2.  A square is a shape with four equal sides  Example:  All its angles are ninety degrees

3.  Another meaning of square is to square a number  The square of a number = the number times itself  1 squared = 1 x 1 = 1  2 squared = 2 x 2 = 4  3 squared = 3 x 3 = 9  4 squared = 4 x 4 = 16  5 squared = 5 x 5 = 25

4.  The area of a square with side 4 cm is 16 square cm

5.  The area of a square with side 3 cm is 9 square cm

6.  The area of a square with side 5 cm is 25 square cm

9. For ANY right angled triangle the square on the hypotenuse equals the sum of the squares on the other two sides. a b c a 2 + b 2 = c 2 a b c a b c = the hypotenuse

10. Blue area = c x c = c squared = c 2

11. Total = Blue + Red Total – Red = Blue = c 2

12. Blue = axa + bxb = a 2 + b 2 = c 2

13. Challenge: i) Find another Pythagorean triad (other than 3,4,5 with all three numbers under 20 ii) How many triads are there where all three numbers are under 100?

14. 3 4 5 6 8 10 5 12 13 9 12 15 8 15 17 12 16 20 7 24 25 15 20 25 10 24 26 20 21 29 18 24 30 16 30 34 21 28 35 12 35 37 15 36 39 24 32 40 9 40 41 27 36 45 14 48 50 30 40 50 24 45 51 20 48 52 28 45 53 33 44 55 40 42 58 36 48 60 11 60 61 16 63 65 25 60 65 33 56 65 39 52 65 32 60 68 42 56 70 48 55 73 24 70 74 21 72 75 45 60 75 30 72 78 48 64 80 18 80 82 13 84 85 36 77 85 40 75 85 51 68 85 60 63 87 39 80 89 54 72 90 35 84 91 57 76 95 65 72 97

15. 1 1 x X 2 = 2 because 1 2 + 1 2 = 1 + 1 = 2 1.5 2 = 2.25 (too big) 1.25 2 = 1.625 (too small) 1.3 2 = 1.69 (too small) 1.4 2 = 1.96 (too small) 1.414 2 = 1.999396 (1.41421356…) 2 = 2 √2 is an irrational number It is NOT a fraction or a repeating decimal

16.  History http://youtu.be/b8DrYz_cKR0 Donald 50 secs to 5min 39 secshttp://youtu.be/b8DrYz_cKR0  Pythagorean triads http://youtu.be/FhPWIQSIQqw (start at 3 min 45 secs) http://youtu.be/FhPWIQSIQqw  Proof of Pythagoras’ theorem (start at 1 min 52 secs) http://youtu.be/y9MqD7LN0xYhttp://youtu.be/y9MqD7LN0xY  Another look at the same proof (60 seconds) http://youtu.be/pVo6szYE13Y http://youtu.be/pVo6szYE13Y  Funny film http://youtu.be/X1E7I7_r3Cwhttp://youtu.be/X1E7I7_r3Cw