Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

experimentX Group Title

Three snails at the point of equilateral triangle start to move at each other. What is the shape of curve?

  • one year ago
  • one year ago

  • This Question is Closed
  1. psi9epsilon Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    assuming they start from vertices, to meet at centre then there are different possibilites they can meet at incentres also or at centroid too

    • one year ago
  2. psi9epsilon Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    in either case it would be along a line or a ray

    • one year ago
  3. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    it can't be a ray ... they aren't moving to center. they are moving to each other ( the other snail) |dw:1347897411584:dw|

    • one year ago
  4. FweaBoyLive Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    they could meet by the vertices and be moving clockwise to each other

    • one year ago
  5. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    nop ... they all in the direction of another snail.

    • one year ago
  6. Agent47 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    is it going to be some polar graph?

    • one year ago
  7. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    don't know ..haven't solved it yet. i tried to do this couple of months ago ... couldn't do it.

    • one year ago
  8. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    How can one move in two direction at once

    • one year ago
  9. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    they are moving in cycle.

    • one year ago
  10. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    A->B ->C->A

    • one year ago
  11. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oh

    • one year ago
  12. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Great riddle let us think, thanks

    • one year ago
  13. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Well I think I know the beginning:

    • one year ago
  14. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I guess there will always be an equilateral triangle between them

    • one year ago
  15. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Something like this:|dw:1347902736343:dw|

    • one year ago
  16. across Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The equilateral triangle shrinks and rotates at a speed proportional to the snails' pace.

    • one year ago
  17. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep.. @across

    • one year ago
  18. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1347902612412:dw| One writes the differential equation Remembering v*dt = dx

    • one year ago
  19. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    d theta = sin theta * dx

    • one year ago
  20. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\frac{ d \theta }{ dx } = \sin \theta\]

    • one year ago
  21. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    This is integrable easily

    • one year ago
  22. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry ... had been away ... carry on

    • one year ago
  23. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\theta(x) = \cos(x)\]

    • one year ago
  24. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    This is 1-st try one needs to improve the geometry

    • one year ago
  25. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1347903100408:dw|

    • one year ago
  26. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1347903134187:dw|

    • one year ago
  27. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I think there is a possibility of that also

    • one year ago
  28. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    might be ... let's assume unit velocity for now ... we will generalize it later.

    • one year ago
  29. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    by the way my soln is a piece of spiral

    • one year ago
  30. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1347903217601:dw| yep .. it should be spiral ...

    • one year ago
  31. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ya did it that way @experimentX

    • one year ago
  32. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @Mikael do u know the equation of a spiral........ Its beyond my knowledge

    • one year ago
  33. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+theta

    • one year ago
  34. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    this is diverging spiral.

    • one year ago
  35. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    also note that I don't the answer of this Q.

    • one year ago
  36. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    This may be funny but this will depend upon the length of the snail

    • one year ago
  37. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Because when they meet there has to be an equilateral triangle with length of the side equal to the length of the snail

    • one year ago
  38. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1347903644328:dw| kinda seems this way.

    • one year ago
  39. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @sauravshakya you have a knack for making problems difficult ... well i agree that this gives insight into things ... but for this case. try to take the size of snail that would simplify the problem. take it as a point size snail.

    • one year ago
  40. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

    • one year ago
  41. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Well I think I have got it - by geberal consideration

    • one year ago
  42. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Here 1) After constant time Delat t ( constant) the pictire undergoes similarity transformation by A) rotating, B) Shrinking by CONSTANT factor Z(DElta t) The only spiral that is self similar is Archimedian Spiral where r is a LInear function of t

    • one year ago
  43. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    http://www.wolframalpha.com/input/?i=Archimedes+spiral

    • one year ago
  44. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Sorry r Linear in theta

    • one year ago
  45. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well ... i didn't know that. let's say we know the answer. any method arising from calculus?

    • one year ago
  46. psi9epsilon Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @experimentX , the question can be solved in numerous ways, and is open to interpretation you can also use graph theory to find the shortest path which infact will define the curve other solutions like rotation of triangle are justified if sufficient and necessary conditions are provided

    • one year ago
  47. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the problem is supposed to be calculus problem.

