There, that should have weeded out the non-math inclined. Anyone still here? No? Oh well, I'll carry on anyway.
Can you figure out what is wrong with this proof? And explain it? Simply?
Friday, February 17, 2006
A Ton of Mathematical Confusion
Okay, okay okay. I know it's Friday before a long weekend, but I have to post this. WARNING: MATHEMATICAL TOPIC TO FOLLOW
There, that should have weeded out the non-math inclined. Anyone still here? No? Oh well, I'll carry on anyway.
Can you figure out what is wrong with this proof? And explain it? Simply?
There, that should have weeded out the non-math inclined. Anyone still here? No? Oh well, I'll carry on anyway.
Can you figure out what is wrong with this proof? And explain it? Simply?
Subscribe to:
Post Comments (Atom)
5 comments:
I guess when you are working with imaginary numbers, things become a little more complicated.
In complex numbers we have
e^w = z = r*e^(i*theta)
Now since e^(i*theta) = cos(theta) + i*sin(theta)
= cos(theta+2k*pi) + i*sin(theta+2k*pi) k = 0,
+or-1, +or-2, +or-3,..etc., etc.
So we can write e^w = z = r*e^(i*(theta+2k*pi)) Now taking logs
w = ln(z) = ln(r) + i*theta + i*2k*pi
So the full expression for ln(1) is found by putting r=1 and theta=0.
This gives ln(1) = i*2k*pi with k = +or-1, +or-2 and so on.
You can see the real part of ln(1) is 0, but there is the complex part
which is not zero.
Does that make any sense?
The problem is that the log is a multivalued "function" when you work
with complex numbers. Think about e^(ix); actually e^(ix + 2kpi) has
the same value (for any integer k), since the sine and cosine are
periodic. So there are many exponents that give the same value.
That seems a little more clear.
Sorry it's not just a simple, obvious, elegant solution. Also, you have an extra i in the bottom line, but it doesn't make a difference.
I have to agree with Maggie on this one.
OK, I thought the problem with the proof was that it was based on religious iconic imagery. You know, math and religion just don't mix.
Is that supposed to be a "pi" sign on baby Jesus' swadling clothes? Frankly, I know that his swadling clothes were plain brown burlap (my great, great, great grandpa was one of the three kings, after all.) However, I think pi is a nice mathmatical represetation for the infinity of the Trinity -- even if math and religion don't mix.
Hey, I just noticed that "infinity" and "Trinity" rhyme. Conspiracy or coincidence?
Post a Comment