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
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.
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
"Godel for Goldilocks" by Prof. Gusfield.
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