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

a₁ algebra of sets algebraic altitude triangle angle axioms boundary calculus circle closed curve complex numbers concept conic consider construction continuous continuous function coördinates corresponding cross-ratio cube decimal defined definition denote derivative differential digits dimension distance domain doubling the cube ellipse equal equation Euler's formula example Exercise expression fact Figure formula function f(x given graph Hence hyperbola infinite integer intersection interval intuitive inverse inverse function Jordan curve theorem Leibniz length limit mathematical mathematical induction maximum minimum nested intervals obtain parallel perpendicular plane polygon positive number primes problem projective geometry proof prove quantity radius rational numbers real numbers root segment sequence side simple solution sphere Steiner's problem straight line surface symbol tangent tends to infinity theorem tion topological transformation variable vertices x-axis x₁ zero