Parabola and catenary

Forum|Forum|4 years ago
May 14, 2021
3 replies
4445 views

There are three random points on the plane through which an arc of a parabola and a similar arc of a catenary pass. What is the probability that the length of the parabola's arc will be greater than the length of the catenary's arc??

1_Catenary-Parabola.zip

Calculus_Derivatives

F

Fred_Kohlhepp

23-Emerald I

Since a catenary describes a condition of minimum potential energy, I would guess that the probability is quite low.

L

LucMeekes

23-Emerald IV

About 20...25 %.

First run over 100 iterations

No, it's more towards 30 %. The next run is over 200 iterations:

And finally over 1000 iterations, but showing only 1 in 5:

Luc

V

ValeryOchkov

Author

24-Ruby IV

Is this a new math constant?

L

LucMeekes

23-Emerald IV

Nah... don't think so.

You would have something if you could prove that a catenary line through 3 points is always x % longer than a Parabola line through the same three points. Since that is not the case....Keep searching.

I've got a puzzle for you: try to find what my select_dhm() function is... (The function I use to provide guess values for the solve block of finding the parameters for the catenary function)

Success!

Luc

V

ValeryOchkov

Author

24-Ruby IV

000100000100010000-0000011010000-00---110000100010000100-011001-0101101-01100000--1101--110101-010-010000101-001-010-0-0001-1-00000--0-10011101000-0-0-00-01010000-0-01-10-0001000-010100-0-00001101011100000110110111--0101-01-101010---000000001000100-000001100111000-10 (Tomorrow I will continue my research)

1 - Sc > Sp

0 - Sc < Sp

- (hiccup) - no solution

* - Sc = Sp (I am waiting for)

It's like a hiccup. You don't know when you will hiccup next time - when next time there will be no solution of the problem of catenaries and parabolas.
By the way, there is a very interesting study of the frequency and strength (- or ---) of hiccups.