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Leonhard euler contributions
Leonhard euler contributions
Leonhard euler contributions
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Mathematics has played an integral part in daily life since the beginning of time. There have been many individuals responsible for paving the road to higher mathematics. Among these individuals is a man who was a physicist and scholar and helped to bring life to modern mathematics. His name was Leonhard Euler. Although he was born in the 18th century, Euler’s mathematic innovations still apply to the world of mathematics that we experience today.
It was a warm spring day (well I would assume that it would have been a warm spring day) when Leonhard Euler graced the world with his presence. April 15, 1707, marked the day that a brilliant mathematician entered into the world. It would become apparent in his early childhood that Euler had a knack for mathematics. Although his abilities could be considered genetic as his father, Paul Euler, was a brilliant mathematician himself who studied under Jakob Bernoulli.
Euler was born in Basel, Switzerland where he was destined to be a clergyman. Yet, it was obvious that Euler had a different calling in life. His aptitude for mathematics was evident even in his early life. His propensity for higher learning was so great that he studied with Johann Bernoulli, who was Jakob’s brother, as a young boy. His time with Johann urged his sense of mathematic discovery. Euler attended University of Basel where he earned his Master’s degree while he was still a teenager. While at the school he barely learned any mathematics because the school was basically a poor school. Due to his own mathematic curiosity and Johann’s private lessons, at the under-ripened age of 16, Euler became a college graduate with a Master’s degree. His curiosity in mathematics allowed Euler to study the works of other brilliant ...
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... all their squares, cubes, and fourth, fifth, and sixth powers. An impressive feat for anyone, but his abilities did not stop there. He was also able to do mental calculations up to at least fifty places of accuracy. He also completely memorized Virgil’s Aeneid in Latin. The text in its entirety is 63,719 words long.
In a summary, Euler was an impressive man from his contributions to higher level mathematics, to his ability to persevere through his condition of being blind, to having one of the most impressive memories in history. Euler may not have been the father of calculus but he was the one who nurtured it and gave life to some of the greatest mathematical concepts, formulas, equations, and numbers. Guass put it best when he said, “The study of Euler’s works will remain the best school for the different fields of mathematics and nothing else can replace it.”
Michael Guillen, the author of Five Equations that Changed the World, choose five famous mathematician to describe. Each of these mathematicians came up with a significant formula that deals with Physics. One could argue that others could be added to the list but there is no question that these are certainly all contenders for the top five. The book is divided into five sections, one for each of the mathematicians. Each section then has five parts, the prologue, the Veni, the Vidi, the Vici, and the epilogue. The Veni talks about the scientists as a person and their personal life. The Vidi talks about the history of the subject that the scientist talks about. The Vici talks about how the mathematician came up with their most famous formula.
Since girls were not permitted to attend any college preparatory schools, she decided to go to a general finishing school. There she studied and became certified to teach English and French. Soon after she altered her mind and decided that she wanted to pursue an education in mathematics. In 1904 Erlangen University accepted Emmy as one of the first female college students. In 1907 she received a Ph.D. in mathematics from this University. From 1908 to 1915 she worked at the Mathematical Institute of Erlangen without getting compensated or titled. The only reason she was permitted to work there was because she was helping her dad out by lecturing for his class when he was out sick. During these years she worked with Algebraist Ernst Otto Fisher and also started to work on theoretical algebra, which would make her a known mathematician in the future. She started working at the mathematical Institute in Göttingen and started to assist with Einstein’s general relativity theory. In 1918 she ended up proving two theorems which were a fundamental need f...
During the course of this almost comic sequence of events, a major chapter in the history of mathematics was closed. The story highlights the way math has developed over time and requires effort to sort through the various cases before a nice formulaic approach can be determined and shared with the world. Math students should be encouraged by reading the lives and work of the scholars before them who persisted at finding the underlying structure of our number systems.
“Thus in arithmetic, during the few months that he studied it, he made such progress that he frequently confounded his master by continually raising doubts and difficulties. He devoted some time to music … Yet though he studied so many different things, he never neglected design and working in relief, those being the things which appealed to his fancy more than any other.”
The argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
No other scholar has affected more fields of learning than Blaise Pascal. Born in 1623 in Clermont, France, he was born into a family of respected mathematicians. Being the childhood prodigy that he was, he came up with a theory at the age of three that was Euclid’s book on the sum of the interior of triangles. At the age of sixteen, he was brought by his father Etienne to discuss about math with the greatest minds at the time. He spent his life working with math but also came up with a plethora of new discoveries in the physical sciences, religion, computers, and in math. He died at the ripe age of thirty nine in 1662(). Blaise Pascal has contributed to the fields of mathematics, physical science and computers in countless ways.
