Pythagoras? Theorem is essentially about areas of shapes. It says that ?the area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides?. However, in practice, when used to find the length of sides in a right-angled triangle, the areas are ignored and we concentrate more on the value of the square of the length of the sides. In this sense, Pythagoras? Theorem may be re-stated as ?the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides?. The emphasis moves from geometry to algebra.
The tns file offers two similar approaches taken by Karen Birnie and John Slane, both of which make connections between dynamic geometry diagrams and dynamically linked measurement data from the spreadsheets. Two lessons in which the different approaches were used are described in "Inspired Connections in Maths Lessons", published in the autumn of 2010. For a pdf version of the entire booklet please click here.