Where to begin? -- Fibonacci's Proposition Two -- Equations : information and interpretation -- The proof -- Thinking around the proof -- But why is it true? Seeing it another way -- Building up the mathematics -- Back to Pythagorean triples -- Logical steps and linear equations -- Parameters, quadratic equations, and beyond -- Any number -- Symbols -- First applications -- Mathematics and the invisible world -- CAT scans -- Social planning and mathematical surprises -- Geometry and Euclid -- An alternative approach : geometry meets algebra -- Symmetry -- Ways of thinking and how we do mathematics -- Final thoughts.
