View Full Version : A little help with a math problem....
Hallo can any of you do some math...:-)
I have a problem I just can not solve,
1) I need to find a and b in the formula
2) find the direction and radius then Peter has "worked" 3 km arc line
Peter must treasure hunt in the woods and have been told that he can find the treasure to closely follow the path of a logarithmic Spira, at a given starting point. If he walk 3 km, on the arc line. He will find the treasure.
Peter knows a logarithmic spiral is as follows: http://img.geocaching.com/cache/fb69b5bb-a291-4c0d-8dce-6bd5b5f32eea.jpg
Startpunkt=STARTPOINT
He has also been told that when he has revolved around 180 degrees (marked with A in the figure), he is 86.23 meters from where he started, and after 360 degrees (marked with B in the figure), he is 75.41 meters where he started.
Fortunately, Peter also knows the formula for a logarithmic spiral: http://img.geocaching.com/cache/fb9feec7-ee06-40b5-9f87-0936c3ed9be3.jpg, and he assumes that the starting point corresponds to Theta = zero.
With this knowledge puts Peter down first and count (long) on the figures. Then he prepared for the trip, and he does not actually become dizzy by.
Taygoo - Have tried to solve this in days now...:-)
AVGWarhawk
06-29-09, 12:41 PM
Peter needs a new hobby.
Task Force
06-29-09, 12:45 PM
That... math... problem... confuses the h*** out of me.:o
you think he will be happy with 1+1=2. lol
antikristuseke
06-29-09, 12:47 PM
I am way too drunk to start with math problems right now.
Raptor1
06-29-09, 12:47 PM
This isn't a math question! It's a conspiracy!
Why is Peter being forced to "treasure hunt"? Who is forcing him? Why does he believe that he will find treasure if he goes in such a way?
Peter is clearly being manipulated by a shadowy group with evil intentions, I say, and it's same group of shadow-dwellers that want us to focus our concentration on him rather than to see the truth!
Rise up! Rise up against the evil conspiracy!
AVGWarhawk
06-29-09, 01:04 PM
This isn't a math question! It's a conspiracy!
Why is Peter being forced to "treasure hunt"? Who is forcing him? Why does he believe that he will find treasure if he goes in such a way?
Peter is clearly being manipulated by a shadowy group with evil intentions, I say, and it's same group of shadow-dwellers that want us to focus our concentration on him rather than to see the truth!
Rise up! Rise up against the evil conspiracy!
I would go with this answer:yep:
Also, 1+1=3:o
Ack.
It's calculus...rectification/integration.
I'll give it a bash, but I am also new to think kind of thing. If I don't reply
soonish assume that it has induced brain paralysis in me...
It's a conspiracyNo just a question I need to solve, so I can get the to real treasure :-)
I'll give it a bashThx.. I have tried 5 hours to day.. my head is :damn:
Good luck Letum
Have you got the spiral's function yet?
VipertheSniper
06-29-09, 02:28 PM
umm maybe there was something lost in translation, I have a few troubles understanding which distance has to be 3 km? Is that walking 3km on the spiral, or 3km in straight line from the startpoint when he walks on the spiral?
Edit: the second option doesn't make much sense now does it? I mean apart from the first 180° there are surely always 2 points on the spiral that are in equidistance to the starting point.
It's the arc length from the startpoint.
VipertheSniper
06-29-09, 02:37 PM
That would mean 2 points to search or not? atleast when I look at that figure I'm inclined to think so.
VipertheSniper I did some edit in the main text.
If Peter work on the arc line, 3 km he will be there.
Just thinking out loud.....
When r=86.23
86.23=a*Exp^180b
When r=75.41
75.41=a*Exp^360b
Can they be worked out as simultaneous?
b must be less than 0.2 and more than 0.1
Just thinking out loud.....
Can they be worked out as simultaneous?
b must be less than 0.2 and more than 0.1
I can not say yet.
I have tried to do this..
86,23+1 = a*e^b*180
75,41-1=a*e^b360
and i get
a= 102,259 b=-0,000883
I go to sleep now.
Don't stay up all night for this. And thx for trying
VipertheSniper
06-29-09, 03:26 PM
I'm beginning to understand now.
Also need some sleep.
Will try again tomorrow if no one else has.
VipertheSniper..
Yea from the startpoint to A there is 86.23 m and from the startpoint to B there is 75.41 m
Good news!
The values are:
a=30
b=0.2
The function is:
30*e^(0.2*t)
To prove:
"When he has revolved around 180 degrees he is 86.23 meters from where he started."
Therefor:
a*e^(b*t)=86.23-a
30*e^(0.2*1pi)=86.23-30
30*e^(0.2*pi)=56.2336863
and
"after 360 degrees he is 75.41 meters where he started."
Therefor:
a*e^(b*t)=75.41+a
30*e^(0.2*2pi)=75.41+a
30*e^(0.2*2pi)=105.4075687
Second part coming soon. Ask if you need any more details.
Onkel Neal
06-30-09, 10:49 AM
Good work, I ran this past my daughter and two of her genius friends, they came up with the same thing:
This is what both Steven and Parag said after looking at the problem.
a = 29.99803486
b = 0.2000111295
theta = 14.88037659 (in radians)
r = 588.3798861 (m)
Note that if you want to describe the location with polar coordinates, you would use r = 14.88037659 - 4*pi = 2.314005976 instead.
ok, here is how i arrived at my answer:
First of all, at theta = 0, r = a. Therefore, the starting point is a. Now, using the information given we can write these two equations: A = a - 86.23 and B = a + 75.41.
We can write two more equations using the facts that at 180 degrees (pi) we are at point A and at 360 degrees (2*pi) we are at point B: A = -a*e^(pi*b) and B = a*e^(2*pi*b). Note that the first equation is negative to match the figure (A is on the negative x-axis).
At this point we have four equations and four unknowns. Solving for the unknowns yields the following: a = 29.99803486 and b = 0.2000111295 (A and B are not important)
Now, we must use arc length to find theta. We will use the following formula: s = [a*e^(b*theta)*(1+b^2)^(1/2)]/b. The formula can be derived using the general formula for arc length (involves a bit of calculus).
Anyway, using that formula (s = 3000 according to the problem), we get theta = 14.88037659 radians. Now, we can use the original ... Read Moreformula for a logarithmic spiral (r = a*e^(b*theta)) to solve for r. Doing so, we get r = 588.3798861 meters. As I said before, the exact location of the treasure can be expressed in the polar coordinates r = 588.3798861 m and theta = 2.314005976 radians.
After reading the explanation, it now seems so obvious (haha, no, not really!) :haha:
Raptor1
06-30-09, 10:51 AM
Hmm, good timing, them posts...almost too good... :hmmm:
Onkel Neal
06-30-09, 10:52 AM
Lol, Letum beat me to it.
AVGWarhawk
06-30-09, 10:58 AM
Now I see it. Clear as mud:up::o
Lol, Letum beat me to it.
Ahh, but you did it the correct way.
I got the function through a hard trial and error/educated guess slog and then
started the calculus integration for the second part.
Neal, is your daughter sure about the second bit?
I find 3000m to be at ~13.76 radians...(4.38pi).
It may well be me that is wrong tho...I'm very much on the edge of my depth.
Thx for that..
i did some math, but never got these numbers
Letum good work..
I will try to use the result.
Do we agree that the start point is (a,0)
And therefore (0,0) is -a from the startpoint?
Neal
Nice to have a good family.. I say many thx to them.. give them a ice from me...:-):D
Task Force
06-30-09, 02:25 PM
Ooooah god this thread is hard to understand.:dead:
Neil one thing...
The formel to the arc linehttp://mathworld.wolfram.com/images/equations/LogarithmicSpiral/Inline22.gif see http://mathworld.wolfram.com/LogarithmicSpiral.html part (6)
And from that formel the arc length measured from the origin http://mathworld.wolfram.com/images/equations/LogarithmicSpiral/Inline19.gif
So schould it not be [a*e^(b*THETA)*(1+b^2)^(1/2)]/b-[a*e^(b*ZERO)*(1+b^2)^(1/2)]/b=300 and then we find Theta..
I this case I get theta to 15,129
Because we walk from Theta=0 to theta=arc line 3000 m
Ooooah god this thread is hard to understand.:dead:
Your modern art I don't understand:cool:
Task Force
06-30-09, 02:34 PM
dats what I was aiming for when I made it.:up::rotfl:
Neil one thing...
The formel to the arc linehttp://mathworld.wolfram.com/images/equations/LogarithmicSpiral/Inline22.gif see http://mathworld.wolfram.com/LogarithmicSpiral.html part (6)
And from that formel the arc length measured from the origin http://mathworld.wolfram.com/images/equations/LogarithmicSpiral/Inline19.gif
So schould it not be [a*e^(b*THETA)*(1+b^2)^(1/2)]/b-[a*e^(b*ZERO)*(1+b^2)^(1/2)]/b=3000 and then we find Theta..
I this case I get theta to 15,129
Because we walk from Theta=0 to theta=arc line 3000 m
And if theta=15,129
R=618,278
and 15,128-4pi=2,56263 radian
(180/pi)*2,56263=146,828 degress from x-acres or course 303.172
So if according to this, if I go from the startingpoint(a,0), west(course 270) a meters(29.99803486) I will be (0,0) and now I go course 303,172 and walk 618,278 meters, then I will be at the treasure???
Onkel Neal
06-30-09, 03:05 PM
Ahh, but you did it the correct way.
Yeah, I asked some college students :D
Yeah, I asked some college students :D
Pfft!
Not asking college students is probably why I did so badly at college. ;)
Neal, is your daughter sure about the second bit?
I find 3000m to be at ~13.76 radians...(4.38pi).
It may well be me that is wrong tho...I'm very much on the edge of my depth.
How did you figure out that number
Because my calculation is wrong...:shifty:
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