Some Derivations

Chemistry

  • Ideal Gas Law
  • S = logW
  • SKLogW
  • Atmospheric Pressure Approximation and Average Height of Molecules
  • Bateman Equations ( For up to 3 successive Decays)

Mathematics

  • Pythagorean Theorem ( Could be original but definitely not an elegant proof)Pythagoras
  • Trigonometric Double Angle Formulas
  • Hyperbola (Conic Section)
  • Quadratic Formula ( Without Completing Square and Minimizing Error Version)quadratic
  • Variation of Parameters ( with Wronskian for Differential Equations)VOP
  • Sum of PowerssumofPowers
  • Surface Area of Sphere (Without using Trig substitution in Integral)SurfaceAreaSphere

Physics

  • Kepler’s 1st Law to Inverse Square Law
  • From Newton to Kepler’s Laws Using Vectors

From Newton to Kepler’s 1st Law Using a Differential EquationNewton-to-k1l2

  • Einstein Special Relativity
  • Why Speed of Light Cannot Be ExceededspeedOfLight
  • Relativistic Kinetic Energy Without Using Binomial Expansion

    Biology

  • Continuous  Logistic Equation for Population Dynamics

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