Question

Surface geometry help?

Answer 1

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

Answer 2

Just looking at the cross sections.

Answer 3

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

Answer 4

I think it's the bottom left one.

Answer 5

But I am not sure :/ .

Answer 6

yea same here

Answer 7

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

Answer 8

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

Answer 9

my bad

Answer 10

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

Answer 11

you need y^2 for sphere

Answer 12

Yeah :P .

Answer 13

would it just be a cylinder

Answer 14

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

Answer 15

no just a circle

Answer 16

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

Answer 17

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

Answer 18

the hare lost the race :P

Answer 19

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

Answer 20

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

Answer 21

Not sure why though.

Answer 22

Because it's not like with translate the circle.

Answer 23

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

Answer 24

why oh why?

Answer 25

why not two parabolas?

Answer 26

you mean a hyperbola? lol

Answer 27

It cannot be a hyperbola. No subtraction term appears.

Answer 28

exactly :)

Answer 29

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?

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

nincompoop get your wise self outta here :P

Answer 36

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

Answer 37

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.

Answer 38

check wolfram.com

Answer 39

nice copy-pasting, dude! :D

Answer 40

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

Answer 41

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

Answer 42

@yummydum i know right, thnx bro :)

Answer 43

the cylinders that we know are just blown-up circles

Answer 44

What a stupid definition...

Answer 45

oh there's the definition lol

Answer 46

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

Answer 47

they are useful

Answer 48

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

Answer 49

Thanks guys for all the help :) .

Answer 50

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

Answer 51

:( .

Answer 52

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

Answer 53

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

Answer 54

you bet