talk 717

Mathematically correct derivation for “Pie Alamo”
Bob Chen

A mathematically correct derivation for “Pie Alamo” or ice cream plus pie. The main challenge is changing the x (i.e., multiply) to + (i.e., add) in the expression ice cream x pie to ice cream + pie. The derivation follows:

1. Without loss of generality, we write the expression 1/ [e(iIC+iÕ)]i = [e(iIC+iÕ)]-i

2. Take the natural logarithm of the above, or ln [e(iIC+iÕ)]-i

3. ln [e(iIC+iÕ)]-i = -i [ (iIC+iÕ)] =IC+Õ

4. Let IC = ice cream, and Õ = pie

5. IC+Õ = ice cream + pie = Pie Alamo

It should be noted that in 3. above, ln ex = x ( and log 10x = x, log 100 = log 102 = 2, …etc.) is the definition of logarithm. Using natural log, or ln; e and not 10 is merely a lazy way to reduce the key strokes. i = Ö-1 is the definition of imaginary number. This long-drawn proof for Pie Alamo is many key strokes more than Pie Alamo’s nine; however, Pat Wong and Crazy Tu will appreciate the mathematical rigor, I hope.