Kronecker's theorem
Salmon's way of finding the tangent to an ellipse.
Sqrt(2) and the incompleteness of the Rationals.
Derivative of tan(x) from scratch!
Beautiful catenary curve invariant property.
Centroids of convex polygons.
Sequences converging to e.
IMO 1959 and Bezout's lemma.
Understanding groups by their Cayley tables.
More induction: Fermat's little theorem and other examples.
Beautiful Olympiad-style inequality proved elegantly by Jensen's.
Alternating Series -- part two.
The precursor to AM-GM.
Sum of squares: a constructive proof using generalized Leibniz's derivative rule.
Jensen's inequality smashes a Putnam problem.
Pi is less than 22/7: the backwards adventure.
Incircle and excircles, part 1.
Extended sine law applications.
Ptolemy's SECOND cyclic quadrilateral theorem.
Hypercubes
The First Brocard Point: an awesome application of the Extended Sine Law.
