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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
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

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psi9epsilonBest ResponseYou've already chosen the best response.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

psi9epsilonBest ResponseYou've already chosen the best response.0
in either case it would be along a line or a ray
 one year ago

experimentXBest ResponseYou've already chosen the best response.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

FweaBoyLiveBest ResponseYou've already chosen the best response.0
they could meet by the vertices and be moving clockwise to each other
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
nop ... they all in the direction of another snail.
 one year ago

Agent47Best ResponseYou've already chosen the best response.0
is it going to be some polar graph?
 one year ago

experimentXBest ResponseYou've already chosen the best response.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

sauravshakyaBest ResponseYou've already chosen the best response.1
How can one move in two direction at once
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
they are moving in cycle.
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
Great riddle let us think, thanks
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
Well I think I know the beginning:
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
I guess there will always be an equilateral triangle between them
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Something like this:dw:1347902736343:dw
 one year ago

acrossBest ResponseYou've already chosen the best response.1
The equilateral triangle shrinks and rotates at a speed proportional to the snails' pace.
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
dw:1347902612412:dw One writes the differential equation Remembering v*dt = dx
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MikaelBest ResponseYou've already chosen the best response.2
d theta = sin theta * dx
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
\[\frac{ d \theta }{ dx } = \sin \theta\]
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
This is integrable easily
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
sorry ... had been away ... carry on
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
\[\theta(x) = \cos(x)\]
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
This is 1st try one needs to improve the geometry
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
dw:1347903100408:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1347903134187:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
I think there is a possibility of that also
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
might be ... let's assume unit velocity for now ... we will generalize it later.
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
by the way my soln is a piece of spiral
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1347903217601:dw yep .. it should be spiral ...
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
ya did it that way @experimentX
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
@Mikael do u know the equation of a spiral........ Its beyond my knowledge
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+theta
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
this is diverging spiral.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
also note that I don't the answer of this Q.
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
This may be funny but this will depend upon the length of the snail
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.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

experimentXBest ResponseYou've already chosen the best response.0
dw:1347903644328:dw kinda seems this way.
 one year ago

experimentXBest ResponseYou've already chosen the best response.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

MikaelBest ResponseYou've already chosen the best response.2
Well I think I have got it  by geberal consideration
 one year ago

MikaelBest ResponseYou've already chosen the best response.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

MikaelBest ResponseYou've already chosen the best response.2
http://www.wolframalpha.com/input/?i=Archimedes+spiral
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
Sorry r Linear in theta
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
well ... i didn't know that. let's say we know the answer. any method arising from calculus?
 one year ago

psi9epsilonBest ResponseYou've already chosen the best response.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

experimentXBest ResponseYou've already chosen the best response.0
the problem is supposed to be calculus problem.
 one year ago

psi9epsilonBest ResponseYou've already chosen the best response.0
well that should have been indicated well in advance before requesting help, makes life easy than scratching heads : )
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
Very highbrow @psi9epsilon yet I have offered a definite solution (right or wrong) but precise. Either disprove it or show my argument deficient.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
well ... sorry my bad :/
 one year ago

psi9epsilonBest ResponseYou've already chosen the best response.0
@Mikael, do not approve or disapprove your solution as it MAY NOT be the ONLY solution
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
I CLAIM that the only spiral that has in 0.002 timeunits A) constant rotation B) Constant zoomdown factor Z Is the above
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
it's a spiral ... at least we know that.
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
0.002 is simply to underscore the constancy of\[\Delta t\]
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Can any one show me how the equation of a spiral looks
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
R(t) = exp(Kt) theta(t) = kt
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
let's solve this Q for particular case. assume side is 5 and speed is 1
 one year ago

experimentXBest ResponseYou've already chosen the best response.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

MikaelBest ResponseYou've already chosen the best response.2
\[R(\theta) = R_0e^{k*\theta}\]
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Have no clue on polar equation or parametric equation
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
well .. that's one hell of one spiral ..
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
http://www.wolframalpha.com/input/?i=polar+plot+r%28theta%29+%3D+1*exp%280.3*theta%29
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Well guys I have to go now.
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
AAND I HAVE PROOF ! Here it is\[R(t + \Delta T) = R(t) * e^{k \Delta T}  constant factor\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=plot+r%28theta%29+%3D+theta
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
\[\theta(t + \Delta T) = \theta(t) + k*\Delta T > constantrotation\]
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
So @experimentX @across @siddhantsharan and whoever want  check this solution !
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
Please CHECK this solution @estudier @mukushla @hartnn
 one year ago

experimentXBest ResponseYou've already chosen the best response.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

MikaelBest ResponseYou've already chosen the best response.2
@experimentX Please accept the proof  it is rock solid. Do not evade  this is THE only Only solution
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
@mathslover please check my solution of exponential spiral
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
hold on ... I'm hunting for spirals
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
By the way THIS IS A GENERAL SOLUTION FORM FOR ANY EQUILATERAL POLYGON WITH NSNAILS IN EACH VERTEX !!!!
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
Hunting is good, but hunting for WRONG is just funny
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
THIS IS A GENERAL SOLUTION FORM FOR ANY EQUILATERAL POLYGON WITH NSNAILS IN EACH VERTEX !!!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
no ... just for fun. man fun is good.
 one year ago

MikaelBest ResponseYou've already chosen the best response.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

experimentXBest ResponseYou've already chosen the best response.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

experimentXBest ResponseYou've already chosen the best response.0
all right ... i'll check.
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
\[R( \Theta) = R_0 e^{k \Theta}\]
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
This GIVES THE SHAPE OF THE PATHS FOR ANY REGULAR POLYGON
 one year ago

MikaelBest ResponseYou've already chosen the best response.2
Square, Pentagon, Hexagon, Triangle whatever your n is
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1347905702311:dw yeah this is definitely a r = k e^(theta)
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1347906117851:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
let's try to solve this problem using calculus method some other day.
 one year ago
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