This applet gives a dynamic proof of the formula for the
sum of
the squares of the first

n natural
numbers. We start with three
times the sum of the squares and rearrange the parts of one of the sums.

- Click on "Color the third column".
- Drag the slider to rearrange the parts of the third column.

The area of the formed rectangle equals three times the sum of
the
squares.

- Click on Show the formulas
to see the result.

Irina Boyadzhiev, 13 February 2013, Created with GeoGebra
Download the file
Irina's GeoGebra Applets