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+--- Thread: Fun Math Problem 'Cussed Ladders' (/thread-9088.html)
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RE: Fun Math Problem 'Cussed Ladders' - Gerson W. Barbosa - 09-21-2017 01:25 AM
(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)
RE: Fun Math Problem 'Cussed Ladders' - SlideRule - 09-21-2017 01:55 AM
(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
RE: Fun Math Problem 'Cussed Ladders' - Gerson W. Barbosa - 09-21-2017 02:18 AM
(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+%5Bl%5E2%3Dh%5E2%2B%281%2B1%2F%28h-1%29%29%5E2%5D%2Cfor+h
Gerson.
RE: Fun Math Problem 'Cussed Ladders' - pier4r - 09-23-2017 08:33 AM
(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!
RE: Fun Math Problem 'Cussed Ladders' - Gamo - 09-23-2017 09:12 AM
Thank You to pier4r
You explanation is very clear
Gamo
RE: Fun Math Problem 'Cussed Ladders' - SlideRule - 09-26-2017 12:46 AM
(09-26-2017 12:36 AM)Mike (Stgt) Wrote:(09-21-2017 01:55 AM)SlideRule Wrote: A solution is presented at Shortest Ladder ProblemOne 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