Day 187 · Jul 5

Birthday of Isaac Newton (1643, old style)

Isaac Newton developed calculus (independently of Leibniz) to solve physics problems. His ‘Method of Fluxions’ treated variables as flowing quantities. He also discovered the generalised binomial theorem, Newton’s method for roots, and classified cubic curves. His Principia Mathematica (1687) introduced the law of universal gravitation and three laws of motion, unifying celestial and terrestrial mechanics. Newton was also a secret alchemist and theologian. He left over ten million words of manuscripts, only a fraction about mathematics and physics.

Newton’s method approximates roots of equations. Starting with x₀ = 1, apply one iteration of Newton’s method to f(x) = x² – 2. What new approximation for √2 do you get?

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