Titlebook: Numbers and Geometry; John Stillwell Textbook 1998 Springer Science+Business Media New York 1998 Area.Prime.Volume.calculus.set

效果

machination

Geometry,fluid, dynamic, and visual. The fundamental geometric quantities (length, area, and volume) are familiar to everyone but hard to define. And some “obvious” geometric facts are not even provable; they can be taken as axioms, but so can their opposites. In geometry, intuition runs ahead of logic. Our

deciduous

nascent

Trigonometry,ize of angles in triangles. Euclid says very little about this. He has theorems about equal angles and the sum of angles, and one angle being twice another or simply larger than another, but he never actually . angles. He does not represent angles by numbers, nor does he represent them by lengths or

GRUEL

Finite Arithmetic,t. Since then, infinity has appeared in many situations, and we have seen many ways to approach and tame it. Still, it is remarkable how often we succeed. Even if the world of ideas is infinite, as Dedekind believed, there is no doubt that . are finite, so success with infinity depends on capturing

生来

BLANK

Conic Sections,se of their affinity with the circle, and with revived interest since the 17th century when it was found that they model the paths of projectiles, comets, and planets. Another motive for studying them is their ability to “construct” numbers not constructible by ruler and compass, such as . Perhaps t

粘连

Elementary Functions, .is an excellent example of such tension and its beneficial effects: geometry confronted arithmetic with the diagonal of the unit square, arithmetic expanded its concept of number in response, and the new number .proved its worth by giving new insight into the old numbers, for example, by generatin

Fulminate

Textbook 1998n these concepts can be suggested by a thorough study of simple examples, such as the circle and the square. This book covers the main ideas of Euclid--geometry, arithmetic and the theory of real numbers, but with 2000 years of extra insights attached. NUMBERS AND GEOMETRY presupposes only high scho

OMIT