Wednesday, 23 September 2009

An Interesting Observation, and a Problem

I came across a couple of neat things reading old journals sent to me by Dave Renfro... here are two that seem worth sharing:
In the Mathematical Spectrum in 1984, Malcolm smithers of the Open University shared a discovery... "I found the following interesting number on my Oric 1 48K" (The Oric1 (16k) was released in 1982 and was the first color computer to sale for under 100 GB Pounds..I still remember working with my son as we both learned computing on a Tandy color computer... alas he has left me in the dust computer wise)

"3435 = $3^{3} + 4^{4} +3^{3} + 5^{5}$" which left me wondering, is there any number between this number and 1=$1^{1}$ that replicates this kind of behavior.. none came quickly to mind, and I was too busy to do a computer search.

Here is an interesting problem from the American Mathematical Monthly from May, 1930:

A piece of pie is cut from a pie with a radius r. The cut is a sector with a central angle of $\theta$. Assuming that the angle $\theta$ is < 180o. What is the radius of the smallest plate that will hold the cut piece of pie?
Have fun. For the calculus student, is the function differentiable over this domain?
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