Two Great Events And The Contributors Of The Events In The Mathematics Field

The pre-20th century saw great events which brought about various inventions and discoveries especially in the mathematics field. There were various people who made great contributions to the mathematics field which are applicable and still in use to date. This paper will therefore look at two among the many great events and the contributors of the events in the mathematics field.

About 250BC there were various inventions and contributions by Archimedes who was considered as being among the greatest mathematicians in history. He is still honored for the various contributions he made in geometry, mechanics, physics and technology. He is listed among the three greatest mathematicians. His greatest contribution to the field of mathematics was particularly in the area of geometry. Aside from being a mathematician he was also an engineer who was accomplished in the field as well as an inventor he is was however thought to be obsessed with geometry.

Among his great contributions were the discovery of how to find the volumes of spheres and he went ahead to discover the exact pi value which he calculated as well as devising the notion of mathematical exponents. pi which is a Greek letter is used in the description of ratios of circle’s circumference an diameter. He pinpointed pi value as being between 3-10/71 and 3-1/7.this he arrived by inscription of a 96 sided polygon inside a circle. The discoveries were published in measurement of the circle. He also discovered the principal of buoyancy and when he discovered it he went out shouting Eureka in the streets. This was the principle of water displacement that he discovered when he was taking a birth. He is also said to be the first one to invent integral calculus about 2000 years just before Newton and Leibniz. Another of his contributions was the power of ten that refers to a way of counting where 0’s in a number that saw the elimination of Greek alphabet in counting system. This he did so that the numbers he came up with would be included in the number system (Ferris, 2010).

He devised a number of geometric formulas that are still in use today in the determination of volume and area. He also discovered how to figure out the area that is enclosed under a parabolic curve. This he did using a very ingenious argument that involved the construction of an infinite number of triangles inscribed that exhausted the area that was in the parabolic segments. This is arguably the most beautiful pieces of mathematics in record. This contribution was of great importance particularly to Isaac Newton who developed calculus. He also found out how calculations of areas of circles could be done as well as establishing the formula that would be used when determining volumes of spheres and cylinders. He went ahead to discuss properties of Archimedean spiral that he described as being the distance from a point that is fixed for instance 0 of any point let’s say P on the spiral is normally proportional to the angle that is located between OP and another fixed line O. through this evaluation of areas that he made that involved the spiral he paved way for the development of calculus that was put to book in the seventeenth century (Ferris, 2010).

In 1837 there was another invention that was discussed by Liouville which was integral equations and which gave Sturm-Liouville theory that was used in solving of equations a new meaning and more emphasis. Joseph Liouville was best known for his famous work on transcendental numbers. He went ahead to construct an infinite class of such like numbers. His work involved various fields in mathematics that are inclusive of fields such as the number theory, differential geometry as well as topology, complex analysis as well as going into the field of mathematics physics as well as astronomy.

The Liouville theorem was one of his most important works which is nowadays just a basic result in complex analysis. Through this number theory he went ahead to prove that transcendent al numbers were in existence through his construction by using numbers that were known as Louville numbers which were actually continued fractions. In mathematical physics he was of great importance through two very fundamental contributions that include the sturm-Liouville theory that he had done together with Charles Francois Sturm and this was the standard procedure that was used in solving a particular type of integral equations through the development of eignen functions as well as the fact that was known as Liouville’s theorem which is a time evolution a measure that is used in the preservation for Hamiltonian systems. In the Hamiltonian dynamics, Liouville also saw the introduction of the notion of action-angle variables that was to be used in describing in a complete manner intergrable system. In the modern times this formulation came to be known as Liouville -Arnold theorem which has a concept that underlying it known as the concept of intergrability that is referred to as Liouville integrability.

There are therefore various mathematics inventions that are still in use today despite the fact that they were put into book very many years ago. This means that all this inventions were important and hence they should be put into use effectively.

References

Ferris,D.(2010). The Contributions of Archimedes in Geometry. Retrieved February 17, 2013 from http://www.ehow.com/info_8407341_contributions-archimedes-geometry.htmlUniversity of St.Andrews Scotland.(2001). A Mathematical Chronology. Retrieved February 17, 2013 from http://www-history.mcs.st-and.ac.uk/Chronology/full.html