Chemistry
 Ideal Gas Law
 S = k logW
 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)
 Trigonometric Double Angle Formulas
 Hyperbola (Conic Section)
 Quadratic Formula ( Without Completing Square and Minimizing Error Version)
 Why the Derivative of e^{x} is e^{x}.
 Variation of Parameters ( with Wronskian for Differential Equations)
 Sum of Powers
 Surface Area of Sphere (Without using Trig substitution in Integral)
Physics

In pdf format:
Part 1: From Newton to Kepler’s First Two Laws

Part 2: Keplers 3rd Law
 Advanced Sesame Street Video: Deriving Kepler’s Laws

 Einstein Special Relativity

 Why Speed of Light Cannot Be Exceeded
 Relativistic Kinetic Energy Without Using Binomial Expansion
Biology
 Continuous Logistic Equation for Population Dynamics