1. Subject knowledge, what is it good for?

2. A puzzle!

3. The theorem of Pythagoras: In a right angled triangle the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the two shorter sides

5. But is it true for semi-circles. i. e
But is it true for semi-circles? i.e. if we replace the squares by semi-circles, is the theorem still true? If it is true for semi-circles, what other shapes is it true for? What if it is not a right-angled triangle? What then?

6. In an acute angled triangle, the area of the square on the longest side is the sum of the areas of the squares on the two shorter sides. In an obtuse angled triangle, the area of the square on the longest side is the sum of the areas of the squares on the two shorter sides.

7. a b c 3 4 5 12 13 7 24 25 8 15 17 9 40 41 11 60 61 35 37

8. n un 1 2 3 4 5 6 8 7 13 21 9 34 10 55