A pattern of quadrilaterals
The pattern is made by repeatedly creating midpoints on the sides of the red quadrilateral, and making blue quadrilaterals in each step.
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?
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
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.
some advanced patterns in GeoGebra, click on "Art et maths"
a definition of a polygon: http://mathworld.wolfram.com/Polygon.html
the names of various regular polygons: http://en.wikipedia.org/wiki/Polygon
by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License