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Hey everybody, it's Carlos. My friend Bre is into architecture and landscape
design. When her teacher required everyone in the class to do a job shadow
on a career that they were interested in, Bre knew just where to go:
Larry's Landscaping. Her week is off to a good start.
She's learning all aspects of the business. She even came up with an awesome design
of her own. The only problem is that she didn't calculate
how much math goes into landscaping. She's stumped trying to find out
the area of this circular garden, and how much edging it will take.
Looks like we need a lesson on understanding pi. Grab a shovel
and let's dig into another problem solved. Here's
Bre's design. First, we need to understand that there's a
relationship between the diameter and the circumference of any circle. Here's how I
explained it to Bre. I asked her to compare the circumference and diameter of
several circular items around the shop, everything from
flower pots to coffee cups. Watch what happens.
No matter how large or small the circle, it always takes
a little more than three diameters to equal the circumference.
If you don't believe me, try it for yourself. It works.
Now, let's measure the circumference and the diameter of each
of these objects and record the measurements in the chart.
Then, we divide the measure of the circumference by the measure of the diameter.
Look at these ratios. You always get a
little more than three. You can even use different units of measurement. It will
always be about three. And if we could be exact
we would get the same number every time, and that number is pi.
Pi is a greek symbol for an irrational number. That means that it
goes on forever without ever repeating. Mathematicians, with the help of
computers, have calculated pi to over a million decimal places.
Whoa. Let's look at this circular
garden. If the circumference divided by diameter equals
pi, then circumference equals pi times
diameter. Knowing the circumference will tell Bre how much edging she needs.
The diameter of this circle is 16 feet, so the
circumference is about 50.24 feet.
Can you believe how easy that is? Now, Bre needs to
determine the area of the circle for planting. Pi is also used
to find the area of a circle. You can find the area of a circle by using the formula
pi r squared, but do you really understand why?
R is the radius, but what is the radius squared?
Here is the radius, and here is the radius squared.
Let's cover the circle with radius squares.
How many do you think it will take? One fits easily.
We can cut up a second radius squared to make it
fit. We need to cut the third radius square up
even more, but it also fits. Just a little
bit of our circle is not covered, so it takes a little more than three
radius squares to cover our circle, just like it took a little more than three
diameters to equal the circumference. The important
relationship to remember is that the are of any circle is approximately
three times its radius squared, or exactly
pi times the radius squared. Back to our garden.
The radius is eight feet, so the area
is pi times eight squared. That's pi
times 64, or approximately
200.96 square feet.
It works every
time, as designed. Bre here is set on her new career path,
and now you know the meaning of pi. Problem solved.
Oh, I love this.