Where does the number pi come from?
Pi comes from the property of a circle,
but before we discover this,
let's go over some definitions.
The circumference of a circle
is the perimeter of a circle,
which is the distance
around the edge of a circle.
The diameter of a circle is
the length of a line segment
with both end points
on the edge of a circle
passing through the center,
which are pictured here in red.
And then finally, the radius of a circle
is the length of a line
segment from the center
to the edge of the circle.
The radius is half of the diameter.
So looking at our circles,
notice how the radius
is half of the diameter,
or we can see the diameter
is equal to two times the radius.
We now discover where
the number pi comes from.
For any circle, regardless of its size,
if we take the circumference,
which again is the
perimeter of the circle,
and then divide by the diameter
which is the length of a segment
with both end points on the circle
passing through the center,
we always get the same
irrational constant,
which is the number pi.
Remember an irrational
number in decimal form
is non-terminating and non-repeating,
and here see a decimal approximation
for the number pi.
So again, this is an amazing property.
And again, if we take any sized circle,
determine the circumference,
and then divide by the diameter,
we always get the irrational constant pi,
and I would highly
encourage you to try this.
Find various sized circles,
measure the circumference,
or the perimeter of the circle,
and then divide by the diameter.
And based upon the accuracy
of the measurements,
you should always get approximately 3.14,
which is a very common
decimal approximation
for the number pi.
And then finally since the circumference
divided by the diameter is equal to pi,
if we take this formula and
solve for the circumference
by multiplying both sides
of the equation by D,
we get the formula for the
circumference of a circle,
where the circumference of a circle
is equal to pi times D
or pi times the diameter.
And because the diameter is equal
to two times the radius or two times R,
we often see the circumference of a circle
expressed as two pi R,
which is two times pi times the radius.
Thank you for watching.
