Expert: Abe Mantell - 12/31/2011

Question
Hello there, I don't know if you're the right person to ask but please could you help with this or let me know who I should be asking. Many thanks!

If Pi is expressed in a format other than Base 10, is it still a perfect number?

I am a visual artist with no maths background so please can you answer me in short words!!!

Hope you can help

Happy 2012

Angela

Answer
Hello Angela,

I think you mean "is pi still irrational (not perfect) if expressed in another base"...yes?
A perfect number is a whole number whose sum of proper divisors equals itself.
For example, 6 since 6=1+2+3, and 28 since 28=1+2+4+7+14.

Anyhow, if an irrational number (in base 10) is expressed in another rational base
(like 2 or 3, etc.), then it will still be irrational.  However, it is not necessarily
true if using an irrational base.  For example, in base "pi"...pi would be 1.

I hope this helps!  :-)

Best wishes for the new year!!!

Abe