09-21-2017, 12:20 AM
Post: #21
 Mike (Stgt) Member Posts: 198 Joined: Jan 2014
If you like problems with ladders, here is another one.

Ciao.....Mike
09-21-2017, 01:25 AM
Post: #22
 Gerson W. Barbosa Senior Member Posts: 883 Joined: Dec 2013
RE: Fun Math Problem 'Cussed Ladders'
(09-21-2017 12:20 AM)Mike (Stgt) Wrote:  If you like problems with ladders, here is another one.

Ciao.....Mike

h = '1/2*(√26+√(25-2*√26-2))+1/2' = 4.83850116068 m (to be checked)
09-21-2017, 01:55 AM (This post was last modified: 09-23-2017 12:32 PM by SlideRule.)
Post: #23
 SlideRule Senior Member Posts: 308 Joined: Dec 2013
RE: Fun Math Problem 'Cussed Ladders'
(09-21-2017 12:20 AM)Mike (Stgt) Wrote:  If you like problems with ladders, here is another one.

"The 'ladder and box' problem is relatively new;
it first appeared in A. Cyril Pearson’s 1907 20th Century Standard Puzzle Book
(London). But its' mathematical underpinnings have been traced back to Nicomedes
(~200 BCE), as well as to Newton (1720) and Thomas Simpson (1745).
The problem ... is just one in a group of 'ladder' problems"

A solution is presented at Shortest Ladder Problem

References:
Pearson, A. C., 1907, 20th Century Standard Puzzle Book. London: George Routledge
& Sons, LTD., New York: E.P. DuMon.

Simpson, T., 1745, A treatise of algebra, reproduction from Cambridge University
Library, London: John Nourse, p. 250.

Wells, D., 1992, The Penguin Book of Curious and Interesting Puzzles, Dover,
p. 130-131, problems 399 and 400.

BEST!
SlideRule
09-21-2017, 02:18 AM
Post: #24
 Gerson W. Barbosa Senior Member Posts: 883 Joined: Dec 2013
RE: Fun Math Problem 'Cussed Ladders'
(09-21-2017 01:55 AM)SlideRule Wrote:  A solution is presented at Shortest Ladder Problem

I just submitted an easily obtainable equation to W|A and chose the second result. I would’t solve the quartic equation by hand, even if I knew how to do it.

http://m.wolframalpha.com/input/?i=solve...5D%2Cfor+h

Gerson.
09-21-2017, 10:19 AM
Post: #25
 Mike (Stgt) Member Posts: 198 Joined: Jan 2014
RE: Fun Math Problem 'Cussed Ladders'
(09-21-2017 01:25 AM)Gerson W. Barbosa Wrote:  h = '1/2*(√26+√(25-2*√26-2))+1/2' = 4.83850116068� m (to be checked)

The task was 'Use your calculator to find the maximum height to the nearest .01 meter.' In practice I do not have a dog's chance to check your answer's correctness in "sub-atomic dimensions". My homework is solvable, your request to check your result is not.

Lazy as I am I used an HP17B2 (under Emu42) to solve the equation here almost ready to enter. Well, the numerical value is nice but not enough. So I used the same equation
Code:
SQ(x-1)+SQ(INV(x)+1)-SQ(5)
in CPack200 (under DOSBox) to get a graph to see all possible solutions at once (what gives me now some kind of certitude I picked the correct answer -- rounded to the nearest cm).

Ciao.....Mike
09-23-2017, 08:33 AM
Post: #26
 pier4r Senior Member Posts: 976 Joined: Nov 2014
RE: Fun Math Problem 'Cussed Ladders'
(09-21-2017 01:55 AM)SlideRule Wrote:  "The 'ladder and box' problem is relatively new;
it first appeared in A. Cyril Pearson’s 1907 20th Century Standard Puzzle Book
(London). But its' mathematical underpinnings have been traced back to Nicomedes
(~200 BCE), as well as to Newton (1720) and Thomas Simpson (1745).
The problem ... is just one in a group of 'ladder' problems

A solution is presented at Shortest Ladder Problem

References:
Pearson, A. C., 1907, 20th Century Standard Puzzle Book. London: George Routledge
& Sons, LTD., New York: E.P. DuMon.

Simpson, T., 1745, A treatise of algebra, reproduction from Cambridge University
Library, London: John Nourse, p. 250.

Wells, D., 1992, The Penguin Book of Curious and Interesting Puzzles, Dover,
p. 130-131, problems 399 and 400.

BEST!
SlideRule

Thanks for sharing!

Wikis are great, Contribute :)
09-23-2017, 09:12 AM
Post: #27
 Gamo Member Posts: 117 Joined: Dec 2016
RE: Fun Math Problem 'Cussed Ladders'
Thank You to pier4r

You explanation is very clear

Gamo
09-26-2017, 12:36 AM
Post: #28
 Mike (Stgt) Member Posts: 198 Joined: Jan 2014
RE: Fun Math Problem 'Cussed Ladders'
(09-21-2017 01:55 AM)SlideRule Wrote:  A solution is presented at Shortest Ladder Problem

One question about the a. m. solution solving for the shortes ladder to a given box, C = f(A, B), length of ladder C as function of box width A and height B. With my poor english I do not grasp the last sentence "Now you may check this by making a length C and trying it with your box!" How may I set (making?) C when the solution shown computes C?

Ciao.....Mike
09-26-2017, 12:46 AM
Post: #29
 SlideRule Senior Member Posts: 308 Joined: Dec 2013
RE: Fun Math Problem 'Cussed Ladders'
(09-26-2017 12:36 AM)Mike (Stgt) Wrote:
(09-21-2017 01:55 AM)SlideRule Wrote:  A solution is presented at Shortest Ladder Problem
One question ... How may I set (making?) C when the solution shown computes C?

Consider C as the independent variable and then compute the size of the corresponding box? Since I didn't create the referenced solution, I interpret the quoted extract as just such a 'reverse' engineering' proposal.

BEST!
SlideRule
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