If I say the word ‘calculus’, most people I know disappear behind a mental shield as if to say, “Ahhhh! Confusing word! Don’t hurt me!” but calculus really isn’t that scary. Silly waves of arithmophobia can be easily overcome with some simple explanations. As Hermione once said, “Fear of a name only increases fear of the thing itself.” (Harry Potter and the Chamber of Secrets).
Back to calculus. A long, long time ago there was a Greek guy named Archimedes. We’ll call him Archie. Archie lived back in the time before life was exciting, so to keep himself occupied, he did math. He started with a square. He gave himself a pat on the back when he learned that he could multiply the length times the width and find out a square’s area. Soon, Archie had graduated to bigger and better shapes—Octagons and Hexagons and Nonagons of all sizes. Then he hit a bump in his mathematical frolicking.
The circle. How could he find the area of a shape with no flat sides? He was stumped for a while, but he decided to start working at the problems. He took a circle and drew a hexagon inside of it. He thought to himself, “Well, Archie, you know that the area of the circle must be more than the area of the hexagon.
Then he drew another hexagon, this one larger than the circle. “Well, now I can find the area of this hexagon and I know it must be larger than the area of the circle.”
So now Archie had a range. He knew the area of the circle existed somewhere between the area of the hexagon inside the circle and the hexagon outside the circle. He was happier, but still wanted a better answer. He decided he could use a shape with more sides and create a closer approximation of the area of a circle. Archie calculated the areas of octagons, nonagons, and crazy-name-a-gons of which you have never heard, inside and outside of the circle. Eventually, after hours and hours of what he considered highly entertaining math, Archie’s approximation became so close to the real answer that it didn’t really matter that he still didn’t have the answer. The difference between his range and the actual value became negligible. Thus, calculus was born.
Calculus allows you to figure out things (such as the area under a curvy line) that ‘normal’ Algebra or Geometry don’t allow. By getting so close to the answer that the difference becomes negligible, Calculus allows math-gurus everywhere to solve problems that don’t have a simple way to arrive at a solution.
So the next time someone mentions the word ‘calculus’, don’t shrivel up inside your comfort shell and quit listening. It’s not as scary as it seems.
Isn’t that cool? I think it is.