The Sum of the Squares of the First n Natural Numbers

This applet gives a dynamic proof of the formula for the sum of the squares of the first n natural numbers.
  • Drag the slider to form the area representing the sum of the squares of several of the first natural numbers.
  • Triple this area.
  • 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 formulae" to see the result.