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#1 2010-07-30 15:07:56

bossk171
Member
Registered: 2007-07-16
Posts: 301

catenary

A catenary is the curve:

If you roll a parabola along the x-axis, the focus of the rolling parabola traces out a catenary. I read this a number of places, but I've yet been able to find, or create, a proof.

Can anyone help? Please?

Last edited by bossk171 (2010-07-30 15:08:18)


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#2 2010-07-30 16:16:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: catenary


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2010-07-30 17:39:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: catenary

Hi;

http://translate.google.com/translate?h … 26prmd%3Db

This page here gives the differential equation for the all the conic sections, yours is on the bottom. The differential equation can used to derive the curve as the focus of the parabola rides on the x axis, it will be found to be a catenary. This derivation is a proof.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#4 2011-07-26 17:39:17

namealreadychosen
Member
Registered: 2011-07-23
Posts: 16

Re: catenary

Is the shape of the streamlines formed by a swimming duck a catenary? Is the shape of a supposedly shatterproof (I have broken them) ruler being bent, each end pressed onto my fingertips, a catenary? I know that the shape of a chain held at both ends is a catenary.

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#5 2011-07-26 21:36:52

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,883

Re: catenary


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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