Fun Learning for PI Day!
PI
It has its own day, its own music and even its own language called Pilish. It has been around since for over 4000 years and is used every day. Yet, Pi remains an unsolved puzzle for mathematicians. Here’s why.
Numberphiles, people who love numbers, adore pi. It is challenging to memorize because there isn’t a constant pattern in pi. It is fixed in its value that is to say, the numbers of pi are unchanging. They are set. However these numbers are random in their sequencing. And just when you think there’s no order at all, pi surprises us again. Like at position 763 after the decimal, there are six nines in a row. This is known as the Feynman Point. Quirky and unpredictable patterns like this make pi so fascinating.
Pi helps us solve day to day calculation in geometry, engineering and even radio waves!
Pi is 3.14 but it is relevant to so much more. We’ll show you how to calculate circumference with pi and easy tricks to memorize. You can apply the formulas to lampshades, door knobs, a round sink, your mom’s makeup cases, a clock and anything else at home that’s circular.
The diameter of a circle is the distance from edge to edge, measuring straight through the center. The measurement around a circle if you were to take
a piece of string and wrap it around it’s edge is called the circumference.
3.14159265358979323846264338327950288419
Pi can be rounded to 3.14 however, it is said to be infinite. Pi is the number produced when the circumference of a circle is divided by it’s diameter.
You can fit 3 diameters into the circumference of a circle, plus a bit more. Hence, Pi = 3 (3 diameters) and an extra .14 of the diameter. Pi = 3.14 no matter what the size of the circle. Whether it’s a pizza or a ring, pi is still the same.
Must Know the Lingo
Radius is 1⁄2 the size of a diameter or d2 Diameter is 2 times the radius or d=2r
Circumference is 3.14 times its diameter or c=πd
Doing the Arithmetic
Example 1:
The radius of a circle is 2 inches.
What is the diameter? diameter =2 times radius d = 2 x (2 in)
d= 4 in
Example 2:
The diameter of a circle is 3 cm.
What is the circumference? C=π x diameter
c= 3.14 x 3 cm
c= 9.42 cm
Example 3:
The radius of a circle is 2 in.
What is the circumference? diameter=2r
d= 2 x (2 in)
d = 4 in
Circumference equals Pi times diameter c = 3.14 x (4 in)
c = 12.56 in
Now It’s Your Turn
The radius of a circle is 3 inches. Calculate the diameter. Calculate the circumference.
The diameter of a circle is 6 inches. Calculate the radius. Calculate the circumference.
The History of PI
The oldest written records of Pi are from ancient Babylonians and Egyptians sometime between 1900 and 1600 BC. Both correctly calculated the first decimal place as 3.1.
In 250 BC, the famous Greek mathematician Archimedes invented a method to estimate Pi using polygons. He approximated a circle as a hexagon, then an octagon, then a decagon, adding more and more sides. Each time, his calculation of Pi became closer to the real value. It was hard work, though, and Archimedes only added one more decimal place, calculating 3.14.
Archimedes’ record stood for 400 years, until Roman mathematician Ptolemy added one more digit in the year 150 AD. He calculated 3.141. In 480 AD, Zu Chongzhi in China used the polygon method to calculate Pi to seven decimal places, finding 3.1415926. This required a 12,288-sided polygon! For the next 900 years, seven decimals held the record.
Around 1400, Madhava of Sangamagrama in India came up with a totally new method for calculating Pi using an infinite series. He discovered that if you keep adding smaller and smaller fractions following a special pattern, it adds up to Pi divided by 4. This is his infinite series:
1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + … = pi/4.
By continuing the pattern, he calculated Pi to ten decimal places.
In 1665, Isaac Newton published an even better way to compute Pi using a branch of math called calculus. He didn’t do the calculation himself, but other mathematicians used his method. By 1946, Pi was known to 620 digits using calculus.
In 1949, mathematicians used one of the first computers, called ENIAC, to calculate Pi to 2,037 decimal places. Soon, new algorithms and faster computers made it possible to get millions of digits. Then billions. Then trillions. The current record was set in 2021, which calculated 63 trillion digits! Just writing that many digits of Pi out by hand would take a million years!
How Many Digits Do You Need?
If you’re thinking that 63 trillion digits is overkill, you’re right. Even NASA scientists only use 40 digits in their calculations for the entire size of the observable universe. So why do mathematicians and computer scientists keep trying to break the record? Pi is a great way to test new computers and algorithms. Plus, mathematicians are always wondering if maybe, just maybe Pi has an end. But as far as we know, it just keeps going on to infinity.
As rivers age, they become more and more meandering, meaning they have more twists and turns. Scientists define the meandering ratio as the winding length of the river divided by its straight distance from source to end. As a river gets older, its meandering ratio approaches exactly Pi.
Inventing PI
It turns out the ancient Greeks also invented pie, which they filled with honey, cheese, and spices. The ancient Romans liked to fill their pies with meat and seafood.