This problem appears in the finals of 13 years old chinese students:
In a circunference of any radius, two particles start from the same point at the same time and start moving at the same constant speed without stopping. One goes through the diameter of the circunference, turning back once it reaches the end, and the other one follows the line of the circunference.
When will both particles meet?
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pi.
2Pi.
>circunference
These are the yellow fuckers who are beating us. We have to do better.
3pi
never
Never. The particle along the circumference travels at an irrational ratio to the particle along the diameter. If we are talking 13 yr olds who may approximate pi as 22/7, then that could be an answer (7 orbits of the surface particle almost corresponds to 22 trips along the diameter of the other)
demonstrate it mathematically.
in the infinite
If you are going with pi=3 then its 2pi
d bei the diameter. One dot travels k times, the other one l times. This gives the equation k×d=l×d×pi.
Thus k/l = pi, aber contradiction to the irrationality of pi
2d·n=dpi·n
2n=pi·n
2n-pi·n=0
(2-pi)n=0
n=0/(2-pi) so no it does not
Kek
Its actually 4pi because 2pi=360
>at the same constant speed
>speed
The fuck is this nebulous "speed"? That could mean so many fucking things. It could be actual velocity (but then you get into vectors), or it could be one "tick" (getting from A at the top to B at the bottom). The latter is not the same "speed" in, say "pixel per second" or something, but it is the same "speed" if working with the logic of "time it takes to reach opposite end of diameter".
this
seems reasonable though, I'm just saying OP's little problem is worded in a retarded way.
when that red thing makes a round blue travels pi so in theory they will be never again in exactly same point
speed can't measure the time it gets to reach the opposite end of the diameter
time is measured in seconds, not speed units
youre that guy who asked how much seconds is 60 units of microwave time ?
X1=X2 = where they meet
t=t = time when they meet
X1=V*t
X2=W*t
V*t=W*t
V=W
m/s=/=rad/s
Prove me wrong
13 year olds can use the Taylor Series' value for pi
what
Aha, you forgot it's particles, not exact points. The answer depends on the ratio between the circle and the particles' radii. Also OP using the term circumference instead of circle is stupid.
I made a simulation jsfiddle.net
the one through the circumference goes faster
This.
You set angular speed, not speed in rad.
fix it then
The answer is right there you dumb niggers. They never meet again
>You cant point out someones mistake
it wasn't me (who posted the thing)
One sec...
jsfiddle.net
Here it is
BTW: they will meet only if PI can be represented as NATURAL / NATURAL number.
You Arena using floating point numbers
and thus approximating pi as a rational mumber. So when the Simulation is fixed IT will give a positive result, even in it is wrong.
indeed, thats why you have to use pi = 3.
If not then 13 yo wont do this.
God i hate posting from my phone
what does it mean that it travells k or n times?
Unfortunately we still don't know if pi is irrational.
can any of you fucking do a simple equation to demonstrate this shit
with either mathematical / physical concepts
When the diameter dot moves 3 lengths the circumference dot will not have completed its first circle yet. Pi does not equal 3
Wat? Ofc wenn know
One dot travels k times along the diameter and the other one l times around the circle. In Order to meet, k and l have to be natural numbers, leading to the shown contradiction
I already did
The picture is drawn incorrectly.
If the particle that goes through the same diameter and "turns back", then there should only ever be one direction for the blue arrows.
Never. Their speed is irrational with respect to each other, and therefore no rational multipliers (which is what crossing the center and going around the outside are a miniscule subset of) can ever make them equal.
1 trip (to bottom from top or vice versa) of P1
is 1/3 of P2 trip
So from bottom to top = 1/3 of circle
from top to bottom = another 1/3
So 3 trips which is down up down = full circle
You cant calculate this with pi as natural number, it will never meet like that.
Look at left top corner of the pic.
look at the left top corner
By the way there are similar theories about pool table ball locations and the position of particles in space in the universe as a whole, where the number of possible futures are similarly limited.
what about something more physical than mathematical?
It is a mathematical question.
i remember studying something similar to
It is pretty useless what the other user shows there. V=W. Great, what now? As both dots have the same speed, V=W is already given from the beginning
Was meant for you
and when you equal k*d=l*d*pi it's because they are meeting at the same spot right?
>radians
>go die autist
You can also formulate the answer like this :
They will meet when the circle particle passes whole circle 2 times.
Or on the 6th trip of d particle
>people arguing about the correct answer
>I can't even understand the question
Never
They started at the same point... they already met
When the particles meet they would have traveled an integer number of times along the diameter or along the semicircle.
Since they traveled at the same speed for the same time the distance traveled will be the same so:
N*D=M*Pi*D/2
hence
2N/M=pi
ut pi can't be written as a fraction and so the particles can never meet.
never,Pi is irrational number, meaning, it cannot be the expression of 2 other numbers. they will never meet, not even in infinity.
Think instead of 2 ideal bouncing balls, red and blue. Both bounce constantly and eternally but at different rates to one another, and the count starts after their first bounce. Lets make the red ball bounce once a second to make things easier. If you time how long it takes the blue ball to bounce, can you determine at which bounce, if at all, do both of them hit the ground simultaneously? Yes, it's pretty easy. You find their least common multiple. For example, lets say the blue ball bounces every 0.55 secs (red is once a second). You know so long the blue ball hits the ground at a whole number, it will sync with the red ball. This happens at 11 secs (lcm of 55 and 100 is 1100). In the case of the circle, there is also a 'count' or a 'bottom of the bounce' which are the 2 locations that the balls can physically meet, top and bottom. There is no common multiple between D and 2(pi)D. So if the particle on the circumference 'bounces' at 1,2,3 etc, the particle on the surface bounces every 3.141... , 6.242... and other unholy intervals which never hit a whole number.
>never
/thread
Why are there replies after this?
It's proof by contradiction. Assuming that the balls do meet, it'll be at k*d = l*d*pi. But that implies that k/l = pi, and pi cannot be expressed as a ratio of 2 whole numbers, which k and l are because they are counts.
They never meet because pi is irrational
they meet here
> finals of 13 years old chinese students
Nice try - do your own damn schoolwork
And learn how to spell Chinese dickwad
Yes
People spend years of their life trying to learn how to solve advanced mathematical problems only to work on the physics engine for the next flappy bird clone
If your not a paid physicist working for Tesla | NASA you've wasted your prime youth on learning unnecessary skills while kids go out and actually get laid
I respect you guys, but this shit is impractical for 99.9% of the population
>Training your brain is impractical
6psi
fuck
One particle travels linearly at a constant speed then reverses direction without accelerating nor decelerating? I give up. What's the answer?
Never.
at 0 time then never again
Is n the number cycles the particles go through? If so, your equation is wrongely based 'cause the particles do not travel the same amount of cycles.
d*pi*n=m*d*2
(distance traveled by the particle going around the circle = distance traveled by the other one)
Plus, they could also meet on the other end of the circle, so the equation is not exactly right, is it?