N rotates around point E on a circle of radius 1. The blue circle always contains the origin and is centered at point N. The blue dotted line is tangent to the green circle (that N rotates on). The red dotted line is the perpendicular from the origin to the blue dotted tangent line. The point of intersection of those two lines is traced.

Although more complicated than some of my other sketches, it still shows what can be created WITHOUT USING TRIGONOMETRY that, in our textbooks, is usually not even mentioned until well after trig is covered in detail.

For the full file, visit http://tube.geogebra.org/material/show/id/266203

## Friday, November 7, 2014

### So what is a focus and directrix?

It is quite possible to use GeoGebra to give students the "flavor" of a topic before getting bogged down in textbook details. This particular sketch can give the flavor of the concepts of focus and directrix, their meaning and visual placement, well before any need for calculation arises. In short, GeoGebra can be a motivator.

## Thursday, November 6, 2014

### Sierpinski Triangle Generated Randomly

This sketch will gradually create the Sierpinski triangle by randomly moving, at each step, halfway towards one of the 3 vertices, chosen randomly.

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