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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,743

Hi bossk171;

I read that too and it is cited in at least 4 spots:

http://www.centralillinoiswoodturners.c … 20Form.pdf

http://www.pballew.net/arithme8.html#catenary

http://www.npr.org/templates/story/stor … Id=6434007

http://www-groups.dcs.st-and.ac.uk/~his … enary.html

I have been unable to find that proof.

According to this page,

http://webcache.googleusercontent.com/s … =firefox-a

Maxwell is the discoverer of the proof you are looking for!

Check this out!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,743

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

hi bosk171

would this help?:http://www.proofwiki.org/wiki/Catenary#Proof

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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