Annoying maths puzzle.

[Redingold]

Somebody posed me this problem, and I can't work it out.

You're standing on a graph, with the x-axis in front of you, and the y-axis to your side. You take 1 step forward, turn through n degrees, take half a step forward, turn through n degrees again, take a quarter of a step forward, turn through n degrees, etc.

In terms of n, where do you end up?

If you could say how you worked it out, that'd be swell.

 

[ThePoodonkis]

So, wait, you're walking turning along the z-axis then?

 

[pantsoffdanceoff]

It would be in polar coordinates. X,Y coordinates don't take degrees into consideration.

 

[Redingold]

So, wait, you're walking turning along the z-axis then?

Yuh.

 

[Redingold]

coordinates 0,0 on the x and y because you dont go forward on them. you go up or sideways.


heres a much better one.

how do you take 2 from 5 and get 4

By forwards, I mean, the direction in which you're facing. Remember that you're standing on this grid.

If you took 2 from 5 and got 4, you're doing something wrong.

 

[AdmiralWolverineLightningbolt]

coordinates 0,0 on the x and y because you dont go forward on them. you go up or sideways.


heres a much better one.

how do you take 2 from 5 and get 4

if you have 5 matchsticks and take 2 away
then you can repostion them as IV, roman numerals for 4

 

[GodsOneMistake]

Ya fuck this, it's summer for me and I refuse to do math

 

[Trilby]

Won't you end up spiralling? In which case you'll end up at the centre of the spiral. I'm sure there's some easy way to work out where you'll be from spiral formulae in polar coordinates.

 

[Redingold]

coordinates 0,0 on the x and y because you dont go forward on them. you go up or sideways.


heres a much better one.

how do you take 2 from 5 and get 4

if you have 5 matchsticks and take 2 away
then you can repostion them as IV, roman numerals for 4

Gah, damn fiddly questions like that. I loves 'em. For example, by adding 1 line, make this correct: IX + III = IX

 

[Lukeje]

Gah, damn fiddly questions like that. I loves 'em. For example, by adding 1 line, make this correct: IX + III = IX

IX + III =/= IX

And on-topic, is n a constant?

 

[fulano]

Somebody posed me this problem, and I can't work it out.

You're standing on a graph, with the x-axis in front of you, and the y-axis to your side. You take 1 step forward, turn through n degrees, take half a step forward, turn through n degrees again, take a quarter of a step forward, turn through n degrees, etc.

In terms of n, where do you end up?

If you could say how you worked it out, that'd be swell.

I don't think the problem is correct. You turn n degress with respect to what? And what the hell is n degrees? It could be anything.

I'm calling it: The problem is wrong, not you for not understanding it.

 

[AdmiralWolverineLightningbolt]

Gah, damn fiddly questions like that. I loves 'em. For example, by adding 1 line, make this correct: IX + III = IX

IX + III =/= IX

that's a cop out answer

for the while, i cant figure it out
but while you smile smugly, figure out this one
IX + II = 411
you can only add one line like yours

 

[fulano]

The problem is wrong. If you don't know how much you are turning, and with respect to what, you can't answer the damn question.

EDIT: Man, even the question is wrong. In terms of n? If you are going to answer where you are, it has to be in terms degrees with respect to an axis or both, not just degrees.

 

[Alex_P]

The problem is wrong. If you don't know how much you are turning, and with respect to what, you can't answer the damn question.

Untrue.
You know you turn by some constant n each time. You can express the answer as a function of n.
The problem gives you enough information to safely assume that n is a rotation in the x-y plane (since that's the one you're capable of moving in). There's ambiguity in whether you're measuring n clockwise or counterclockwise (although it's also perfectly reasonable to just assume that, if you face towards +x, positive n is towards +y) but that doesn't stop you from being able to calculate anything.

EDIT:

EDIT: Man, even the question is wrong. In terms of n? If you are going to answer where you are, it has to be in terms degrees with respect to an axis or both, not just degrees.

That means "express the answer as a function of n".

-- Alex

 

[Alex_P]

This is a real problem and it's calculable. Stop treating it like a damn riddle, y'all.

You can calculate your current position after any given move m as using a series.

