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The Meaning & Use of Pi by Joseph A. Castellano, Ph.D.

The Meaning & Use of Pi by Joseph A. Castellano, Ph.D. How Pi ( π ) is Derived. Take a circle of string, 1 meter in diameter, cut it, stretch it out and measure its length:. The length of the string is 3.14159 m. The circumference of every circle is always 3.14159 times its diameter.

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The Meaning & Use of Pi by Joseph A. Castellano, Ph.D.

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  1. The Meaning & Use of Pi by Joseph A. Castellano, Ph.D.

  2. How Pi (π) is Derived • Take a circle of string, 1 meter in diameter, cut it, stretch it out and measure its length: The length of the string is 3.14159 m. The circumference of every circle is always 3.14159 times its diameter. This constant is known as pi and denoted by the Greek letter, π. d = 1 m L = 3.14159 m π= 3.14159

  3. How Pi (π) is Used • To calculate C, the circumference of a circle using the diameter, d or the radius, r: C d = 2 r . r r C = π 2 r or d C = π d

  4. How Pi (π) is Used • To calculate A, the area of a circle using the radius, r: . r A = πr2

  5. How Pi (π) is Used • To calculate A, the area of a circle using the diameter, d: . d A = π d2 ___ 4

  6. How Pi (π) is Used • To calculate the surface area of a sphere As, using the radius, r: As = 4 πr2 . r

  7. How Pi (π) is Used • To calculate the volume of a sphere Vs, using the radius, r, or the diameter, d: Vs = 4/3 πr3 . or r Vs = 1/6 π d3

  8. Summary • The circumference of a circle is 3.14159 times its diameter. This value is defined by the Greek letter π (Pi) • The circumference of a circle, C is equal to: C = d π or C = 2 r π

  9. Summary • The area of a circle, A, is equal to: A = πr2 or A = (π d2)/4 The surface area of a sphere, As, is equal to: As = 4 πr2 The volume inside a sphere, Vs, is equal to: Vs = 4/3 πr3 or Vs = 1/6 π d3

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