Puzzle #11: The Answer (Pi-Fingered Aliens)

I posted Puzzle #11 on Pi Day (3/14/15 in the U.S.).  I noted that the sequence of numbers in 3.14159… reflects not just π, but also ten, the base we use for our numbers.

The question was:

What is 30.12120111…?

After no answers showed up on this blog for two months, I posted the puzzle to the Brainteaser Forum at Wilmott.com. “Traden4Alpha”, a brilliant Wilmott member, made quick work of the problem and posted this answer:

It’s a useful constant for those with pi fingers who are visiting Earth.

What does this mean?  If somehow these aliens each had π fingers, then they might have developed a number system based on π.  When visiting Earth, the aliens must account for humanity’s choice of ten as our number base.  It would help them to know that 30.12120111… is ten in base π.

To see how this works, recall that our number system is built on powers of ten:

π=100 + 10-1 + 10-2 + 10-3 +10-4 + 10-5 + …

This equation is an infinite assembly manual* for making π from powers of ten. We start with three ones, then one tenth, then four hundredths, and so on.

Similarly, the aliens could write ten in base π like this:

ten=π1 + π0 + π-1 + π-2 + π-3 +π-4 + π-5 + …

I appreciate that Traden4Alpha found such a practical application for this little puzzle.

*At least it’s not one of these Ikea manuals.

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