Mathematical Masterpieces: Further Chronicles by the ExplorersSpringer Science & Business Media, 2007年10月16日 - 340 頁 In introducing his essays on the study and understanding of nature and e- lution, biologist Stephen J. Gould writes: [W]e acquire a surprising source of rich and apparently limitless novelty from the primary documents of great thinkers throughout our history. But why should any nuggets, or even ?akes, be left for int- lectual miners in such terrain? Hasn’t the Origin of Species been read untold millions of times? Hasn’t every paragraph been subjected to overt scholarly scrutiny and exegesis? Letmeshareasecretrootedingeneralhumanfoibles. . . . Veryfew people, including authors willing to commit to paper, ever really read primary sources—certainly not in necessary depth and completion, and often not at all. . . . I can attest that all major documents of science remain cho- full of distinctive and illuminating novelty, if only people will study them—in full and in the original editions. Why would anyone not yearn to read these works; not hunger for the opportunity? [99, p. 6f] It is in the spirit of Gould’s insights on an approach to science based on p- mary texts that we o?er the present book of annotated mathematical sources, from which our undergraduate students have been learning for more than a decade. Although teaching and learning with primary historical sources require a commitment of study, the investment yields the rewards of a deeper understanding of the subject, an appreciation of its details, and a glimpse into the direction research has taken. Our students read sequences of primary sources. |
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algebraic algorithm appear applied approximate arithmetic become beginning Bernoulli calculate called chapter circle claims coefficients complex compute consider constant contained continuous convergence corresponding cube curvature curve derivatives determine digit discovered dividing division divisors equal equation Euler example Exercise expression Fermat Figure final formula function further Gauss geometry give given idea infinite integers introduction known Lagrange later length linear manifold mathematics means method modulo multiplied nature Newton numbers obtain original Pascal’s pattern plane polynomial positive powers present prime prime numbers problem progressions proof prove quadratic quadratic forms quadratic residue quantity reader reciprocal remains represented root sequence side simple solution solve space sphere squares summation formula sums of powers Suppose surface theorem theory triangle values write
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第 5 頁 - If a straight line one extremity of which remains fixed be made to revolve at a uniform rate in a plane until it returns to the position from which it started, and if, at the same time as the straight line is revolving, a point move at a uniform rate along the straight line, starting from the fixed extremity, the point will describe a spiral in the plane.