Online Math Center

Middle School Geometry: An Introduction To Pi

The new school year is well and truly up and running, with kids across the country dipping their toes into new subjects, new topics, and new challenges. For middle school math students, certain math topics begin to pull away from the ease of earlier lessons and push students towards more difficult topics and problems to solve.


One concept that is introduced to middle school math learners in geometry class is that of pi. No, we are not talking about delicious desserts! We are talking about pi, a defined number that we can use to find out all sorts of useful things about circles.


We’re going to dive into pi and find out what pi is, why we use it, and how we use it in the real world. 

What is pi and how do we find it?

Believe it or not, pi (π) is the most studied number in the history of mathematics. People have been fascinated by it for hundreds of years. But, what is it? And how do we find out its value?


In simple terms, pi is a defined number (a mathematical constant) the ratio of a circle’s circumference to its diameter. 


That number is 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679… 


For simplicity, we usually round pi down to 3.14159, or 22/7. 


We know that a circle’s circumference is the length all the way around the circle, whereas the diameter is the length across the circle. The circumference divided by the diameter of a circle is always π, no matter how large or small the circle is!


Let’s try an example to get a rough estimate. If our circle’s diameter is 8.5cm and our circle’s circumference is 26cm.


To find pi, we divide 26 by 8.5 → 26/8.5 = 3.0588235294117645. That is quite close to pi.


Similarly, we can use pi to find either the diameter of a circle or its circumference, depending on what information we are given. 


If the diameter of the circle is 13 cm, we can cross multiply and establish that the diameter is:


13 x π = diameter = 40.8407044967. 


Then, to check we are correct, we can divide our answer by 13, and the result should be pi. 


How Do We Use Pi?

As we’ve seen, we can use pi to establish the characteristics of circles. With as little information as the diameter, the circumference, or the radius (which is half of the diameter), we can find out quite a bit about a circle, including its area. 


The area of a circle is equal to πr^2, where r is the radius.


Pi has a multitude of applications in our society. Pi is extremely important in physics, medicine, engineering, and biomedicine. Of course, pi helps us greatly in mathematics too! In the real world (away from the fantasy land of math lessons) we can use pi to calculate all manner of things. 


For example, did you know that using pi, we can measure waves? Ocean waves, light waves, sound waves… each of these waves can be measured using pi. 


Pi is also used to track important information on a large scale, such as population dynamics and the number of deaths in a population. Biochemists use pi to study and understand how our DNA is structured and how it works, and clock designers use pi to design pendulums for clocks.


Let’s not forget about the likes of us, who can use pi to establish once and for all which pizza deal offers you the best value for money! 


Pi Day, Your New Favorite Holiday

Pi has such a massive impact on our society that people have begun to celebrate this wonderful number each year. It is celebrated on the date most close to pi’s value, March 14th (3/14 → 3.14…).


Although it isn’t a serious holiday, it is a fun day to be in math or physics class! You might even get lucky and our teacher might bring a cake or a pie or a pizza for the students to measure (and then devour!).


Be sure to check out this link for more fun facts about pi and Pi Day.

Get ahead with OMC math courses

Pi is a number that helps young math students understand math and numbers on a whole new level. The challenges they face in geometry class will be a piece of cake (or pie!) if they can wrap their head around these types of topics, and get the appropriate support in class. 


Ensure that your child gets the attention they deserve throughout their geometry lessons, and every other math class they face up to this school year. Enroll now in an OMC Middle School math course to secure your child’s place and start them on their journey towards top grades in math.

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