It's now the 20th... I don't mind paying to be a contributor, It's just that I don't feel right about being overcharged for it. If I could get the difference back then that would work out great.
PF 1 Year subscription auto renewed for a higher price!?
I checked my email this morning and noticed that I had an email from PayPal saying that I had "sent $25.00 USD to Greg Bernhardt as a subscription payment." So, I logged into PayPal and sure enough, there was a transaction.
First off, I...
Thanks Doodle Bob. I'll certainly look into those texts as well. A quick search for Do Carmo yields impressive commentary on his works. I look forward to reading it.
It's been a while but I am almost positive that you just combine the diameters or radii and just use the circumference formula c = pi*d = 2pi*r
So, the shortest length of rope that can we wound around two circles of diameters 6ft and 18ft is pi*(6+18) = 24pi ft.
Maybe you could somehow prove that the duality is the result of vibrations ocurring in higher dimensional space. If you can do that then you would truly have an awesome project.
Can anyone please forward me to some free or cheap resources for learning the fubdamentals of Reimann Geometry? I am very interested in the prospects of higher dimensional mathematics and would very much like to, at the very least, be able to understand the fundmentals and maybe even some...
I thank you both... i did make a few typos in my original post such as using arcsin instead of arctan...
anyway, in my calculus class we get extra credit if we can prove things... such as logb(a) and loga(b) are mutliplicative inverses...
my teacher wants me to show how to find the log of...
I know that with base e you use the natural log of complex numbers rule...
ln(x+yi) = ln|x| + arcsin(y/x)i
...because the limit e somehow corresponds to radians about the unit circle
thus, when you take ln(-1) you can do
ln(-1 + 0i) = ln|-1| = arsin(0/-1)i
ln(-1) = 0 + pi*i
ln(-1) = pi*i
My...