so i think you'd just end up with another riemann sphere like in the $w^2=z$ case, except that you need to go through an argument of $6pi$ to get back to the surface instead of $4pi$
The real challenge (to myself) is to get a very nice solution to $$\int_0^1 \frac{(1-x+x\log(x))\operatorname{Li_3(x)}}{(x-1) x \log(x)} \ dx=\frac{5}{4}\zeta(4)-\gamma \zeta(3)+\zeta'(3)$$
@TheArtist: It's a joke on a joke from a movie; a wedding decorator's incompetent team mixed up the M and the W on a "WELCOME" sign and it read as "MELCOWE". That really stuck to my head and "Mel, the cow" is my original spin off :D`
@JeffE Mine explicitly allows "colourless liquids" and forbids everything else. At some point, I really must exploit this by drinking vodka in seminars. – David Richerby 1 hour ago
@user130018 I was watching John Oliver the other day. He was doing a show on how it is like winning the lottery getting american citizenship if you served as a translator over seas.
@user130018 And one of the people who actually made it to the USA had the name, simply because they somehow couldn't figure out what his first name was
My objective:
Use cylindrical coordinates to find the volume of the prism whose base is the triangle in the xy-plane given by y = 0, x = 1, and y = $\frac{7}{2} x$, and whose top is given by z = 8 - y.
In Cartesian coordinates, this is straightforward to me: $\int_{0}^{1}\int_{0}^{7/2x}\in...
@Alizter I wanted to get Bostock and Chandler Pure Math 1 and 2. But there is no Applied Math 1 and 2. But maybe I don't want to read the applied math parts after all.
@ZachSaucier: Yeah, I don't know how to work with $\text{mod}$ yet. All I understand are clocks and the k value is like the max number to which that clock will go after which it recycles
@alizter The list of books I showed you earlier on today are Cambridge A Levels, but for a single math subject only, not further math, which is why they covered much less.
@Zach: Set up the triangle with vertices $(0,0)$, $(1,0)$, and $(1,1)$ in polar. Draw a picture of what happens for a general $\theta$ in your range, and use it to figure out the limits of $r$ for that $\theta$.
No, I mean differential geometric. Up to homothety, which I suppose ends up being the same as up to conformal transformation, since the result is the same.
I'm aware that conformal structures are the same as the holomorphic structure in the case of orientable surfaces. But it's not obvious that "up to homothety" and "up to conformal equivalence" are the same. Anyway.
My objective:
Use cylindrical coordinates to find the volume of the prism whose base is the triangle in the xy-plane given by y = 0, x = 1, and y = $\frac{7}{2} x$, and whose top is given by z = 8 - y.
In Cartesian coordinates, this is straightforward to me: $\int_{0}^{1}\int_{0}^{7/2x}\in...
