Fluid Theorem: A ^ 2 ^ 3-Level Calculus
Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are two legs of a right triangle and c is the hypotenuse, the longest side of the triangle.
This 1-inch long, simple, yet eloquent equation contains a beauty, a magic that is unnoticeable at first glance; I have been introduced to this beauty by Dartmouth alumni Professor Strogatz at an Engineering Diversity Weekend program last September.
As I finished my breakfast, I had the opportunity to join the campus tour or attend a mock math class, named, “Calculus at Cornell by Professor Strogatz.” Since I have a strong affinity for math, I decided to attend the mock math class.
As we settled down, Professor Strogratz, a tall, middle-aged man strode in front of the room. He announced, “Good morning. Although your travel agenda says you are in a calculus class, we will focus on a simple trigonometric equation: the Pythagorean equation, particularly its ‘odd number’ triplets, and see where it guides us to.” I was relieved. After all, I had just started Calculus at my high school; how was I going to comprehend college-level Calculus?
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We all began to share the most common ones:
“3 4 5” “5 12 13” “7 24 25” “9 40 41”
As we continued, the Professor asked, “Do you guys see any patterns?”
Someone pointed out that we can find the third number by adding one to the second number. However, the Professor wanted to know how to find the second number. He gave us five minutes to find a way to calculate the second number using solely pattern.
A pattern? In high school, we received an equation, memorized it and then plugged in numbers to arrive at an answer. I had never looked at the Pythagorean Theorem in this light
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