How did Gauss do calculations?
Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you “fold” the series of numbers in the middle and add them in pairs—1 + 100, 2 + 99, 3 + 98, and so on—all the pairs sum to 101. There are 50 such pairs, and so the grand total is simply 50×101.
How did Carl Friedrich Gauss contribute to math?
Gauss wrote the first systematic textbook on algebraic number theory and rediscovered the asteroid Ceres. He published works on number theory, the mathematical theory of map construction, and many other subjects.
What is it called when you add 1 2 3 4 5?
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc. The nth partial sum is given by a simple formula: This equation was known to the Pythagoreans as early as the sixth century BCE. Numbers of this form are called triangular numbers, because they can be arranged as an equilateral triangle.
What was the answer to Gauss’s problem?
Gauss used this same method to sum all the numbers from 1 to 100. He realized that he could pair up all the numbers. That meant he had 50 pairs, each with a sum of 101. He could then multiply 50 x 101 to arrive at his answer: 5050.
What is the formula of sum of squares?
Formulas for Sum of Squares
|Sum of Squares Formulas|
|In Statistics||Sum of Squares: = Σ(xi + x̄)2|
|For “n” Terms||Sum of Squares Formula for “n” numbers = 12 + 22 + 32 ……. n2 = [n(n + 1)(2n + 1)] / 6|
Who is math King?
Leonhard Euler, a Swiss mathematician that introduced various modern terminology and mathematical notation, is called the King of mathematics. He was born in 1707 in Basel, Switzerland, and at the age of thirteen, he joined the University of Basel, where he became a Master of Philosophy.
Why is 1729 called Ramanujan number?
Ramanujan said that it was not. 1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.