My introduction to surds this year was by setting a problem to my class:
Calculate the exact value of the length of each missing side:
Initially the class knew exactly where to start. Pythagoras. Great. The problem arose when calculating the length of the hypotenuse of the red triangle. The class wanted a calculator. This led to a discussion about exact values and accuracy.
Then I set the class the challenge of drawing the Spiral of Theodorus and to calculate the hypotenuse of each triangle and also to calculate the area of each triangle. Continue reading