The golden ratio φ=(1+√5)/2 is where geometry, algebra, Fibonacci numbers, limits, continued fractions, pentagons, spirals, and phyllotaxis meet. This complete Woody Calculus visual lesson derives phi, proves the Fibonacci limit, distinguishes a true golden spiral from Fibonacci-style arcs, and separates real mathematics from popular mythology.
Learn epsilon-delta proofs through visual intuition, exact definitions, and complete worked examples. This Woody Calculus real analysis lesson explains how to choose delta from epsilon, build local bounds, avoid common proof mistakes, and prove limits rigorously.
Improper integrals are Calculus 2 limit problems in disguise. This Woody Calculus lesson teaches how to handle infinite intervals, vertical asymptotes, bad points inside an interval, p-integrals, comparison tests, convergence, and divergence with a clear step-by-step system.