What is Mathematics?: An Elementary Approach to Ideas and Methods

a₁ algebra of sets algebraic altitude triangle angle calculus CALIFORNIA/SANTA CRUZ complex numbers concept conic consider continuous function coördinates corresponding cross-ratio cube cubic equation decimal defined definition denote differential digits distance domain doubling the cube elements ellipse equal equation example Exercise expression fact field F Figure formula function f(x given circle Hence hyperbola infinite integers interval intuitive inverse Jordan curve theorem Leibniz length limit mathematical mathematical induction mathematicians minimum nested intervals obtain parallel plane polygon positive integer positive number primes problem problem of Apollonius projective geometry proof properties prove quantity radius rational numbers real numbers root ruler and compass segment sequence side simple solution square Steiner's problem straight line surface symbol tangent tends to infinity theorem tion topological transformation UNIVERSITY OF CALIFORNIA/SANTA variable vertices x₁ zero