Finding where you "end up" involves taking the limit of that series.

-- Alex

 

[fulano]

The problem is wrong. If you don't know how much you are turning, and with respect to what, you can't answer the damn question.

Untrue.
You know you turn by some constant n each time. You can express the answer as a function of n.
The problem gives you enough information to safely assume that n is a rotation in the x-y plane (since that's the one you're capable of moving in). There's ambiguity in whether you're measuring n clockwise or counterclockwise (although it's also perfectly reasonable to just assume that, if you face towards +x, positive n is towards +y) but that doesn't stop you from being able to calculate anything.

-- alex

I'm assuming we are rotating with respect to the z axis(which you are led to assume but not outwardly told).

Look, if you are indeed talking about polar coordinates, then there is no debate: It is clockwise, and to iron it further home, you would have to be talking about a function like sine, cosine, tangent, etc. that takes into account the angle of rotation(theta), but then again, you are also told that you take steps forward or backwards, whatever. There, you got another variable there. And yet, you want to answer this thing only with respect to theta.

Sorry, but no can do.

 

[Alex_P]

... but then again, you are also told that you take steps forward or backwards, whatever. There, you got another variable there. And yet, you want to answer this thing only with respect to theta.

A "step" is a unit of distance. 1 step = the grid unit; there you go. If somebody else later comes and says "No, a step isn't 1 unit on the grid", you can just multiply your answer by a conversion factor. None of this prevents you from forming a meaningful answer.

I'll post it when I don't have somewhere to be in five minutes.

-- Alex

 

[Kubanator]

The problem is wrong. If you don't know how much you are turning, and with respect to what, you can't answer the damn question.

Untrue.
You know you turn by some constant n each time. You can express the answer as a function of n.
The problem gives you enough information to safely assume that n is a rotation in the x-y plane (since that's the one you're capable of moving in). There's ambiguity in whether you're measuring n clockwise or counterclockwise (although it's also perfectly reasonable to just assume that, if you face towards +x, positive n is towards +y) but that doesn't stop you from being able to calculate anything.

-- alex

I'm assuming we are rotating with respect to the z axis(which you are led to assume but not outwardly told).

Look, if you are indeed talking about polar coordinates, then there is no debate: It is clockwise, and to iron it further home, you would have to be talking about a function like sine, cosine, tangent, etc. that takes into account the angle of rotation(theta), but then again, you are also told that you take steps forward or backwards, whatever. There, you got another variable there. And yet, you want to answer this thing only with respect to theta.

Sorry, but no can do.

Uh what? You always take steps in the facing direction. This isn't a problem you answer in terms of numbers, you answer in a formula. It's grade 12+ math. There is only 2 variable. The number of times you have gone through this, and the angle of rotation. And it doesn't matter if you rotate on the Y or Z axis, those letters are simply representations of dimentions. This is a 2D problem.

Ok, assuming that t = angle of rotation, and n = the step you are on, we can say:

1/2^n = distance of the step
and
t*(n-1) = angle you are facing on the next step.

So, lets solve it. What we need is a way of finding X/Y co-ordinates from these 2 numbers.

Ok, to find the distance the person moved in the Y axis on that step, it's sin(t*(n-1))/2^n.
For the X axis, it's cos(t*(n-1))/2^n.

Ok, now you simply have to choose how many repetitions you go through, because you won't get a specific answer, rather you'll get an answer that grows infinitely precise.

 

[ILPPendant]

Spoiler: Ignore: did not read OP properly

In before someone says final coordinates are (1 + cos n, sin n).

EDIT: Gah!

EDIT 2: Never let it be said I copied someone else so I'll explain what I did.

Our starting point is effectively on the coordinates (1,0) and after each iteration we rotate by n degrees and move one half the distance we moved previously. This means that for the Nth iteration we will sum from i to N 2[sup]-i[/sup]cos n and then add one for the x coordinate and 2[sup]-i[/sup]sin n for the y coordinate.

A quick round of algebra shows these sums to come out as 2[sup]-N[/sup](2[sup]N[/sup] - 1)cos n (or sin n). Taking the limit to infinity leaves us with just cos n or sin n.

Hence the result.

 

[Trendkill6]

the answer is 42.