Born in France on March 31st, 1596, Rene Descartes grew to be known as ‘The Father of Modern Philosophy”. Not only was Rene a philosophical man but he contributed greatly to Mathematics and his ideas have influenced our daily lives in a productive way. DesCartes was raised in a very religious christian family, his father was a member of the parliament and strongly believed in education at a young age. DesCartes studied at the Jesuit college at the mere age of eight. As a child and throughout his adulthood physical incapabilities enabled DesCartes to function as swift or promptly as his peers. Growing up and until the day of his death, Descartes’s health was always a major precaution he was forced to remain aware of. The Jesuit college granted him the immunity of resting in mornings before class. It was this education that led him to contribute philosophical and mathematical theories and devices that still hold a great value to mathematicians and everyday people even today in the 21st century. From a very young age he had interests in mathematics and analytical geometry. Descartes’s contributions to modern day society were affected by his young adulthood, soon he created mathematical and scientific ideas, and lastly philosophical ideas.
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
Born in the Netherlands, Daniel Bernoulli was one of the most well-known Bernoulli mathematicians. He contributed plenty to mathematics and advanced it, ahead of its time. His father, Johann, made him study medicine at first, as there was little money in mathematics, but eventually, Johann gave in and tutored Daniel in mathematics. Johann treated his son’s desire to lea...
Calculus, the mathematical study of change, can be separated into two departments: differential calculus, and integral calculus. Both are concerned with infinite sequences and series to define a limit. In order to produce this study, inventors and innovators throughout history have been present and necessary. The ancient Greeks, Indians, and Enlightenment thinkers developed the basic elements of calculus by forming ideas and theories, but it was not until the late 17th century that the theories and concepts were being specified. Originally called infinitesimal calculus, meaning to create a solution for calculating objects smaller than any feasible measurement previously known through the use of symbolic manipulation of expressions. Generally accepted, Isaac Newton and Gottfried Leibniz were recognized as the two major inventors and innovators of calculus, but the controversy appeared when both wanted sole credit of the invention of calculus. This paper will display the typical reason of why Newton was the inventor of calculus and Leibniz was the innovator, while both contributed an immense amount of knowledge to the system.
Few mathematicians had the good chance to change the course of mathematics more than once; Luitzen Egbertus Jan Brouwer is one of the remarkable people who managed to do so. He came as a young student where before he could finish school he had already published his first original research papers on rotations in 4-dimensional space. Brouwer was a Dutch mathematician who founded mathematical intuitionism, which is a doctrine that views the nature of mathematics as mental constructions governed by self-evident laws, and whose work completely transformed topology which is the study of the most basic properties of geometric surfaces and configurations.
Carl Friedrich Gauss was born April 30, 1777 in Brunswick, Germany to a stern father and a loving mother. At a young age, his mother sensed how intelligent her son was and insisted on sending him to school to develop even though his dad displayed much resistance to the idea. The first test of Gauss’ brilliance was at age ten in his arithmetic class when the teacher asked the students to find the sum of all whole numbers 1 to 100. In his mind, Gauss was able to connect that 1+100=101, 2+99=101, and so on, deducing that all 50 pairs of numbers would equal 101. By this logic all Gauss had to do was multiply 50 by 101 and get his answer of 5,050. Gauss was bound to the mathematics field when at the age of 14, Gauss met the Duke of Brunswick. The duke was so astounded by Gauss’ photographic memory that he financially supported him through his studies at Caroline College and other universities afterwards. A major feat that Gauss had while he was enrolled college helped him decide that he wanted to focus on studying mathematics as opposed to languages. Besides his life of math, Gauss also had six children, three with Johanna Osthoff and three with his first deceased wife’s best fri...
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
The abstractions can be anything from strings of numbers to geometric figures to sets of equations. In deriving, for instance, an expression for the change in the surface area of any regular solid as its volume approaches zero, mathematicians have no interest in any correspondence between geometric solids and physical objects in the real world. A central line of investigation in theoretical mathematics is identifying in each field of study a small set of basic ideas and rules from which all other interesting ideas and rules in that field can be logically deduced. Mathematicians are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory. Part of the sense of beauty that many people have perceived in mathematics lies not in finding the greatest richness or complexity but on the contrary, in finding the greatest economy and simplicity of representation and proof.