## Poll

5 votes (26.31%) | |||

2 votes (10.52%) | |||

1 vote (5.26%) | |||

3 votes (15.78%) | |||

7 votes (36.84%) | |||

4 votes (21.05%) | |||

2 votes (10.52%) | |||

5 votes (26.31%) | |||

2 votes (10.52%) | |||

4 votes (21.05%) |

**19 members have voted**

I used to assign questions like this when I taught diff-eq, In my opinion, it's a bit advanced and not intrinsically interesting. Maybe that's the issue more than stumping folks. The one before this involved Riemann surfaces for the log function. Maybe you're missing your college days ...Quote:WizardI'm proud to say I have stumped the forum, apparently, except for Don, who may jump in in 3.5 hours.

I think source material from elementary number theory, geometry and recreational mathematics is more in the spirit of such questions.

For the line which is the rope, x=0 being the center...

y = a cosh (x/a)

y = 50

a = 10

So x = 22.924 which is the x coordinate of the right pole. The total distance between would be double that or 45,85.

That could also be approximated by:

Ln (50 / 10 * 2) * 10 * 2 = 46.05

Quote:teliotI think source material from elementary number theory, geometry and recreational mathematics is more in the spirit of such questions.

Sometimes I take pleasure in a problem that helps me dust off some long-forgotten skills.

Anyway, if you care to suggest the next problem, I'm sure the forum would be up to the challenge.

For a catenary, I think:

y = cosh (x/a)-a = 40

and the arc length is = sinh (x/a) which must equal 50 meters, half of the rope length.

so:

cosh(x/a) = (40/a)-a

sinh(x/a) = 50/a

Using Wizard's hint that cosh^2 (x/a) -sinh^2 (x/a) = 1

I get ((40+a)^2 )/a^2 - (50/a)^2=1

So a^2 = a^2 +40a+1600-2500

900= 40a

thus,

a=22.5

Thus sinh(x/22.5) = 50/22.5

so the half-distance between the poles, x = 22.5* arcsinh(50/22.5)

And the distance between the poles =2x= 45*arcsinh(50/22.5) which is approximately 69.2468 meters

Quote:gordonm888I just saw this a little while ago and I have struggled with this. Not sure this is the right answer.

It isn't what I get. Let's say there was a short pole 10 meters high directly between the poles. If the rope went from the left pole, directly to the top of the center pole and up to the right, wouldn't it's length be 2*((69.2468/2)^2 + 40^2)^0.5 = 105.9642 meters. We're given it is only 100 meters, so I don't think the poles could be that far apart.

You know, I enjoy reading old math books as well. Over the last few days I re-read "Elementary Number Theory" by Burton. My goal was was to remember the easy way to prove the "Four Square Theorem" using the Quaternions, but it didn't come back. Sigh ...Quote:WizardAnyway, if you care to suggest the next problem, I'm sure the forum would be up to the challenge.

This is actually a very easy read ...

http://www.mathcs.duq.edu/~haensch/411Materials/Quaternions.pdf

Quote:teliotYou know, I enjoy reading old math books as well. Over the last few days I re-read "Elementary Number Theory" by Burton. My goal was was to remember the easy way to prove the "Four Square Theorem" using the Quaternions, but it didn't come back. Sigh ...

This is actually a very easy read ...

http://www.mathcs.duq.edu/~haensch/411Materials/Quaternions.pdf

I think I regret I asked. That is beyond my level. Pass the dunce cap, I'll be sitting in the corner.

p.s. Are Quaternions those things programmers use for moving graphics? I hope Ahigh sees this.

No dunce cap for you!Quote:WizardI think I regret I asked. That is beyond my level. Pass the dunce cap, I'll be sitting in the corner.

p.s. Are Quaternions those things programmers use for moving graphics? I hope Ahigh sees this.

You know the Quaternions, i, j, k and such ... Diana said she used the Quaternions in one of the slots she programmed -- she was very proud of it. I never saw her actual implementation, but you know she had some tricks.

A long time ago I sent you a book, The Incredible Dr. Matrix. Maybe try and find that and re-read a bit of it? I would say it was one of the best math books ever. There are some wonderful tidbits in there that might inspire some questions.

Quote:WizardA 100 meter rope is suspended from the top of two 50-meter poles. The lowest point of the rope is 10 meters from the ground. How far apart are the poles?...

I tried to solve the problem with math, but eventually had to give up and learn the math from YouTube. It was fun, though--thanks for the problem!