Collected Proofs

• The completely-visual proof of the log-sum rule. (Exercise from Donald Knuth's The Art of Computer Programming)
• A \cup C = B \cup C and A \cap C = B \cap C implies A = B. (From my discrete mathematics course)
• A special case of the Chinese Remainder Theorem, which can be modeled by and proved from a patterned, sub-divided rectangle. (Used in a problem from Knuth's TAoCP)
• The algebraic rule (a+b)^2 = a^2 + 2ab + b^2 visually with a physical square diagram. (From my evolution and ecology Biology course)
• p^2 + pq = p for alleles in a Harvey-Weinberg equilibrium population. (Evolution-ecology course)
• Three different explanations for the formula n(n+1)/2 for determining the number of possible genotypes given n alleles. (Evolution-ecology course)
• Path independence of conservative vector fields, building off of the famous Escher piece. (Vector analysis course, Hofstadter's Godel, Escher, Bach)
• Generalization of the Jacobian of higher-dimensional spherical coordinate systems. (Vector analysis course TA)
• The Lame proof of the worst-case complexity of the Euclidean algorithm, using the Fibonacci series. (Discrete mathematics course)
• "Godel for Goldilocks" by Prof. Gusfield.