The Leading eBooks Store Online 4,138,907 members ⚫ 1,351,551 ebooks

New to

Learn more

Beyond the Quartic Equation

Beyond the Quartic Equation by R. Bruce King
Buy this eBook
US$ 89.00
(If any tax is payable it will be calculated and shown at checkout.)
One of the landmarks in the history of mathematics is the proof of the nonex- tence of algorithms based solely on radicals and elementary arithmetic operations (addition, subtraction, multiplication, and division) for solutions of general al- braic equations of degrees higher than four. This proof by the French mathema- cian Evariste Galois in the early nineteenth century used the then novel concept of the permutation symmetry of the roots of algebraic equations and led to the invention of group theory, an area of mathematics now nearly two centuries old that has had extensive applications in the physical sciences in recent decades. The radical-based algorithms for solutions of general algebraic equations of degrees 2 (quadratic equations), 3 (cubic equations), and 4 (quartic equations) have been well-known for a number of centuries. The quadratic equation algorithm uses a single square root, the cubic equation algorithm uses a square root inside a cube root, and the quartic equation algorithm combines the cubic and quadratic equation algorithms with no new features. The details of the formulas for these equations of degree d(d = 2,3,4) relate to the properties of the corresponding symmetric groups Sd which are isomorphic to the symmetries of the equilateral triangle for d = 3 and the regular tetrahedron for d — 4.
Birkhäuser Boston; January 2009
158 pages; ISBN 9780817648497
Read online, or download in secure PDF format
Title: Beyond the Quartic Equation
Author: R. Bruce King
  • News
  • Contents
No entry found