Why is the eccentricity of a catenary equal to sqrt(2)?
$begingroup$
I understand that eccentricity defines how circular a conic section is... but a catenary isn't a conic section - so why is its eccentricity equal to that of a rectangular hyperbola: $sqrt 2$ ? How does it have an eccentricity in the first place?
Are there other figures that aren't conics that still has an eccentricity?
algebraic-geometry conic-sections
asked Jan 23 at 5:39
Maxim WinterMaxim Winter
1
$endgroup$
add a comment |
$begingroup$
I understand that eccentricity defines how circular a conic section is... but a catenary isn't a conic section - so why is its eccentricity equal to that of a rectangular hyperbola: $sqrt 2$ ? How does it have an eccentricity in the first place?
Are there other figures that aren't conics that still has an eccentricity?
algebraic-geometry conic-sections
asked Jan 23 at 5:39
Maxim WinterMaxim Winter
1
$endgroup$
$begingroup$
Where did you read about this eccentricity?
$endgroup$
– Aretino
Jan 23 at 16:28
$begingroup$
I read about this eccentricity here: fxsolver.com/browse/formulas/Catenary+curve
$endgroup$
– Maxim Winter
Jan 24 at 6:02
add a comment |
$begingroup$
I understand that eccentricity defines how circular a conic section is... but a catenary isn't a conic section - so why is its eccentricity equal to that of a rectangular hyperbola: $sqrt 2$ ? How does it have an eccentricity in the first place?
Are there other figures that aren't conics that still has an eccentricity?
algebraic-geometry conic-sections
asked Jan 23 at 5:39
Maxim WinterMaxim Winter
1
$endgroup$
I understand that eccentricity defines how circular a conic section is... but a catenary isn't a conic section - so why is its eccentricity equal to that of a rectangular hyperbola: $sqrt 2$ ? How does it have an eccentricity in the first place?
Are there other figures that aren't conics that still has an eccentricity?
algebraic-geometry conic-sections
algebraic-geometry conic-sections
asked Jan 23 at 5:39
Maxim WinterMaxim Winter
1
asked Jan 23 at 5:39
Maxim WinterMaxim Winter
1
asked Jan 23 at 5:39
Maxim WinterMaxim Winter
1
asked Jan 23 at 5:39
Maxim WinterMaxim Winter
1
asked Jan 23 at 5:39
Maxim WinterMaxim Winter
1
1
$begingroup$
Where did you read about this eccentricity?
$endgroup$
– Aretino
Jan 23 at 16:28
$begingroup$
I read about this eccentricity here: fxsolver.com/browse/formulas/Catenary+curve
$endgroup$
– Maxim Winter
Jan 24 at 6:02
add a comment |
$begingroup$
Where did you read about this eccentricity?
$endgroup$
– Aretino
Jan 23 at 16:28
$begingroup$
I read about this eccentricity here: fxsolver.com/browse/formulas/Catenary+curve
$endgroup$
– Maxim Winter
Jan 24 at 6:02
$begingroup$
Where did you read about this eccentricity?
$endgroup$
– Aretino
Jan 23 at 16:28
$begingroup$
Where did you read about this eccentricity?
$endgroup$
– Aretino
Jan 23 at 16:28
$begingroup$
I read about this eccentricity here: fxsolver.com/browse/formulas/Catenary+curve
$endgroup$
– Maxim Winter
Jan 24 at 6:02
$begingroup$
I read about this eccentricity here: fxsolver.com/browse/formulas/Catenary+curve
$endgroup$
– Maxim Winter
Jan 24 at 6:02
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3084126%2fwhy-is-the-eccentricity-of-a-catenary-equal-to-sqrt2%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3084126%2fwhy-is-the-eccentricity-of-a-catenary-equal-to-sqrt2%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Where did you read about this eccentricity?
$endgroup$
– Aretino
Jan 23 at 16:28
$begingroup$
I read about this eccentricity here: fxsolver.com/browse/formulas/Catenary+curve
$endgroup$
– Maxim Winter
Jan 24 at 6:02