What will a sphere look like if it's unwrapped?
I actually google alot, but all results are related to 3D design apps like blender bla bla bla, No direct answers or even something to help. I tried to imagine it like some triangles arranged and all their top vertices are coincident, Any illustrations for that? If you can't understand, I meant like if we unwrap a cone, it will be a circular sector, what about the sphere?
geometry 3d spheres
asked Dec 5 '18 at 12:28
Ahmed I. ElsayedAhmed I. Elsayed
1134
add a comment |
I actually google alot, but all results are related to 3D design apps like blender bla bla bla, No direct answers or even something to help. I tried to imagine it like some triangles arranged and all their top vertices are coincident, Any illustrations for that? If you can't understand, I meant like if we unwrap a cone, it will be a circular sector, what about the sphere?
geometry 3d spheres
asked Dec 5 '18 at 12:28
Ahmed I. ElsayedAhmed I. Elsayed
1134
1
Google "map projections" (which is specifically about unwrapping the Earth, but applies equally well to any sphere). This problem has been thought about for centuries, and no one has found a canonical, "good" answer.
– Arthur
Dec 5 '18 at 12:30
There is no way to unwrap a sphere perfectly. As stated in the comment above, if you’re familiar with projections, you’d know that ALL projections of the Earth involve some form of distortion, either in shape or size. The reason should be clear.
– KM101
Dec 5 '18 at 13:08
add a comment |
I actually google alot, but all results are related to 3D design apps like blender bla bla bla, No direct answers or even something to help. I tried to imagine it like some triangles arranged and all their top vertices are coincident, Any illustrations for that? If you can't understand, I meant like if we unwrap a cone, it will be a circular sector, what about the sphere?
geometry 3d spheres
asked Dec 5 '18 at 12:28
Ahmed I. ElsayedAhmed I. Elsayed
1134
I actually google alot, but all results are related to 3D design apps like blender bla bla bla, No direct answers or even something to help. I tried to imagine it like some triangles arranged and all their top vertices are coincident, Any illustrations for that? If you can't understand, I meant like if we unwrap a cone, it will be a circular sector, what about the sphere?
geometry 3d spheres
geometry 3d spheres
asked Dec 5 '18 at 12:28
Ahmed I. ElsayedAhmed I. Elsayed
1134
asked Dec 5 '18 at 12:28
Ahmed I. ElsayedAhmed I. Elsayed
1134
asked Dec 5 '18 at 12:28
Ahmed I. ElsayedAhmed I. Elsayed
1134
asked Dec 5 '18 at 12:28
Ahmed I. ElsayedAhmed I. Elsayed
1134
asked Dec 5 '18 at 12:28
Ahmed I. ElsayedAhmed I. Elsayed
1134
1134
1
Google "map projections" (which is specifically about unwrapping the Earth, but applies equally well to any sphere). This problem has been thought about for centuries, and no one has found a canonical, "good" answer.
– Arthur
Dec 5 '18 at 12:30
There is no way to unwrap a sphere perfectly. As stated in the comment above, if you’re familiar with projections, you’d know that ALL projections of the Earth involve some form of distortion, either in shape or size. The reason should be clear.
– KM101
Dec 5 '18 at 13:08
add a comment |
1
Google "map projections" (which is specifically about unwrapping the Earth, but applies equally well to any sphere). This problem has been thought about for centuries, and no one has found a canonical, "good" answer.
– Arthur
Dec 5 '18 at 12:30
There is no way to unwrap a sphere perfectly. As stated in the comment above, if you’re familiar with projections, you’d know that ALL projections of the Earth involve some form of distortion, either in shape or size. The reason should be clear.
– KM101
Dec 5 '18 at 13:08
1
1
Google "map projections" (which is specifically about unwrapping the Earth, but applies equally well to any sphere). This problem has been thought about for centuries, and no one has found a canonical, "good" answer.
– Arthur
Dec 5 '18 at 12:30
Google "map projections" (which is specifically about unwrapping the Earth, but applies equally well to any sphere). This problem has been thought about for centuries, and no one has found a canonical, "good" answer.
– Arthur
Dec 5 '18 at 12:30
There is no way to unwrap a sphere perfectly. As stated in the comment above, if you’re familiar with projections, you’d know that ALL projections of the Earth involve some form of distortion, either in shape or size. The reason should be clear.
– KM101
Dec 5 '18 at 13:08
There is no way to unwrap a sphere perfectly. As stated in the comment above, if you’re familiar with projections, you’d know that ALL projections of the Earth involve some form of distortion, either in shape or size. The reason should be clear.
– KM101
Dec 5 '18 at 13:08
add a comment |
1 Answer
1
active
oldest
votes
There is no way by which a sphere can be "unwrapped" in the same sense as a cylinder or a cone can be unwrapped. The reason is that a sphere has intrinsic curvature - essentially, the geometry on a sphere is too different from the geometry on a plane. Angles of a triangle on a sphere do not add up to 180°, on a cone or a cylinder they do.
answered Dec 5 '18 at 12:37
WouterWouter
5,91721436
add a comment |
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%2f3027014%2fwhat-will-a-sphere-look-like-if-its-unwrapped%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
There is no way by which a sphere can be "unwrapped" in the same sense as a cylinder or a cone can be unwrapped. The reason is that a sphere has intrinsic curvature - essentially, the geometry on a sphere is too different from the geometry on a plane. Angles of a triangle on a sphere do not add up to 180°, on a cone or a cylinder they do.
answered Dec 5 '18 at 12:37
WouterWouter
5,91721436
add a comment |
There is no way by which a sphere can be "unwrapped" in the same sense as a cylinder or a cone can be unwrapped. The reason is that a sphere has intrinsic curvature - essentially, the geometry on a sphere is too different from the geometry on a plane. Angles of a triangle on a sphere do not add up to 180°, on a cone or a cylinder they do.
answered Dec 5 '18 at 12:37
WouterWouter
5,91721436
add a comment |
There is no way by which a sphere can be "unwrapped" in the same sense as a cylinder or a cone can be unwrapped. The reason is that a sphere has intrinsic curvature - essentially, the geometry on a sphere is too different from the geometry on a plane. Angles of a triangle on a sphere do not add up to 180°, on a cone or a cylinder they do.
answered Dec 5 '18 at 12:37
WouterWouter
5,91721436
There is no way by which a sphere can be "unwrapped" in the same sense as a cylinder or a cone can be unwrapped. The reason is that a sphere has intrinsic curvature - essentially, the geometry on a sphere is too different from the geometry on a plane. Angles of a triangle on a sphere do not add up to 180°, on a cone or a cylinder they do.
answered Dec 5 '18 at 12:37
WouterWouter
5,91721436
answered Dec 5 '18 at 12:37
WouterWouter
5,91721436
answered Dec 5 '18 at 12:37
WouterWouter
5,91721436
answered Dec 5 '18 at 12:37
WouterWouter
5,91721436
5,91721436
add a comment |
add a comment |
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3027014%2fwhat-will-a-sphere-look-like-if-its-unwrapped%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
1
Google "map projections" (which is specifically about unwrapping the Earth, but applies equally well to any sphere). This problem has been thought about for centuries, and no one has found a canonical, "good" answer.
– Arthur
Dec 5 '18 at 12:30
There is no way to unwrap a sphere perfectly. As stated in the comment above, if you’re familiar with projections, you’d know that ALL projections of the Earth involve some form of distortion, either in shape or size. The reason should be clear.
– KM101
Dec 5 '18 at 13:08