StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...

A History of Mathematics - Essay Example

Cite this document
Summary
Squaring the circle is the ancient problem of producing a geometrical square of the same area as that of any given circle, under the restriction that only an unmarked straight edge and a compass may be used. It is one of the earliest great problems of mathematics, going back to as far as the most ancient recovered mathematical documents.
Download full paper File format: .doc, available for editing
GRAB THE BEST PAPER98.1% of users find it useful
A History of Mathematics
Read Text Preview

Extract of sample "A History of Mathematics"

Download file to see previous pages

His idea used as basis the fact that the Greek mathematicians of his time knew how to square regular polygons. He proposed that if a regular polygon were to be inscribed in a circle, and if the number of sides of the polygon were doubled again and again, the polygon would eventually become indistinguishable from the circle. This solution was still incorrect, because making the polygon coincide with the circle required an infinite number of permutations. The Europeans of the Renaissance, Leonardo da Vinci among them, tried in vain to solve the problem.

They did not realize that it was impossible to square a circle using the straight edge and compass method. The Scottish mathematician James Gregory (1638 - 1675) proposed that the ratio of the area of any sector of a circle to that of inscribed or circumscribed regular polygons cannot be expressed with a finite number of terms, thus concluding that squaring the circle is impossible. Ferdinand von Lindemann (1852 - 1939) published in 1882 his proof that pi is not an algebraic, but a transcendental number (not a solution of any polynomial with rational coefficients).

This essentially means that there is no way to determine if any physical object or quantity has an exact measure of pi (regardless of the unit system). Because squaring the circle involves the use of pi, Lindemann's proof ended the quest for the plane technique of squaring the circle. Trisecting an AngleAnother classic mathematical problem is that of trisecting an angle, again with the restriction of using only an unmarked straight edge and a compass. Although there are certain angles that can be trisected with this method, the problem is to trisect an arbitrary angle.

It has been proven that this is impossible. It can be solved, however, without the said restriction. There is no certainty of when this specific problem first arose. It is known that Hippocrates in the 5th century B.C. considered the problem. For centuries the problem of trisecting an angle (using Euclidean constructions) was pondered upon by mathematicians, but these early mathematicians focused on plane methods of trisecting an arbitrary angle, and thus failed. The first known mathematician who worked on the problem was the Greek Hippias (460 - 400 BC).

He came up with the curve called the quadratix, which was originally used for squaring the circle, and was also used to solve the problem of angle trisection. Archimedes (287 - 212 BC) came up with a curve, the Archimedean spiral, and also used it to solve the problem. The Greek mathematician Nicomedes (280 - 210 BC) also worked on the problem. He came up with the curve known as the conchoid, and used it for angle trisection. These solutions, however, break the straight-edge-and-compass restriction.

It was only in 1837 that it was proven that there is no solution for the original problem of trisecting any angle with only an unmarked straight edge and a compass. The French mathematician Pierre Wantzel proved the impossibility of solving the problem under the straight edge and compass restriction.AntiphonAntiphon was an orator, writer, teacher, and philosopher. He was a contemporary of Socrates. He died, like Socrates, because of political troubles. There

...Download file to see next pages Read More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“A History of Mathematics Essay Example | Topics and Well Written Essays - 1000 words”, n.d.)
A History of Mathematics Essay Example | Topics and Well Written Essays - 1000 words. Retrieved from https://studentshare.org/miscellaneous/1518464-a-history-of-mathematics
(A History of Mathematics Essay Example | Topics and Well Written Essays - 1000 Words)
A History of Mathematics Essay Example | Topics and Well Written Essays - 1000 Words. https://studentshare.org/miscellaneous/1518464-a-history-of-mathematics.
“A History of Mathematics Essay Example | Topics and Well Written Essays - 1000 Words”, n.d. https://studentshare.org/miscellaneous/1518464-a-history-of-mathematics.
  • Cited: 0 times

CHECK THESE SAMPLES OF A History of Mathematics

History of Mathematics

The aim of this essay is to briefly summarize the development process of mathematics as a science, specifically its origin and early development.... Particularly, the essay will focus on discussing the achievements in mathematics made by the minds of ancient Greece....
6 Pages (1500 words) Essay

History of Mathematics: the Fibonacci Sequence

In the paper “history of mathematics: the Fibonacci Sequence” the author discusses what is the Fibonacci Sequence.... The only use of mathematics identified was for ecclesiastical calendars and growth in mathematical knowledge is limited to the representation of number by means of the fingers.... Apart from his famous paintings, Da Vinci is also best known for his application of mathematics to science and theory of perspective (Boyer & Merzbach 280)....
2 Pages (500 words) Essay

Mathematics Book Report

2008 Mathematics Book Report of Book: A History of Mathematics Carl B.... With full of facts and a wealth of information, this book deserves to have the name "A History of Mathematics" Works CitedCarl B.... A History of Mathematics.... There are several books about the history of mathematics but it stands out.... There are several books about the history of mathematics but it stands out.... It is the perfect guide for anyone who knows well about the basics of mathematics. 02 Feb....
2 Pages (500 words) Essay

Influence of Hindu and Arabs in Mathematics

"But the glory of having invented general methods in this most subtle branch of mathematics belongs to the Indians.... The author analyses the history of this process, methods, and influence of different countries on it.... The author of the essay under the title "Influence of Hindu and Arabs in mathematics" touches upon the information concerning the appearance of the numeral system.... The translations of classical works of ancient India into the Chinese language include mathematics Brahman....
1 Pages (250 words) Essay

Brief Summary of Historical Orientation of Mathematics

A History of Mathematics.... hellip; As far as the history of mathematics is concerned, the same can be traced back to 3000 BCE.... Write a brief summary of Historical Orientation of Mathematics combining Political Events, Cultural Events and Mathematical Ideas As far as the history of mathematics is concerned, the same can be traced back to 3000 BCE.... This essay presents a brief summary of the historical orientation of mathematics combining political events, cultural events, and mathematical ideas....
1 Pages (250 words) Essay

Father Marin Mersenne and the New Mathematical Approach during the Scientific Revolution of the 17th Century

A History of Mathematics.... history of mathematics.... Collins Dictionary of mathematics.... Wichita State University, Department of mathematics and Statistics, Math 750J Project.... 1: General Survey of the history of Elementary Mathematics.... His own famous contribution to mathematics was development of the ‘Mercenne numbers' that are primes of the form 2p-1 where p is itself a prime; important to number theory (Selkirk, 1992:34)....
2 Pages (500 words) Assignment

The Personality of Aristotle

Without formal rules for proving and establishing the fact, it would be impossible to formalize mathematics or science, so this was an important time in the history of mathematics.... It is mentioned that Aristotle established the basic principles of mathematics, distinguishing between the axiom and the postulate.... Another factor that made Aristotle important is his recording of things studied, which provided evidence for those who later wrote histories of mathematics....
4 Pages (1000 words) Essay

Assessment Plan on College Algebra

The paper aims at analyzing the student learning outcomes in the area of college algebra, and also developing an assessment plan to enhance the understanding of college algebra.... The student learning outcomes are generated through accumulated academic competencies.... hellip; Learning outcomes entails wider aspects of the program that include wider elements; for instance, graduation levels, faculty levels academic publications....
5 Pages (1250 words) Research Paper
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Contact Us