A good Car Talk Puzzler

"Califbill" fired this volley in news:i8GdnbaYqouhiTDQnZ2dnUVZ snipped-for-privacy@earthlink.com:

Actually touching. Any thickness to the rope would prevent the bottom of the catenary from being 75' down. It has to be a one-dimensional rope - length only, no thickness.

LLoyd Touching, could not have a loop between.

I over-thought this one. Any real rope is going to have a curve at the bottom, where the direction reverses, so it will never be quite 75' down.

However, then I realized that if the problem were that tricky, there is no way that any distance between poles would allow the rope to reach a point

75' down. So I gave up. d8-)

Those are the ones they use to tie up the spherical cows, right? ;-)

Cheers! Rich

I must be doing things wrong I can do this with one utility pole.

"Califbill" fired this volley in news:O- KdnZYm1sXZIDDQnZ2dnUVZ snipped-for-privacy@earthlink.com:

You don't get it. It's a one-dimensional "rope" It has _zero_ thickness, so it will fit in a space of zero dimension wide.

Think two line segments, infinitely close together, and still intersecting at the bottom.

Lloyd

Rich Grise fired this volley in news:iokfs0$n4t $ snipped-for-privacy@dont-email.me:

Yup, and to wrap inverted torii.

LLoyd

75 feet implies a level of precision which generously allows for a reasonable thickness of rope - real world, 3D rope - to achieve the specified results.

Jon

"Jon Danniken" fired this volley in news:iokh5n$u4l$ snipped-for-privacy@speranza.aioe.org:

Where the heck do you figure that? A line segment can be _exactly_ any length you wish it to be, and can be topograpically "folded" to represent two line segments of _exactly_ half the original length... AND the two folded sections can be infinitely close together, and still not violate any geometric rules.

LLoyd

I figured the parabola equation was needed and couldn't figure on how to plot it in the real world to make trough parabolic mirrors years ago. I assumed the hanging chain was a parabola. Thinking back, I wonder if that was the reason that the mirror was off a bit. I tryed to fix it while testing the curve with a plumb bob and sighting down the string, but started exponentially getting further off so I went back to the original.

Things that make ya go hmmm.

SW

"Califbill" fired this volley in news:O- KdnZYm1sXZIDDQnZ2dnUVZ snipped-for-privacy@earthlink.com:

You don't get it. It's a one-dimensional "rope" It has _zero_ thickness, so it will fit in a space of zero dimension wide.

Think two line segments, infinitely close together, and still intersecting at the bottom.

Lloyd

Reply: If it is zero dimension between the poles then the stated question is not answered. Said two (2) (pair) poles.

75 feet implies a level of precision which generously allows for a reasonable thickness of rope - real world, 3D rope - to achieve the specified results.

Jon

Reply: Not me that you quoted.

"Jon Danniken" fired this volley in news:iokh5n$u4l$ snipped-for-privacy@speranza.aioe.org:

Where the heck do you figure that? A line segment can be _exactly_ any length you wish it to be, and can be topograpically "folded" to represent two line segments of _exactly_ half the original length... AND the two folded sections can be infinitely close together, and still not violate any geometric rules.

LLoyd

Reply:

150' of rope is +- 12" 149.5 to 150.4.

"Califbill" fired this volley in news:8NednZbs5LkqbjDQnZ2dnUVZ snipped-for-privacy@earthlink.com:

You aren't dealing with the reality that two "perfect" poles of any dimension you wish to name (length, diameter) can be positioned zero distance apart.

You wish to name your own rules for geometry. The basic ones apply, nonetheless.

LLoyd

"Califbill" fired this volley in news:huWdneC_A9-5aTDQnZ2dnUVZ snipped-for-privacy@earthlink.com:

So, you're assuming that the author of the puzzle stipulated a "tolerance"

Such a tolerance was not called out. In absence of one, 150' means one- hundred-fifty feet -- NOT +- a foot.

Tolerances cut both ways. If you name one, you must use sufficient precision to make sure your specs are met. In the absense of one, all measurements are _exact_.

LLoyd

Correct, although in practice a length of rope 150 feet long is usually understood to be a little on the long side. Additionally, given that a length of rope 150 feet long is going to stretch a bit when hanging by its own weight, the poles need not be touching.

Jon

So did I and now they want me to work the Easter holiday and this is our slow time.

Wes

-- "Additionally as a security officer, I carry a gun to protect government officials but my life isn't worth protecting at home in their eyes." Dick Anthony Heller

"Califbill" fired this volley in news:huWdneC_A9-5aTDQnZ2dnUVZ snipped-for-privacy@earthlink.com:

So, you're assuming that the author of the puzzle stipulated a "tolerance"

Such a tolerance was not called out. In absence of one, 150' means one- hundred-fifty feet -- NOT +- a foot.

Tolerances cut both ways. If you name one, you must use sufficient precision to make sure your specs are met. In the absense of one, all measurements are _exact_.

LLoyd

Reply: Implied by the lack of a decimal point. Go look up 'precision' in math.

"Jon Danniken" fired this volley in news:iokvqm$665$ snipped-for-privacy@speranza.aioe.org:

Again, not a valid assumption. The puzzle did not include any "real world" conditions. It specified a lenght of 150', which, unless you are given tolerances or allowances for conditions, must be assumed to be 150'.

LLoyd

"Califbill" fired this volley in news:QI- dneIw_-bhiDPQnZ2dnUVZ snipped-for-privacy@earthlink.com:

Then I must suggest that you are lacking any "puzzle solving skills".

Puzzles are meant to be solved with the conditions specified. This isn't a bidding contest between suppliers of nylon line (no, NOT "rope").

People who cannot either expand their view to handle "real world" situations nor constrain theirs to handle unique situations are called "veebleforks" in some engineering circles. They're the ones who draw pictures of things that cannot be built.

LLoyd