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Topic: Turtle Race (Read 1928 times) |
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Whiskey Tango Foxtrot
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Turtle Race
« on: Dec 6th, 2006, 12:47pm » |
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Here's a classic:
A turtle and a rabbit are about to run a race, and the rabbit wants to be fair so he gives the turtle a reasonably large head start. The rabbit runs ten times as fast as the turtle and he waits until the turtle has traveled one fifth of the total distance of the race. That said, who wins the race, the rabbit or the turtle? By how much?
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| « Last Edit: Dec 6th, 2006, 1:10pm by Whiskey Tango Foxtrot » |
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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Whiskey Tango Foxtrot
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Re: Turtle Race
« Reply #2 on: Dec 6th, 2006, 1:07pm » |
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Haha, okay. I should give some more information. I'll edit it.
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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SMQ
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Re: Turtle Race
« Reply #3 on: Dec 6th, 2006, 1:38pm » |
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Is there something more to this than the seemingly obvious answer of the rabbit, by 7/10 the length of the course?
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Whiskey Tango Foxtrot
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Re: Turtle Race
« Reply #4 on: Dec 6th, 2006, 1:45pm » |
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Yes, but I wanted someone else to propose an answer like you just did. I say the turtle won. Does anyone else agree?
P.S. The rabbit didn't fall asleep like last time.
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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Sameer
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Re: Turtle Race
« Reply #5 on: Dec 6th, 2006, 2:17pm » |
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on Dec 6th, 2006, 1:45pm, Whiskey Tango Foxtrot wrote:Yes, but I wanted someone else to propose an answer like you just did. I say the turtle won. Does anyone else agree?
P.S. The rabbit didn't fall asleep like last time. |
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Not unless you put some twist somewhere.
Time it takes rabbit to finish the race tr = d/Vr = d/10Vt
The total distance travels in the time = d/5 (given by rabbit) + Vt*tr
= d/5 + Vt*d/10Vt = 3d/10
Thus turtle loses by 7/10th distance.
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
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Whiskey Tango Foxtrot
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Re: Turtle Race
« Reply #6 on: Dec 6th, 2006, 2:44pm » |
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I say the rabbit never passes the turtle, and the rabbit loses by a hare. No seriously, though. The turtle wins. I asked my friend Zeno. 
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| « Last Edit: Dec 6th, 2006, 2:48pm by Whiskey Tango Foxtrot » |
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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towr
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Re: Turtle Race
« Reply #7 on: Dec 6th, 2006, 2:57pm » |
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You know, I considered posting a reference to "Pyramids", featuring the philosopher Xeno (well, not quite featuring, the book is about Teppic really, and pyramids, and geometry) Anyway, the point is, he quite unsuccesfully tried to demonstrate arrows can't catch up to a turtle.
So I would have suggested, if Xeno was anywhere near, the rabbit would definitely have won.
That was before the riddle changed even. However I opted to go with a hint to the Abbott and Costello routine.
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| « Last Edit: Dec 6th, 2006, 2:58pm by towr » |
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Sameer
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Re: Turtle Race
« Reply #8 on: Dec 6th, 2006, 3:51pm » |
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on Dec 6th, 2006, 2:44pm, Whiskey Tango Foxtrot wrote:| I say the rabbit never passes the turtle, and the rabbit loses by a hare. No seriously, though. The turtle wins. I asked my friend Zeno. |
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Maybe Xeno can be used when we master the control and concept of time!!!
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Sameer
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Re: Turtle Race
« Reply #9 on: Dec 6th, 2006, 3:55pm » |
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And since WTF has already fiddled with paradoxes let's go with Aristotle's wheel Paradox.
Consider wheel with radius R sitting on Ground. Consider a small wheel attached to its centre with radius r. R>r
Consider the point of wheel touching the ground as A. The corresponding point on small wheel is C.
Let the big wheel turn the complete cicle reaching point B. Let the corresponding point for small wheel be D.
Then it is easy to see that AB=CD. Since AB is the circumference of big wheel, it is same as CD the circumference of small wheel. Hmmm...
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Whiskey Tango Foxtrot
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Re: Turtle Race
« Reply #10 on: Dec 6th, 2006, 4:19pm » |
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Yea, Xeno. Sameer, you trickster. B=D and AB=CB. 2(pi)R relates the circumferences to the radius, as well as the distance traveled.
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Sameer
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Here's a picture
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Whiskey Tango Foxtrot
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Re: Turtle Race
« Reply #12 on: Dec 6th, 2006, 5:07pm » |
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Oh. That one. Aristotle's Wheel, right? There are a plethora of ways to disprove this one. I'll give two. First, there is not a one-to-one correspondence between points on the two wheels. Second, and related to the first, imagine you had two strings, one fixed to each wheel while it moved.
