Some Derivations


  • Ideal Gas Law


  • S = logW
  • SKLogW
  • Atmospheric Pressure Approximation and Average Height of Molecules


  • Bateman Equations ( For up to 3 successive Decays) 


  • Pythagorean Theorem ( Could be original but definitely not 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


  • Kepler’s 1st Law to Inverse Square Law 

  • From Newton to Kepler’s Laws Using Vectors


  • From Newton to Kepler’s 1st Laws Using a Differential Equation 

  • Einstein Special Relativity 

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



  • Continuous  Logistic Equation for Population Dynamics

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