Accompanied by the likes of “I don’t understand any of this - can you explain?” and “Can I go to the bathroom?”, one of the most common questions asked in classrooms today is, “How will this help me in everyday life?”
Students often fail to understand the significance of their learning and how it will help them in the future. For instance, kids wonder how knowing the facts about the American Revolution will help them in practical ways, such as paying their taxes.
I want to address this problem right now. Let me explain to you the overwhelming significance of a very common topic taught in high school today: the constants π and e.
You may think this topic has nothing to do with everyday life in modern society. You would be wrong. I’m going to explain why these mysterious numbers can have an actual effect on your life.
First, let’s have some quick definitions. π and e are numerical constants that never end and can never be represented as a fraction. π is approximately 3.14, and e is approximately 2.72.
Because these numbers never end or repeat, they can seem weird to most students. Kids can’t relate them to regular integers, and so they often disregard these numbers as arbitrary information for “higher math.” That’s code for “I see no use for this topic so I’m not going to bother learning it.”
As a result, kids never realize the amazing advantages these two numbers have given people, businesses, and entire civilizations throughout human history.
Let’s learn about π first. Defined as the ratio between the diameter of a circle and its circumference, π has been around for almost 4,000 years. Ancient civilizations such as Egypt, Greece, and Babylon had surprisingly accurate representations of it, with the Greeks having known about 500 correct digits.
So this number is old. But how is it used? And why should any student care?
Well, for one, π is used in many important branches of science. Statistics, the science that allows people to make accurate predictions and conclusions based off of limited data, uses π in many of its formulas.
In other words, the branch of math and science that allows people to conduct accurate polls - such as those representing voter opinions from taxes to immigration- relies heavily on π. Without statistics, it would be a lot harder for politicians to legislate for the preference of the people because they wouldn’t be able to accurately predict what people want.
Physics also relies heavily on π. As any student of physics knows well, many important equations relevant to physics - including Einstein’s ever-so-famous equations of general relativity - use π.
A police officer uses π in this way. For instance, say a car crash has occurred. In order to determine whose fault the crash was, police use calculations with π to find speeds of cars through knowledge of other values of the car, such as the distance it traveled or the time it took to stop. See, even the job of a police officer, which is fairly common, uses π all the time!
Put simply, π allows us to relate certain moving objects to others. It lets us predict locations of planets for observation and accurately calculate the locations of given objects at given times.
Frisch physics student Caleb Chapman noted how important π was to his studies. He said he uses π for everything, from calculating the pressure of force under an elephant’s foot to the force a key feels when being spun around one’s hand. “WIthout π, half of the physics curriculum couldn’t exist- it’s just that essential,” Chapman said.
These are just some uses of the number. π also allows us to do everything from calculating the volume of objects in architecture to measuring voltage in engineering. Many jobs that students want to work at one day - from one as sophisticated as a scientist to one as detailed as a designer - use π in their daily calculations.
But what about students who care more about a practical life as opposed to one of theoretical science? I mean, not every kid actively chases the life of a rich inventor; many just want to get by and live a happy life.
Well, this is where e comes in. Often called Euler’s number, e is defined as the limit of a complicated arithmetic series that is defined as the sum of infinite numbers of n factorial to the power of negative one.
I’d say that’s pretty confusing, no?
Luckily, the uses of e are not nearly as mind-boggling; one doesn’t need to understand the definition of e in order to benefit from it.
e is most commonly used in finance, specifically compound interest. When somebody deposits money in a bank, often the rate at which their balance increases due to interest can be represented by an equation including e.
This is an important place where e is very practically used, so it is a good example of how constants are relevant in life. In other words, it isn’t just some odd number only with significance to a Nobel prize mathematician; rather, the common Joe on the street uses it whenever his bank compounds interest on his deposit or loan.
Sammy Markowitz, a Frisch sophomore, works with a lot of math problems relating to finance. He commonly uses e to calculate interest and therefore sees the importance of the constant. “e makes all of finance much easier,” Markowitz said. “It is the basis to interest and finance itself, and so it helps me understand where money is coming, going, and how much of it belongs where.”
The uses don’t end with finance. e can be used in physics, just like π. It can be used to find how fast or slow something cools, to study electric circuits, and to calculate the properties of springs.
See, constants can be used for fun! Say I want to build something cool, like a car that could run through fire on a very breakable bridge. That sounds fairly interesting, doesn’t it?
π would be used to find the pressure of the wheels to make sure they don’t break the unstable bridge, e would be used to find a material that would stay intact in a fire, and both constants would be used to create the right electrical circuit for the job.
The same general uses of these constants could apply to any invention anybody could come up with. Want another example? Say I wanted to make a self-cleaning vacuum to get me out of doing my chores. I would need π in order to calculate the area of the floor, e to deal with the electrical components in the device, and overall, the constants would be used all over the place.
See, even a high schooler who just enjoys inventions can use π and e in his or her hobbies.
The world often turns away from anything that confuses it. But if students took some time to learn what π and e really mean, as opposed to immediately dismissing them, they would be able to use it for the rest of their lives. That would be true whether they’re building a toy in their backyard and need to measure the size of a circle or they’re working at NASA and need to make sure a rocket doesn’t crash.