Gauss

=**Johann Carl Friedrich Gauss ** **"Prince of Mathematics."** =

** Biography: ** Johann Carl Friedrich Gauss was born in Brunswick, Germany, on April 30, 1777 and died on February 23, 1855. 78 years of amazing rich scientific activity. Gauss had an early passion for numbers and calculations. When Gauss was three years old he was correcting his father’s arithmetic. Then when he was seven years old, Gauss amazed his teachers by instantly adding all the integers from 1 to 100. Fourteen years later, he made a regular 17-gon by ruler and compass - the first advance in the field since the ancient Greeks. When he was 14 he revived a scholarship from the Duke of Brunswick to go to the Collegium Carolinum in Brunswick for three years and then he went to study mathematics at the University of Gottingen for three more years. Before he turned 25 years old, he was already known for his work in mathematics and astronomy. When he was 30 he become the Director of the Gottingen Observatory. His theories in mathematics ranged from theory of numbers, algebra, analysis, geometry, probability, and the theory of errors. At the same time, he carried on intensive research in many branches of science, including observational astronomy, celestial mechanics, surveying, geomagnetism, electromagnetism, mechanism optics, and actuarial science. Gauss is sometimes called the "prince of mathematics" because of his theories. He would often call Mathematics “the queen of the sciences” and Arithmetic “the queen of mathematics.”

** Publications: **

His publications, abundant correspondence, notes, and manuscripts showed him to have been one of the greatest scientific virtuosos of all time.

In 1801 Gauss published //Disquisitiones Arithmeticae,// often regarded as the work that marked the beginning of the modern theory of numbers. It combined the work of past scientists with his, and was presented in such an elegant and complete way that it rendered previous works on the subject obsolete.

** Theories in Mathematics: **

Gauss made many outstanding contributions to the theory of numbers, including research on the division of a circle into equal parts. This solved a famous problem in Greek geometry, namely, the inscription of regular polygons in a circle. First, Gauss proved that a regular polygon with seventeen sides can be constructed with a ruler and compass; he then showed that any polygon with a prime number of sides can be constructed with the instruments. Gauss also gave three proofs- · That every equation in algebra has at least one root. · Gauss was the first to adopt a strict approach to the treatment of infinite series of numbers. · He also opened up a new line of research by updating the definition of a prime number.



** Astronomical Calculations: **

Gauss determined the orbit of Ceres and was able to predict its correct position. Gauss was able to determine orbits from observed data. He used the method of least squares to determine the most likely value of something from a number of available observations. Gauss also created the Gaussian law of error, which is best known in studies of probability and statistics as the normal distribution.



** Non-Euclidean Geometry: **

Gauss was almost certainly the first to develop the idea of non-euclidean geometry theories that through a given point not on a given line, there exists only one line parallel to the given line. As adviser to the government of Hanover, Gauss had to consider the problem of surveying hilly country. This led him to develop the idea that the measurements of a curved surface could be developed in terms of Gaussian coordinates. Instead of considering the surface as part of a three-dimensional space, Gauss set up a network of coordinates on the surface itself, showing that the geometry of the surface can be described completely in terms of measurements in this network. Defining a straight line as the shortest distance between two points, measured along the surface, the geometry of a curved surface can be regarded as a two-dimensional non-Euclidean geometry.