Dido525 2 years ago Surface geometry help?

1. Dido525

2. Dido525

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

3. Dido525

Just looking at the cross sections.

4. yummydum

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

5. Dido525

I think it's the bottom left one.

6. Dido525

But I am not sure :/ .

7. yummydum

yea same here

8. Dido525

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

9. nincompoop

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

10. nincompoop

11. Dido525

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

12. nincompoop

you need y^2 for sphere

13. Dido525

Yeah :P .

14. yummydum

would it just be a cylinder

15. Dido525

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

16. nincompoop

no just a circle

17. some_someone

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

18. Dido525

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

19. nincompoop

the hare lost the race :P

20. yummydum

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

21. Dido525

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

22. Dido525

Not sure why though.

23. Dido525

Because it's not like with translate the circle.

24. yummydum

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

25. nincompoop

why oh why?

26. nincompoop

why not two parabolas?

27. yummydum

you mean a hyperbola? lol

28. Dido525

It cannot be a hyperbola. No subtraction term appears.

29. yummydum

exactly :)

30. 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?

31. Dido525

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

32. yummydum

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

33. Dido525

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

34. some_someone

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

35. nincompoop

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

36. yummydum

nincompoop get your wise self outta here :P

37. Dido525

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

38. some_someone

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.

39. some_someone

check wolfram.com

40. yummydum

nice copy-pasting, dude! :D

41. some_someone
42. yummydum

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

43. some_someone

@yummydum i know right, thnx bro :)

44. nincompoop

the cylinders that we know are just blown-up circles

45. Dido525

What a stupid definition...

46. nincompoop

oh there's the definition lol

47. Dido525

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

48. nincompoop

they are useful

49. Dido525

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

50. Dido525

Thanks guys for all the help :) .

51. nincompoop

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

52. Dido525

:( .

53. nincompoop

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

54. Dido525

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

55. nincompoop

you bet