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| « Last Edit: Dec 6th, 2006, 5:07pm by Whiskey Tango Foxtrot » |
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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ThudnBlunder
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Re: Turtle Race
« Reply #13 on: Dec 6th, 2006, 5:54pm » |
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on Dec 6th, 2006, 5:07pm, Whiskey Tango Foxtrot wrote:| First, there is not a one-to-one correspondence between points on the two wheels. |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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Whiskey Tango Foxtrot
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Re: Turtle Race
« Reply #14 on: Dec 6th, 2006, 6:02pm » |
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Whoops. There's a pretty stinky brain fart for you all to enjoy. 
Let me try to mask the scent of my flatulent debauchery with an attempt at mending my previous post.
Despite a one-to-one correspondence between the two, they are not necessarily of equal length. [Insert string example here] Please forgive.
Also, if you look at an arrow in flight, at an instant in time, it appears the same as a motionless arrow. If we look again at another instant, it again appears motionless. How do we then see motion?
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| « Last Edit: Dec 6th, 2006, 6:03pm by Whiskey Tango Foxtrot » |
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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flamingdragon
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Re: Turtle Race
« Reply #15 on: Dec 6th, 2006, 6:31pm » |
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We see it with our eyes. 
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ThudnBlunder
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Re: Turtle Race
« Reply #16 on: Dec 6th, 2006, 7:31pm » |
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on Dec 6th, 2006, 6:02pm, Whiskey Tango Foxtrot wrote:
Never mind, at least your doing maths spares us more of your Vogon prose. 
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| « Last Edit: Dec 6th, 2006, 7:36pm by ThudnBlunder » |
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Whiskey Tango Foxtrot
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Re: Turtle Race
« Reply #17 on: Dec 6th, 2006, 8:10pm » |
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Well, at least I'm only the third worst. 
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towr
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Re: Turtle Race
« Reply #18 on: Dec 7th, 2006, 12:52am » |
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on Dec 6th, 2006, 7:31pm, THUDandBLUNDER wrote:| Never mind, at least your doing maths spares us more of your Vogon prose. |
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Prose?
I thought only their poetry was infamous, never heard a word about their prose.
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ThudnBlunder
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Re: Turtle Race
« Reply #19 on: Dec 7th, 2006, 1:56am » |
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on Dec 7th, 2006, 12:52am, towr wrote:
Prose?
I thought only their poetry was infamous, never heard a word about their prose.
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'Vogon' is here intended to mean the third worst in the Universe.
The second worst poetry in the Universe is, of course, that of the Azgoths of Kria. During a recitation by their poet master Grunthos the Flatulent of his poem "Ode to a Small Lump of Green Putty I Found in My Armpit One Midsummer Morning" four of his audience died of internal haemorrhaging and the president of the Mid-Galactic Arts Nobbling Council survived only by gnawing off one of his own legs.
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| « Last Edit: Dec 7th, 2006, 1:35pm by ThudnBlunder » |
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rmsgrey
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Re: Turtle Race
« Reply #20 on: Dec 7th, 2006, 8:05am » |
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The two points on the wheel have different instantaneous velocities - the point on the circumference is instantaneously stationary at the start and end positions, while the point on the smaller wheel has a horizontal velocity with magnitude proportional to R-r - when measured in the appropriate rest frame, the distance CD is indeed equal to the circumference of the smaller wheel, just as AB is equal to the circumference of the larger wheel in the rest frame where the ground is stationary.
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jenny
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Re: Turtle Race
« Reply #21 on: Dec 7th, 2006, 1:23pm » |
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does anyone besides me here have a life
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Whiskey Tango Foxtrot
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Re: Turtle Race
« Reply #22 on: Dec 7th, 2006, 1:29pm » |
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A what?
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towr
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Re: Turtle Race
« Reply #23 on: Dec 7th, 2006, 1:41pm » |
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on Dec 7th, 2006, 1:23pm, jenny wrote:| does anyone besides me here have a life |
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I'm not sure "besides" is wholly appropriate. People that have a life wouldn't post online wondering whether people besides them have a life, would they? They'd have better things to do 
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SMQ
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Re: Turtle Race
« Reply #24 on: Dec 7th, 2006, 1:43pm » |
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Jenny, you probably weren't looking for a serious answer, but for myself, yes, I have a job I enjoy in real life, a serious relationship, own my house, and so by most measures a "life". I also enjoy wordplay, mathplay, and almost any opportunity to exercise parts of my brain that don't get much used in my work (and even less outside of work). Without claiming to speak for anyone else, I suspect most of the regulars around here would say something similar.
This here is a great crowd to hang out with if you're into such things, but we certainly have a tendency toward (over)analyzing even the most trivial points of a riddle/problem. Welcome!
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