Surface geometry help?

- anonymous

Surface geometry help?

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- anonymous

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- anonymous

I think it's a elliptic paraboloid but I am not sure...

- anonymous

Just looking at the cross sections.

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- anonymous

its either one of the bottom two graphs, i know that

- anonymous

I think it's the bottom left one.

- anonymous

But I am not sure :/ .

- anonymous

yea same here

- anonymous

What the heck is that shape even called? >.>

- nincompoop

\[x^2+z^2 = sphere\]

- nincompoop

my bad

- anonymous

Really? Isn't x^2+y^2+z^2= r a sphere?

- nincompoop

you need y^2 for sphere

- anonymous

Yeah :P .

- anonymous

would it just be a cylinder

- anonymous

No. The cross sections are parabolas so there is no way it's a cylinder.

- nincompoop

no just a circle

- anonymous

\[x^2+z^2 = 7\]
is a circle :)

- anonymous

I know but... ;_; ... I thought the cross sections would be parabolas :/ .

- nincompoop

the hare lost the race :P

- anonymous

which is again why i am not sure if it is the bottom left or the bottom right

- anonymous

K, so it the the bottom right apparantly : / .

- anonymous

Not sure why though.

- anonymous

Because it's not like with translate the circle.

- anonymous

i guess since its missing the \(y^2\)

- nincompoop

why oh why?

- nincompoop

why not two parabolas?

- anonymous

you mean a hyperbola? lol

- anonymous

It cannot be a hyperbola. No subtraction term appears.

- anonymous

exactly :)

- nincompoop

wow I suck at "surface" geometry LOL
so it is a circle yes? why not pick the one with a circle in the first place?

- anonymous

Because I assumed the cross sections would be parabolas so it did not seem logical to pick a cylinder :/ .

- anonymous

hey wouldnt it have to be x^2+y^2=7 to be parabolic?
i think thats why its a cylinder

- anonymous

Well if I take z=0 then we get x^2=7 which is a parabola.

- anonymous

well x^2+y^2=7 is a circle.

- nincompoop

nawwww… even if you drew just a 2-D circle, in microscopic view it is still "cylindrical" in shape

- anonymous

nincompoop get your wise self outta here :P

- anonymous

Well I DO AGREE it is indeed a circle about the x-z axis but how does that make it a cylinder? :/ .

- anonymous

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of different notations used for the other two coordinates. Either r or rho is used to refer to the radial coordinate and either phi or theta to the azimuthal coordinates. Arfken, for instance, uses (rho, phi, z), while Beyer uses (r, theta, z). In this work, the notation (r, theta, z) is used.
The following table summarizes notational conventions used by a number of authors.

- anonymous

check wolfram.com

- anonymous

nice copy-pasting, dude! :D

- anonymous

https://www.wolframalpha.com/input/?i=cylindrical+coordinates&lk=4&num=2

- anonymous

jk jk...yea wolfram does say that it is a circle

- anonymous

@yummydum i know right, thnx bro :)

- nincompoop

the cylinders that we know are just blown-up circles

- anonymous

What a stupid definition...

- nincompoop

oh there's the definition lol

- anonymous

I don't like all these coordinate systems :/ .

- nincompoop

they are useful

- anonymous

I don't see how... Just stick to rectangular coordinates :/ .

- anonymous

Thanks guys for all the help :) .

- nincompoop

you mean just 2-D? awwww do you prefer them pixelated too? L M A O :P

- anonymous

:( .

- nincompoop

don't be sad… the knowledge you will acquire is transferrable to different physical sciences.

- anonymous

As long as it's applicable to engineering...

- nincompoop

you bet

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