Contribution of Mathematics Field
Archimedes had huge contribution in mathematics filed since he loved mathematics so much. He used his entire life to discover the mathematics field. He has contribution in integral calculus, calculate the value of pie and fluid displacement.
One of his contributions in mathematics fields are invention of integral calculus and recorded in a text named Method. In the text of Method contains many of his researches such as the determination of the area of parabola, the area and volume of a sphere and an ellipsoid. Also, the text contain many geometric formulas, prove and explanation. By using the integral calculus, he calculated the section of areas surround by geometric figure and the slope of the tangent lines of a curve or surface. His contribution in integral calculus helped Sir Isaac Newton to continue the development of calculus.
From another work of Archimedes, Measurement of The Circle, recorded the method for approximating the value of pi (π). Pi means ratio between a circle's circumference and its diameter. Based on the theorem of Euclid, Arc...
Abstract—The transition to calculus was a remarkable period in the history of mathematics and witnessed great advancements in this field. The great minds of the 17th through the 19 Centuries worked rigorously on the theory and the application of calculus. One theory started another one, and details needed justifications. In turn, this started a new mathematical era developing the incredible field of calculus on the hands of the most intelligent people of ancient times. In this paper, we focus on an amazing mathematician who excelled in pure mathematics despite his physical inability of total blindness. This mathematician is Leonard Euler.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
in 212 B.C. at the age of 75 in Syracuse. It is said that he was killed
Ball, Rouse. “Sir Isaac Newton.” A Short Account of the History of Mathematics. 4th ed. Print.
Pi occurs in various mathematical calculations. The circumference (c) of a circle can be determined by multiplying the diameter (d) by : c = d. The area (A) of a circle is determined by the square of the radius (r): A = r2. Pi is applied to mathematical problems involving the lengths of arcs or other curves, the areas of ellipses, sectors, and other curved surfaces, and the volumes of solids. It is also used in various formulas of physics and engineering to describe such periodic phenomena as the motion of pendulums, the vibration of strings, and alternating electric currents.
One of the most well known contributors to math from Greece would be Archimedes. He
This paper presents a development of mathematical analysis, illustrating the contribution of Euler to the development of calculus in the specific examples. Mathematical analysis is a combination of divisions of mathematics that includes differentiation, integration, limits, infinite series and analytic function. First ideas of the concepts of mathematical analysis were established by the ancient Greek mathematicians. All the divisions of calculus, including analysis, had a similar idea: division on the infinitely small elements but the nature of analysis was unfamiliar to the authors of an idea. They developed the principle of infinity and established a method to calculate the area and volume of some plane figures and solids.
Euclid and Archimedes are two of the most important scientists and mathematicians of all time. Their achievements and discoveries play a pivotal role in today’s mathematics and sciences. A lot of the very basic principles and core subjects of mathematics, physics, engineering, inventing, and astronomy came from the innovations, inventions, and discoveries that were made by both Euclid and Archimedes.
part he stayed there for most of his life. He was the son of Phidias,
Leonardo da Vinci was one of the greatest mathematicians to ever live, which is displayed in all of his inventions. His main pursuit through mathematics was to better the understanding and exploration of the world. He preferred drawing geographical shapes to calculate equations and create his inventions, which enlisted his very profound artistic ability to articulate his blueprints. Leonardo Da Vinci believed that math is used to produce an outcome and thus Da Vinci thought that through his drawings he could execute his studies of proportional and spatial awareness demonstrated in his engineering designs and inventions.
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.
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.
They constructed the 12-month calendar which they based on the cycles of the moon. Other than that, they also created a mathematical system based on the number 60 which they called the Sexagesimal. Though, our mathematics today is not based on their system it acts like a foundation for some mathematicians. They also used the basic mathematics- addition, subtraction, multiplication and division, in keeping track of their records- one of their contributions to this world, bookkeeping. It was also suggested that they even discovered the number of the pi for they knew how to solve the circumference of the circle (Atif, 2013).
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.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...