Task: Work out a method for determining the sum of the first 100 consecutive numbers. Are you as clever as Gauss, the brilliant mathematician?
Carl Friedrich Gauss (1777-1855) is recognized as being one of the greatest mathematicians of all time. During his lifetime he made significant contributions to almost every area of mathematics, as well as physics, astronomy, and statistics. Like many of the great mathematicians, Gauss showed amazing mathematical skill from an early age, and there are many stories which show how clever he could be.
The most well-known story is a tale from when Gauss was still at primary school. One day Gauss' teacher asked his class to add together all the numbers from 1 to 100, assuming that this task would occupy them for quite a while. He was shocked when young Gauss, after a few seconds thought, wrote down the answer 5050. The teacher couldn't understand how his pupil had calculated the sum so quickly in his head, but the eight-year-old Gauss pointed out that the problem was actually quite simple.
It is remarkable that a child still in elementary school had discovered a method for summing sequences of numbers, but of course, Gauss was a remarkable child. Fortunately, his talents were discovered, and he was given the chance to study at university. By his early twenties, Gauss had made discoveries that would shape the future of mathematics.
While the story may not be entirely true, it is a popular tale for maths teachers to tell because it shows that Gauss had a natural insight into mathematics. Rather than performing a great feat of mental arithmetic, Gauss had seen the structure of the problem and used it to find a shortcut to a solution.
Hint #1:
Gauss came up with an algebraic expression that could be used to quickly sum the first 100 numbers. Try writing a simple expression.
Hint #2:
Think about how a zipper works. Imagine the number line as a zipper.