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Presentation transcript:

Whiteboardmaths.com © 2004 All rights reserved

The Circumference of a Circle diameter(d) Circumference (C) How many times does the diameter fit around the circumference? Choose your number. 11½22½33½4  = d radius In terms of the radius: C =? C =2  r

It’s the same for all circles! The Circumference of a Circle

Find the circumference of the following circles. C =  d C = 2  r 8 cm cm 2 C =  d C=  x 8 C = 25.1 cm (1 dp) C =  d C=  x 9.5 C = 29.8 cm (1 dp)

C = 2  r C = 2 x  x 3 C = 18.8 mm (1 dp) C = 2  r C = 2 x  x 2.1 C = 13.2 m (1 dp) The Circumference of a Circle Find the circumference of the following circles. C =  d C = 2  r 3 mm m 3

23 cm 7.5 cm Find the circumference of the tyre and steering wheel. C =  d C=  x 23 C = 72.3 cm (1 dp) C = 2  r C = 2 x  x 7.5 C = 47.1 cm (1 dp)

The Circumference of a Circle Find the perimeter of the following semi-circles. C =  d C = 2  r 8 cm cm 2 Perimeter = ½  d + d = ½ x  x = 20.6 cm (1 dp) Perimeter = ½  d + d = ½ x  x = 24.4 cm (1 dp)

Perimeter = ¼ ( 2  r) + 2r = ¼ x 2 x  x x 6 = 21.4 cm (1 dp) Perimeter = ¾(2  r) + 2r = ¾ x 2 x  x x 8.5 = 57.1 cm (1 dp) The Circumference of a Circle Find the perimeter of the ¼ and ¾ circles. C =  d C = 2  r cm 8.5 cm

The Circumference of a Circle Find the diameter/radius of the following circles. C =  d C = 2  r C = 25 cm find the diameter. 5 6  d = 25 d = 25/  d = 8.0 cm (1 dp) 2  r = 30 r = 30/(2  ) r = 4.8 cm (1 dp) C = 30 cm find the radius.

 =  to 10,000 dp

The current world record for memorising pi is held by Krishan Kumar Chahal from India, who memorised it to 43,000 decimal places in All we are asking is that you memorise it to three!!

“There’s a beauty to pi that keeps us looking at it. The digits of pi are extremely random. They really have no pattern and in mathematics that’s really the same as saying they have every pattern”. Peter Borwein The Indian mathematician Srinivasa Ramanujan found algebraic and numerical relationships that were close approximations to pi. (See Hardy’s Taxi Number) Srinivasa Ramanujan ( )

References and Further Reading: The Joy of  David Blatner The Man Who Knew Infinity The life story of the mathematical genius Ramanujan by Robert Kanigel