    • one year ago
  48. psi9epsilon Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well that should have been indicated well in advance before requesting help, makes life easy than scratching heads : )

    • one year ago
  49. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Very high-brow @psi9epsilon yet I have offered a definite solution (right or wrong) but precise. Either disprove it or show my argument deficient.

    • one year ago
  50. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well ... sorry my bad :/

    • one year ago
  51. psi9epsilon Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @Mikael, do not approve or disapprove your solution as it MAY NOT be the ONLY solution

    • one year ago
  52. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I CLAIM that the only spiral that has in 0.002 time-units A) constant rotation B) Constant zoom-down factor Z Is the above

    • one year ago
  53. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    it's a spiral ... at least we know that.

    • one year ago
  54. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    0.002 is simply to underscore the constancy of\[\Delta t\]

    • one year ago
  55. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Can any one show me how the equation of a spiral looks

    • one year ago
  56. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    R(t) = exp(Kt) theta(t) = kt

    • one year ago
  57. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    let's solve this Q for particular case. assume side is 5 and speed is 1

    • one year ago
  58. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @sauravshakya there are numerous way in which you can have a spiral ... try to look for polar equation or parametric equation ... this is same a circle except the radius changes.

    • one year ago
  59. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[R(\theta) = R_0e^{k*\theta}\]

    • one year ago
  60. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Have no clue on polar equation or parametric equation

    • one year ago
  61. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well .. that's one hell of one spiral ..

    • one year ago
  62. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    http://www.wolframalpha.com/input/?i=polar+plot+r%28theta%29+%3D+1*exp%280.3*theta%29

    • one year ago
  63. sauravshakya Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well guys I have to go now.

    • one year ago
  64. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    AAND I HAVE PROOF ! Here it is\[R(t + \Delta T) = R(t) * e^{k \Delta T} ---- constant factor\]

    • one year ago
  65. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.wolframalpha.com/input/?i=plot+r%28theta%29+%3D+theta

    • one year ago
  66. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\theta(t + \Delta T) = \theta(t) + k*\Delta T ----> constant-rotation\]

    • one year ago
  67. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    So @experimentX @across @siddhantsharan and whoever want - check this solution !

    • one year ago
  68. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Please CHECK this solution @estudier @mukushla @hartnn

    • one year ago
  69. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    another spiral http://www.wolframalpha.com/input/?i=parametric+plot+x%28t%29+%3D+t+cos%28t%29%2C+y%28t%29+%3D+t+sin%28t%29+from+t%3D0+to+t%3D2+pi

    • one year ago
  70. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    @experimentX Please accept the proof - it is rock solid. Do not evade - this is THE only Only solution

    • one year ago
  71. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    @mathslover please check my solution of exponential spiral

    • one year ago
  72. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    hold on ... I'm hunting for spirals

    • one year ago
  73. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    By the way THIS IS A GENERAL SOLUTION FORM FOR ANY EQUILATERAL POLYGON WITH N-SNAILS IN EACH VERTEX !!!!

    • one year ago
  74. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Hunting is good, but hunting for WRONG is just funny

    • one year ago
  75. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    THIS IS A GENERAL SOLUTION FORM FOR ANY EQUILATERAL POLYGON WITH N-SNAILS IN EACH VERTEX !!!!

    • one year ago
  76. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no ... just for fun. man fun is good.

    • one year ago
  77. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    If I am right - PLEASE say so. Check - this is justified because you asked the. And I solved it (or not - but check) question

    • one year ago
  78. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i thought this would work out .. lol http://www.wolframalpha.com/input/?i=parametric+plot+x%28t%29+%3D+e^t+cos%28t%29%2C+y%28t%29+%3D+e^t+sin%28t%29+from+t%3D0+to+t%3D2+pi

    • one year ago
  79. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    all right ... i'll check.

    • one year ago
  80. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[R( \Theta) = R_0 e^{k \Theta}\]

    • one year ago
  81. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    This GIVES THE SHAPE OF THE PATHS FOR ANY REGULAR POLYGON

    • one year ago
  82. Mikael Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Square, Pentagon, Hexagon, Triangle whatever your n is

    • one year ago
  83. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1347905702311:dw| yeah this is definitely a r = k e^(theta)

    • one year ago
  84. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1347906117851:dw|

    • one year ago
  85. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    let's try to solve this problem using calculus method some other day.

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.