a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 11

The Meaning & Use of PiThe Meaning & Use of Pibyby

Joseph A. Castellano, Ph.D.Joseph A. Castellano, Ph.D.

a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 22

How Pi (How Pi (ππ) is Derived) is DerivedTake a circle of string, 1 meter in diameter, Take a circle of string, 1 meter in diameter, cut it, stretch it out and measure its length:cut it, stretch it out and measure its length:

d = 1 m

L = 3.14159 m

π = 3.14159

The length of the string is3.14159 m. The circumferenceof every circle is always3.14159 times its diameter.This constant is known as piand denoted by the Greekletter, π.

a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 33

How Pi (How Pi (ππ) is Used) is UsedTo calculate C, the circumference of a circle To calculate C, the circumference of a circle using the diameter, d or the radius, r:using the diameter, d or the radius, r:

CC

..rr rr

dd

d = 2 rd = 2 r

C = C = ππ 2 2 rr

C = C = ππ d doror

a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 44

How Pi (How Pi (ππ) is Used) is UsedTo calculate A, the area of a circle using the To calculate A, the area of a circle using the radius, r:radius, r:

. rrA = A = ππ rr22

a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 55

How Pi (How Pi (ππ) is Used) is UsedTo calculate A, the area of a circle using the To calculate A, the area of a circle using the diameter, d:diameter, d:

.dd A = A = ππ d d22 ______44

a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 66

How Pi (How Pi (ππ) is Used) is UsedTo calculate the surface area of a sphere As, To calculate the surface area of a sphere As, using the radius, r:using the radius, r:

As = 4 As = 4 ππ rr22

.rr

a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 77

How Pi (How Pi (ππ) is Used) is UsedTo calculate the volume of a sphere Vs, To calculate the volume of a sphere Vs, using the radius, r, or the diameter, d:using the radius, r, or the diameter, d:

Vs = 4/3 Vs = 4/3 ππ rr33

oror

Vs = 1/6 Vs = 1/6 ππ d d33

.rr

a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 88

SummarySummaryThe circumference of a circle is 3.14159 The circumference of a circle is 3.14159 times its diameter. This value is defined by times its diameter. This value is defined by the Greek letter the Greek letter ππ (Pi) (Pi)

The circumference of a circle, C is equal to:The circumference of a circle, C is equal to:

C = d C = d ππ

oror

C = 2 r C = 2 r ππ

a xa x22 + b x + c = 0 + b x + c = 0

xx22 + y + y22 = z = z22

3.14159….

3.14159….

Meaning of Pi Meaning of Pi 99

SummarySummaryThe area of a circle, A, is equal to:The area of a circle, A, is equal to:

The surface area of a sphere, As, is equal to:The surface area of a sphere, As, is equal to:

The volume inside a sphere, Vs, is equal to:The volume inside a sphere, Vs, is equal to:

As = 4 As = 4 ππ rr22

Vs = 4/3 Vs = 4/3 ππ rr33

ororVs = 1/6 Vs = 1/6 ππ d d33

or A = (or A = (ππ d d22)/4)/4A = A = ππ rr22