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The Circumference Diameter Ratio

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Step 4: Measure the circumference and diameter of the circle. ... If C is the circumference and d is the diameter of a circle, then there is a ... – PowerPoint PPT presentation

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Title: The Circumference Diameter Ratio


1
The Circumference/Diameter Ratio
  • The circumference of a circle is the distance
    around the circle
  • Which is bigger, the circumference of a can of
    tennis balls or the height of the can?
  • The height is slightly greater than 3 times the
    diameter of a ball, or 3 time 2.5
  • The circumference of the can is slightly greater
    than the circumference of a ball

2
The Circumference/Diameter Ratio
  • Investigation 1
  • A Taste of Pi
  • Step 1 In a new sketch, draw AB.
  • Step 2 Construct point C, the midpoint of AB.
  • Step 3 Draw circle C with radius CB.
  • Step 4 Measure the circumference and diameter
    of the circle.
  • Step 5 Select both measurements and calculate
    the curcumference divided by the diameter.
  • Step 6 Drag point B to make the circle
    different sizes. What do you notice about the
    calculated value?
  • C-66 Circumference Conjecture
  • If C is the circumference and d is the diameter
    of a circle, then there is a number p such that
    C pd.
  • If d 2r where r is the radius, then C 2pr.

3
The Circumference/Diameter Ratio
  • The number p (Pi), has been known for centuries
    to be the ratio between the circumference and
    diameter of a circle
  • Mathematicians in ancient Egypt used the
    approximation (4/3)4.
  • Early Chinese and Hindu mathematicians used v10.
  • Other useful approximations are 22/7 or 355/113
  • As a decimal, p is approximately 3.1416
  • In 1897, the Indiana House of Representatives
  • passed a bill legislating a vague (and
    incorrect)
  • value for p. Fortunately the Senate tabled the
    measure.
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