GAUSS HISTORY
German Mathematician, Carl Friedrich Gauss (1777-1855) had discover another approach to divisibility questions is through the arithmetic of remainder, or commonly known as the theory of congruence. In 1801, when Gauss was 24 years old, he introduced the foundation of modern number theory in his book Disquisitiones Arithmeticae.
Gauss was one of those remarkable infant prodigies. As a child of age three, he corrected an error in his father’s payroll calculations. His arithmetical powers so overwhelmed his schoolmasters, that by the time, Gauss was 7 years old, they admitted nothing more they could teach the boy. It is said that in his first arithmetic class Gauss astonished his teacher by instantly solving what is intended to be a “busy work” problem. Find the sum of all numbers from 1 to 100. The young Gauss later confessed to having recognized the pattern,
1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, …,50 +51 = 101.
Because there are 50 pairs of numbers each of which adds up to 101, the sum of all number must be 50*101=5050.This technique provides another way of deriving the formula
1+2+3+…+ n = n(n=1)
2
The most extraordinary achievement of Gauss was more in the realm theoretical astronomy than of mathematics. From the scanty data available, Gauss was able to calculate the orbit of Ceres with amazing accuracy, and the elusive planet was rediscovered at the end of the year in almost exactly the position he had forecasted. The success brought Gauss worldwide fame. Although Gauss adorned every branch of mathematics, he always held number theory in high esteem and affection.
Gauss was one of those remarkable infant prodigies. As a child of age three, he corrected an error in his father’s payroll calculations. His arithmetical powers so overwhelmed his schoolmasters, that by the time, Gauss was 7 years old, they admitted nothing more they could teach the boy. It is said that in his first arithmetic class Gauss astonished his teacher by instantly solving what is intended to be a “busy work” problem. Find the sum of all numbers from 1 to 100. The young Gauss later confessed to having recognized the pattern,
1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, …,50 +51 = 101.
Because there are 50 pairs of numbers each of which adds up to 101, the sum of all number must be 50*101=5050.This technique provides another way of deriving the formula
1+2+3+…+ n = n(n=1)
2
The most extraordinary achievement of Gauss was more in the realm theoretical astronomy than of mathematics. From the scanty data available, Gauss was able to calculate the orbit of Ceres with amazing accuracy, and the elusive planet was rediscovered at the end of the year in almost exactly the position he had forecasted. The success brought Gauss worldwide fame. Although Gauss adorned every branch of mathematics, he always held number theory in high esteem and affection.
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