Math Is Fun Forum

bossk171

Member

Registered: 2007-07-16

Posts: 305

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: catenary

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!

http://www.answers.com/topic/roulette-game

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: catenary

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
The knowledge of some things as a function of age is a delta function.