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Primary Magazine - Issue 14: A little bit of history


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 28 July 2009 by ncetm_administrator
Updated on 28 September 2009 by ncetm_administrator

Primary Magazine Issue 14Carl Friedrich Gauss
 

A little bit of history - Carl Friedrich Gauss

Carl Friedrich Gauss was born into a poor, uneducated and very strict family on 30 April 1777, in Brunswick, Germany. His father had a number of jobs including as a mason, gardener, labourer, an assistant to a merchant, and the treasurer of a small insurance fund. Gauss described his father as ‘worthy of esteem’ but ‘domineering, uncouth and unrefined’. He wanted Gauss to become a mason as he had been, so didn’t really encourage his interest and education in mathematics and science. It was his mother who supported him. She was Gauss’ father’s second wife, a highly intelligent but only semiliterate woman who worked as a maid before beginning her reputedly unhappy marriage to him. She and Gauss’ teacher persuaded his father to allow Gauss to attend a college preparatory school when he was eleven, and to study after school instead of spinning to help support the family. They both recognised him to be a child prodigy.

From a very early age he proved to be an incredibly gifted child. So much so that the Duke of Brunswick gave him a fellowship to a local college which he went to for three years, from the age of fourteen. The Duke also funded his studies at the University of Göttingen for a further three years.

It is said that Gauss was able to calculate without any help before he could talk! One of the stories of his early genius was when, at the age of three, he corrected, mentally, an error his father had made on paper while calculating some finances. He taught himself to read and astounded his teacher when he was eight years old by instantly solving a problem he had given the class. This is now a well-known mathematical problem, why not try it?!


Gauss’ problem
: find the sum of the first 100 integers. The solution is at the end of this article.
Gauss' problem

His teacher at the time saw the promise that he had and supplied him with books to encourage his intellectual development.

When he began college at fourteen, he had a scientific and classical mind far in advance of the rest of his peers. He knew about elementary geometry, algebra, and analysis and often ‘discovered’ important theorems before studying them in class. Among other things, he discovered Bode’s law of planetary distances, found a square root in two different ways to the nearest 50 decimal places and formulated the principle of least squares while working on unequal approximations and the distribution of prime numbers!

While he was at university, Gauss independently rediscovered several important theorems. His first major achievement was when he was able to show that any regular polygon with any number of sides that is a Fermat Prime (near square prime numbers) can be constructed by compasses and a ruler. This was a major discovery in an important field of mathematics dating back to the Ancient Greeks. This led him to choose mathematics as a career. He was so pleased with his discovery that he asked for a regular heptadecagon (shape with 17 sides) to be inscribed on his tombstone. He didn’t get one however, because the stonemason decided that it would be too difficult to construct and would end up looking more like a circle!

His passion for numbers and calculations extended to the theory of numbers, algebra, analysis, geometry, probability, and the theory of errors. He also researched many branches of science, including observational astronomy, celestial mechanics, geomagnetism and electromagnetism. His publications, correspondences, notes, and manuscripts show him to have been one of the greatest scientific minds of all time. In 1799 he earned his doctorate from the University of Helmstedt.

Giuseppe PiazziIn January 1801, an astronomer named Piazzi briefly observed and then lost a new planet, which, for the rest of that year, astronomers tried in vain to relocate. Gauss decided to have a try. He applied some of his scientific and mathematical theories and found it again. Today this ‘planet’ is known as Ceres, the largest member of the asteroid belt. This established his reputation as a mathematical and scientific genius of the highest order and so began his transition from mathematician to astronomer and physical scientist. At this time, he was still being supported financially by the Duke of Brunswick but really wanted to become independent and be settled in an established post. The most obvious role for him would be to become a maths teacher, but he felt ‘repelled by drilling ill-prepared and unmotivated students in the most elementary manipulations’, so he decided on a career in astronomy.

In 1807, aged 30, he became the director of the observatory in Göttingen, where he worked for 47 years until his death on 23 February 1855 at 77.

His personal life wasn’t quite so successful. In 1805 he married Johanna Osthoff and they had two children, but she died in 1809 soon after giving birth to a third child, who also died. He became very lonely and depressed, never really recovering from her death. Less than a year later, he married his wife’s best friend. He had two sons and a daughter with her. This wife was seldom well and died in 1831 after a long illness. He didn’t have a happy relationship with his children, dominating his daughters and quarrelling with his sons, two of whom emigrated to the US. His relationship with his youngest daughter was restored when she took over the household after her mother’s death and looked after him for the last 24 years of his life.

More information about Gauss can be found at these websites:

Did you try the Gauss problem? There are a number of ways to work this out. Gauss’ presumed method was to realise that totalling pairs of numbers from opposite ends of the list gave the same sum: 1 + 100 = 101, 2 + 99 = 101, 2 + 98 = 101 etc. He knew there were 50 pairs so he multiplied 101 by 50 to give 5 050. Why not give this problem to your class and see what they make of it? You never know, you might have a budding Gauss!! As a starting point, you could ask them to total the numbers to five, then 10 and 20 and to look for patterns to try for the numbers to 100.
 

 
 
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