A History of Mathematics: An IntroductionA History of Mathematics, Third Edition, provides students with a solid background in the history of mathematics and focuses on the most important topics for today's elementary, high school, and college curricula. Students will gain a deeper understanding of mathematical concepts in their historical context, and future teachers will find this book a valuable resource in developing lesson plans based on the history of each topic. This book is ideal for a junior or senior level course in the history of mathematics for mathematics majors intending to become teachers. |
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Page 178
... Diophantus's problems are indeterminate ; that is , they can be written as a set of k equations in more than k unknowns . Often there are infinitely many solutions . For these problems , Diophantus generally gave only one solution ...
... Diophantus's problems are indeterminate ; that is , they can be written as a set of k equations in more than k unknowns . Often there are infinitely many solutions . For these problems , Diophantus generally gave only one solution ...
Page 181
... Diophantus did not mention explicitly is that the initial factoring must be carefully chosen so that the solution for x is a positive rational number . In the present case , the difference between the two expressions is 1. Diophantus ...
... Diophantus did not mention explicitly is that the initial factoring must be carefully chosen so that the solution for x is a positive rational number . In the present case , the difference between the two expressions is 1. Diophantus ...
Page 191
... Diophantus's age at his death from his epigram at the opening of the chapter . 8. Solve Diophantus's Problem I - 27 by the method of I - 28 : To find two numbers such that their sum and product are given . Diophantus gives the sum as 20 ...
... Diophantus's age at his death from his epigram at the opening of the chapter . 8. Solve Diophantus's Problem I - 27 by the method of I - 28 : To find two numbers such that their sum and product are given . Diophantus gives the sum as 20 ...
Contents
PART ONE Ancient Mathematics | 1 |
3 | 43 |
References and Notes | 49 |
Copyright | |
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al-Khwarizmi algebra algorithm Almagest angle Apollonius Archimedes arithmetic astronomical axis Babylonian basic Bernoulli Book Brahmagupta calculate century chapter Chinese Chinese Mathematics chord circle coefficients conic sections consider construction cube cubic equation curve derived Descartes determine diameter difference differential Diophantus discussed distance divided Elements ellipse equal Euclid Euclid's Elements Euler example Fermat FIGURE fluxion formula fractions function geometric given number Greek mathematics Hipparchus hyperbola Ibid ideas Indian infinite integral intersection Islamic known Leibniz length logarithm mathematicians method modern notation motion multiplied Newton noted parabola parallel perpendicular plane polynomial positive probably problem procedure proof proportion Proposition proved Ptolemy Ptolemy's Pythagorean Theorem quadratic equation quantities radius ratio rectangle represent result right triangle rule side sine solution solve sphere square root straight line subtract tangent theorem translated treatise trigonometry velocity