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

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Presentation transcript:

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

 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

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

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

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

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

Blue area = c x c = c squared = c 2

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

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

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?

1 1 x X 2 = 2 because = = = 2.25 (too big) = (too small) = 1.69 (too small) = 1.96 (too small) = ( …) 2 = 2 √2 is an irrational number It is NOT a fraction or a repeating decimal

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