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Pi plus e - November 4, 2010
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Edit (Nov 7th, 2010): Just a note that mrburkemath has determined what pi+e is.

Isn't it wonderful how the simplest problems are the hardest to solve. I think there is some sort of analogy for life in there somewhere.

It just shows how little we understand of mathematics--that unanswered questions are so close to the surface, and also that very few fields are not open to a new insight that opens up whole new questions to ask and answer.

pi + e = pie!

is that a factorial or are you just happy to see me... wait, what?

So if it's edible, then it's rational? Unless of course it's kumquat, which is completely irrational and transcendental.

not to mention inedible.

I've always hated irrational numbers, they by definition don't make sense, and transcendental numbers are most nonsensical of the lot

And then there are the stellar numbers (or ultra transcendental) - a further subset which are numbers that are not the answers to differential equations with integer coefficients. Yes, I did just make that up.
So if Pi + e = Pie; what is Pi * e ?

The first thing I noticed, upon seeing the third panel, was that his mouth and the lines above his eyebrows look like a sketch of secant from 0 to 2 \pi...

I wonder if there are actually any numbers that would satisfy the equation x+y=xy!

oops, that was supposed to be a reply to mrburkemath's comment

xy-x=y
x(y-1)=y
x=y/(y-1)

Many solutions!

curious question... is that xy and lots of excitement or xy! as in factorial?

x=2, y=2

I suppose you want integer solutions
x + y = xy
y - xy = - x
y(1-x) = - x
If 1-x = 0, then x = 0, which is impossible, so
y = - x/(1-x)
y = x/(x-1)
so (x-1) | x, therefore x = 2 and y = 2 or x = 0 and y = 0

Given a pie (uneaten)
a pie is swept out by 2*\pi radians
so pie = 2\pi
\pi = pi
so pie = 2pi
e=2

See! Its clearly proof that you can approximate constants using food.

Tune in next week for when I approximate \hbar using food you can find in a bar!

No one has rigorously proven that P pie is transcendental, and no one has rigorously proved that S pie is transcendental.

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