Author Topic: Area of a circle (Read 4499 times) Tweet Share

dcc · « **Reply #15 on:** September 03, 2009, 06:01:26 pm »

Quote from: /0 on August 19, 2009, 06:24:54 pm

$e^{ix} = e^{i(x+2\pi k)}$

$ix = i(x+2\pi k)$

$ix = ix+ 2 \pi k$

$2\pi k = 0$

$k = 0$

$\therefore e^{ix} = e^{ix}$

Anyone watching this: all the proofs on this page are incorrect, or are missing large assumptions.

The exponential function is not single-valued for complex numbers. A consequence of this is that the complex logarithm is not single-valued either.

Over9000's area of a triangle formula is only true if we make assumptions. One could use reasoning similar to this to propose that:

$\sin(0) = \sin(2\pi) \implies 0 = 2 \pi \implies 0 = 1$ .

QuantumJG · « **Reply #16 on:** September 15, 2009, 08:39:32 pm »

Quote from: Over9000 on August 19, 2009, 05:34:53 pm

I just found out today that the Area of a circle is $\frac{2log_e(i)}{i}r^{2}$
Which is very helpful when working out the area.

Much better than that other gay one $A= \pi r^{2}$
wtf is a $\pi$ anyway

Wud definitely come in handy if ur $\pi$ button broke on ur calc

if A = $\frac{2log_e(i)}{i}r^{2}$

$e^{ix} = cos(x) + isin(x)$

therefore $e^{ix} = i, when x = \dfrac{\pi}{2}$

implying A = $\frac{2log_e(e^{\dfrac{\pi i}{2}})}{i}r^{2} = \pi r^2$

cool

Ilovemathsmeth · « **Reply #17 on:** November 30, 2009, 05:26:56 pm »

i is amazing =D I never knew you could even take a log of it.

humph · « **Reply #18 on:** November 30, 2009, 10:29:20 pm »

Quote from: Ilovemathsmeth on November 30, 2009, 05:26:56 pm

i is amazing =D I never knew you could even take a log of it.

Only once you've appropriately defined the complex logarithm

And there are plenty of different ways to define it, depending on where you take your branch cut.

QuantumJG · « **Reply #19 on:** December 18, 2009, 12:01:39 pm »

Quote from: Ilovemathsmeth on November 30, 2009, 05:26:56 pm

i is amazing =D I never knew you could even take a log of it.

when you do calc 1 they will introduce you to representing complex numbers (denoted by z) as,

$z = r e^{i \theta} = r(cos( \theta ) + i sin( \theta )) = rcis( \theta )$

The cis notation is basically a specialist maths way of expressing complex numbers.

Search the forums now!

We have moved!

Author Topic: Area of a circle (Read 4499 times) Tweet Share

dcc

Re: Area of a circle

QuantumJG

Re: Area of a circle

Ilovemathsmeth

Re: Area of a circle

humph

Re: Area of a circle

QuantumJG

Re: Area of a circle

Recent Posts

User:
Password: