brain teaser!!!!

[ironmaster15213]

Where's Chuck Norris when you need him??????

[MusicMan]

oh man i just wrote a calculus exam, my head is hurting enough without reading this...

[Kilroy]

Well, 'cmon mr college math!

[Agent99]

Okay, what would MacGyver do? He would remove his belt, lasso one end around the dog, and attach the other end inside the circle to the floor on a hook he formed out of paper clips. I’m close, huh? He would simply slip out the opposite side before the dog, limited to running around the circumference of the circle, got to the spot where he made his exit.

[jonf]

Well, 'cmon mr college math!

he didn't say he PASSED the midterm

[MusicMan]

Well, 'cmon mr college math!

its actually university math duh...

and someone should flip a coin to see if i passed it

[Kilroy]

I thought they were all called "Colleges" in the states. Here I was trying to use the RIGHT term.

[MusicMan]

I thought they were all called "Colleges" in the states. Here I was trying to use the RIGHT term.

i go to University of Windsor ontario... i just live across the river in the states

[ironmaster15213]

No matter how I think about this I keep coming back to a sphere instead of a one dimensional circle. In other words you have a ball or sphere shaped structure and you are in the middle of it, all you would have to do is climb to the top and exit. You would be out of the circle and the dog would not be able to catch you cause it's still on the ground running around the structure. God I gotta get a life

[Kilroy]

So you have to do the border twice a day? That could get very tiresome.

i go to University of Windsor ontario... i just live across the river in the states

[MusicMan]

So you have to do the border twice a day? That could get very tiresome.

yeah its a pain in the butt.. but my nexus pass saves me sitting in the line-ups every morning and night

[Golfbum]

Is the dog asleep yet?
Has "RICHARD" solved the problem?
Does anyone really care?
Who would actually be dumb enough to get caught inside the imaginary circle?

[MusicMan]

Lol!

[Andy4Par]

Just jump up with both feet. Your out of the circle. Question doesn't say there is a time limit.

[Hacker]

According to the description of the problem, the dog isn't allowed off of the imaginary line that defines the circumference of the circle so just start running towards the edge of the circle and jump over the dog. It isn't allowed to jump up to bite you because a circle is a two dimentional shape so the dog must keep it's feet on the ground.

Problem solved........

[Golfbum]

According to the description of the problem, the dog isn't allowed off of the imaginary line that defines the circumference of the circle so just start running towards the edge of the circle and jump over the dog. It isn't allowed to jump up to bite you because a circle is a two dimentional shape so the dog must keep it's feet on the ground.

Problem solved........

White guys can't jump

["Richard"]

The answer is to run in a smaller circle inside of the box. As long as the circumference of your circle is less than 4x the size of the bigger circle, you will be moving faster than the dog, at the point where the dog is furthest away from you, you'll be able to make a break for the edge of the circle... and you'll make it.

Ex:

If radius =5m and circum=31.4

You can run in a circle 1.2m away from the radius of the larger circle. Since the circumference of your circle is 7.53... you'll be moving faster than the dog is, you'll eventually get to a point where he is as far away in his circle as possible.... you then make a break for it. You have 3.8m to go, and the dog will have 15.7m so he won't be able to catch you.

FINALLY!!!! YOU ARE CORRECT

[Gapwedge]

[quote="Richard";159066]The dog cannot enter the circle and remains on the circumference of the circle at all times.[/quote]

There is an easier way that involves a lot less running.
[FONT=Arial][/FONT]
[FONT=Arial]The trick is to start from the centre of the circle and run to the circumference, keeping the dog to your back at all times. In short, you will run along the arc of a logarithmic spiral while the dog must run the circumference of the circle. [/FONT]
[FONT=Arial] [/FONT]
[FONT=Arial]Using this approach, the maximum distance the dog can run is 2[/FONT][FONT=Symbol][FONT=Symbol]p[/FONT][/FONT][FONT=Arial]R (anything longer and you will not escape from the circle). The curve of the logarithmic spiral is of the form r=a exp(b[/FONT][FONT=Symbol][FONT=Symbol]q[/FONT][/FONT][FONT=Arial]), where r is the distance from the centre of the circle, [/FONT][FONT=Symbol][FONT=Symbol]q[/FONT][/FONT][FONT=Arial] is the angle (in radians) from the x-axis, and a and b are constants related to the speed differential. The arc length the spiral, which is the distance you must run, is given by s = (a/b) (SQRT (1+b^2)) exp (b[/FONT][FONT=Symbol][FONT=Symbol]q[/FONT][/FONT][FONT=Arial]). [/FONT]
[FONT=Arial] [/FONT]
[FONT=Arial]I will save you the math, as it gets messy rather quickly. However, it is relatively easy to see t[/FONT][FONT=Arial]hat the arc length you must run is bounded by the radius R of the original circle (on the low side) and half the circumference of a circle of radius R/2 (on the high side). [/FONT]
[FONT=Arial] [/FONT]
[FONT=Arial]Half the circumference of a circle of radius R/2 is equal to [/FONT][FONT=Symbol][FONT=Symbol]p[/FONT][/FONT][FONT=Arial]R/2. We stated above the dog runs 2[/FONT][FONT=Symbol][FONT=Symbol]p[/FONT][/FONT][FONT=Arial]R, which is 4 times as far. We also stated the arc length will be less than [/FONT][FONT=Symbol][FONT=Symbol]p[/FONT][/FONT][FONT=Arial]R/2, which means you will easily reach the point on the circumference where the dog started before he runs the complete circle. [/FONT]
________
[URL="http://www.ford-wiki.com/wiki/Jaguar_V12_engine"]JAGUAR V12 ENGINE HISTORY[/URL]

[Indio]

Good lord people, whats all this new math, algebra and geometry crap! We all know that mutts will always stop to sniff a 'wet spot'.... just take a leak, start walking past it and the dog will stop to see who it is that has invaded his territory! The with the blink of an eye you are headed to the first tee before the mangey mutt has even figured out that it wasn't a cute little french poodle that did the job!

["Richard"]

There is an easier way that involves a lot less running.

LOL... that way is not easier at all!!! But it does involve a lot less running

[Golfbum]

Good lord people, whats all this new math, algebra and geometry crap! We all know that mutts will always stop to sniff a 'wet spot'.... just take a leak, start walking past it and the dog will stop to see who it is that has invaded his territory! The with the blink of an eye you are headed to the first tee before the mangey mutt has even figured out that it wasn't a cute little french poodle that did the job!

Glad to see you are back with a full sense of humor!

[Indio]

Glad to see you are back with a full sense of humor!

Sense of humor???? Sheesh, I am finally serious for once and Rick thinks I am being funny!

["Richard"]

back? from where?? did you have a heart attack to?

[Indio]

back? from where?? did you have a heart attack to?

Don't know what thats about, I didn't go anywere. I guess a guy gets busy and doesn't come on for a day or 2 and they think he has been gone a long time. They just missed the forum idiot thats all

[Gapwedge]

oh man i just wrote a calculus exam, my head is hurting enough without reading this...

Alcohol and calculus do not mix - don't drink and derive.
________
Hr-V

[MusicMan]

i quit drinking last month...

[jonf]

i quit drinking last month...

Now is that the "i had WAY too much tequila last night...i'm not drinking ever again" that lasts until the next big party, or is that the real, mature "damn, this stuff ain't good for me"....that lasts until the next big party.

[MusicMan]

a little from column A a little from column B... trying to get in shape

[Hacker]

Alcohol and calculus do not mix - don't drink and derive.

That's almost as good the the shirts we wore in University that said "Friends don't let friends take Arts"

[Gapwedge]

That's almost as good the the shirts we wore in University

My favorite T-shirt from undergrad days:

And God said,

??D = ?
??B = 0
??E = -?B/?t
??H = J + ?D/?t

and then there was light.
________
Gt-one