# Dynamic Patterns

## A pattern of quadrilaterals Dynamic pattern of quadrilaterals. Drag the points!

The pattern is made by repeatedly creating midpoints on the sides of the red quadrilateral, and making blue quadrilaterals in each step.

#### Exercise 1

Let the slider be 1 in the worksheet above and drag the red points. What is always true about the blue quadrilateral, however you drag the red points?

#### Exercise 2

When the slider is set on 1, there is one blue quadrilateral. How many blue quadrilaterals are there when the slider is 2? When the slider is 3? Find an expression, in terms of n, for the number of blue quadrilaterals when the slider is n!

#### Exercise 3 - Make a pattern of quadrilaterals

Construct a pattern of quadrilaterals as in the video above. If you want to do many quadrilaterals, it is tedious to do each step by hand. It is possible to make each step automatically by using the spreadsheet, or by using lists. The demo at the top of this page is made using listst, and vectors.

## A pattern of circles Dynamic pattern of circles. Drag the point!

#### Exercise 4

In the demo above, the blue circles all have the same radius. Where should the red point be placed in order for the blue circles to have the same radius as the yellow circle? If all circles, blue and yellow, have the same radius; the red segments form a polygon. How many sides does this polygon have?

#### Exercise 5 - Make a pattern of circles

Construct a pattern of circles as in the video above.

# further info:

some advanced patterns in GeoGebra, click on "Art et maths"
http://dmentrard.free.fr/GEOGEBRA/Maths/accueilmath.htm

a definition of a polygon: http://mathworld.wolfram.com/Polygon.html

the names of various regular polygons: http://en.wikipedia.org/wiki/Polygon

http://en.wikipedia.org/wiki/Envelope_(mathematics)

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License

www.malinc.se