Information On Algebra And Geometry example essay topic

Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and geometric ways of thinking were considered to be two separate parts of math and were not unified until the mid 17th century.

The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhin d Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes ("Letters"). Although not very important to the development of algebra, Archimedes (212 BC - 281 BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove the theories of mathematics ("Archimedes").

Although little is known about him, Diophantus (200 AD - 284 AD), an ancient Greek mathematician, studied equations with variables, starting the equations of algebra that we know today. Diophantus is often known as the "father of algebra" ('Diophantus'). However, many mathematicians still argue that algebra was actually started in the Arab countries by Al Khwarizmi, also known as the "father of algebra" or the "second father of algebra". Al Khwarizmi did most of his work in the 9th century. Khwarizmi was a scientist, mathematician, astrologer, and author. The term algorithm used in algebra came from his name.

Khwarizmi solved linear and quadratic equations, which paved the way for algebra problems that are now taught in middle school and high school. The word algebra even came from his book titled Al-jar. In his book, he expanded on the knowledge of Greek and Indian sources of math. His book was the major source of algebra being integrated into European disciplines ("Al-Khwarizmi"). Khwarizmi's most important development, however, was the Arabic number system, which is the number system that we use today. In the Arabic number system, the symbols 1 - 9 are used in combination to make and infinite amount of numbers ("Letters").

Another famous Arab mathematician was Omar Khayyam. Omar was also a poet, philosopher, and astronomer. Omar's works were translated in 1851, which was research on Euclid's axioms. In the medieval period, he expanded on Khwarizmi's and the Greeks mathematic works. He only worked with cubic equations only and focused on geometric and algebraic solutions of equations. In 1145 AD, Al-Khwarizmi's book was translated by Robert Chester, which made it possible for algebra to be introduced to Europe.

After algebra was introduced in Europe, European mathematicians developed and expanded on algebra concepts. Even though algebra began in the Arabic countries, once European mathematicians obtained the information of algebra, they became the leaders of mathematical discoveries in the world ("Mathematics"). From the period of 1145 AD - the late 16th century, many mathematicians developed on algebraic concepts. However, it was not until the 1680's that the most remarkable discoveries were made using algebra. Sir Isaac Newton was a very famous mathematician, English physicist, astronomer, philosopher, and alchemist. During his period of study, he used algebra to describe universal gravitation, develop the laws of motion, found orbits of the planets to be elliptical, discovered that light was made of particles, discovered the rate of cooling objects, and the binomial theorem.

His most important works were the development of calculus. However, Newton did not work alone on creating the calculus system ("Isaac Newton"). Independently alongside Newton, Wilhelm Gottfried Leibniz (1646-1716) also developed calculus. Leibniz was a mathematician, philosopher, scientist, librarian, and a lawyer. He created the functions that are used today to describe quantities related to a curve, as well as point and slope. Using algebra, he also developed the first mechanical calculator that could divide and multiply.

The most extraordinary discovery that Leibniz made, however, was the binary number system, which is used in computers today. Many mathematicians speculate on what would have happened if Leibniz would have done more research with the binary number system ("Gottfried Leibniz"). During the medieval period, algebra and geometry were not considered to be the same parts of math. The belief was that all equations had some geometric interpretation. For example, X squared and X cubed was considered to be volume problems but X to the fourth was considered imaginary.

Stiefel says, "Going beyond the cube just as if there were more than three dimensions [... ] is against nature" (Woodcock). Algebra and geometry were actually considered to be completely different subsets of math ("Rene Descartes"). I think that it just took time before mathematicians realized that algebra and geometry were linked together and could be described by one another. Obviously, some mathematicians did recognize that there were some links between algebra theories being proved by geometry, but I don't think that there was enough information on algebra and geometry to totally unify the two. I also think that the development of Euclidean and Non-Euclidean geometry helped to finish the unifying of algebra and geometry into one science. The mathematicians of medieval times had no choice but to believe that algebra and geometry were two different subsets of math because they had no proof that the two subjects were really linked together.

Mathematicians needed the work of other mathematicians, like Descartes, before they could really understand the unity of algebra and geometry. Rene Descartes (1596-1650) was a philosopher and a mathematician. Descartes was also known as Cartes ius and was the creator of the Cartesian coordinate system. Descartes also formulated the basis of modern geometry and showed how to make geometry problems into problems in algebra.

Descartes was the real start of algebra and geometry becoming unified. Rene's work led to the development of analytical geometry, which is the study of geometry using the principles of algebra. With Rene's work, geometry has been more easily explained and showed how results from equations can be expressed as a vector or shape ("Rene Descartes"). Using Analytic Geometry, geometry has been able to be taught in school-books in all grades.

Some of the problems that are solved using Rene's work are vector space, definition of the plane, distance problems, dot products, cross products, and intersection problems. The foundation for Rene's Analytic Geometry came from his book entitled Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences ("Analytic Geometry"). The history of algebra is very complex and went through many centuries of development to the algebra that we know today. Algebra is still being developed and will never quit being developed and added on to. Algebra is a relatively new form of math in the European countries and the Americas. Algebra helped mathematicians and scientists to develop many tools and theorems that people over the world use on a daily basis.

Although algebra and geometry were considered separate subsets of math, the two subjects are now unified. Who knows what inventions and discoveries will be made with algebra in the future if mathematicians continue to study the discipline of mathematics.