Speaking Easy: An Anecdote About Gauss →
In a math course I took at university, my professor told the class a story about Gauss that I absolutely adored.
Gauss, if you are not aware, is a well-known mathematician, but this story takes place in a grade school classroom. The teacher assigned the class some busy-work; he gave the class the tedious task of adding the numbers 1 to 100. In no time at all, Gauss had the solution. He had discovered a shortcut to the solution.
How did he do it? With a little ingenuity and an understanding of the commutative property of addition:
- Commutative Property of Addition: When two numbers are added, the sum is the same regardless of the order of the addends. Ex. 1 + 2 = 2 + 1
So, 1 + 2 + … + 99 + 100 is the same as 100 + 99 + … + 2 + 1.
Setting up these two sums as equations and adding them together yields this:
This reduces to: x = 5050.
The generalized formula for adding a series of numbers is
n(n+1)/2
where n is the number of integers to be added.
What impressed me the most about this story was how a brilliant young lad was able to outwit a lazy teacher, and it so beautifully illustrates how a strong understanding of mathematics can be a powerful tool for reducing the complexity of calculations.
