Pardon my ignorance, but if you can transform the sharp edges of a rectangle into a smooth curve, why do we need rectangles anyway; i.e. wouldn't the same thing happen if we just decided to start with two triangles?
@presbarkeep well you need four dimensions. Let me elaborate; think of a 2D world, completely flat. they can't imagine a third dimension, so to them it would seem impossible to 'flatten' a circle, whereas we can clearly see that it is flat. Well, a four dimensional being would see it as obvious that our sphere is flat to them. just like the circle is flat to us.
@xatnu Wrong. As the fourth dimension is nothing more than the added element of time, there can be no four-dimensional being, however, three-dimensional beings would see the sphere as a sphere, only at a possible shift in location, although not neccesarily a definitive shift, if the sphere remained still, or was not moved.
u can represent half sphere like a pyramid with 4 triangles, and making a square at the bottom from them. This shape has 4 faces, 5 vertices, 8 edges. Euluer formula says F-E+V must be 0, and it is not. Result is 1. There what u see is WRONG, u cannot represent a half sphere on a flat surface if you do u scratch, or collapse points.
@ilterisderici i think u are wrong... actually, there is an homeomophism between R^2 and S^2-{p}, where p is any point of the sphere. moreover, S^2 can be represented by (x,y) coordinates, so S^2-{p} is equals to R^2 locally... and complete sphere cannot be represented by any flat surface... but two flat sufaces work... there is a difference between homeomorphism and homotopy... using homeomorphism, u cannot collapse points, because if u do, u loose the isomorphism... but u can using homotopy.
Pardon my ignorance, but if you can transform the sharp edges of a rectangle into a smooth curve, why do we need rectangles anyway; i.e. wouldn't the same thing happen if we just decided to start with two triangles?
tygerk 7 months ago
@tygerk You are right, the same thing would happen with 2 triangles. We just chose rectangles arbitrarily.
bothmer 7 months ago
uhm,... i dont like this. unless someone can tell me how you flatten a sphere into 3d space without significant stretching or tearing.
presbarkeep 1 year ago
@presbarkeep well you need four dimensions. Let me elaborate; think of a 2D world, completely flat. they can't imagine a third dimension, so to them it would seem impossible to 'flatten' a circle, whereas we can clearly see that it is flat. Well, a four dimensional being would see it as obvious that our sphere is flat to them. just like the circle is flat to us.
xatnu 1 year ago
@xatnu Wrong. As the fourth dimension is nothing more than the added element of time, there can be no four-dimensional being, however, three-dimensional beings would see the sphere as a sphere, only at a possible shift in location, although not neccesarily a definitive shift, if the sphere remained still, or was not moved.
JeffersonDinedAlone 8 months ago
fail. torus is beSSer
generatorium 1 year ago
How did the squares become circles?
kokafones 2 years ago
ok guys, this is not right
u can represent half sphere like a pyramid with 4 triangles, and making a square at the bottom from them. This shape has 4 faces, 5 vertices, 8 edges. Euluer formula says F-E+V must be 0, and it is not. Result is 1. There what u see is WRONG, u cannot represent a half sphere on a flat surface if you do u scratch, or collapse points.
ilterisderici 2 years ago
@ilterisderici i think u are wrong... actually, there is an homeomophism between R^2 and S^2-{p}, where p is any point of the sphere. moreover, S^2 can be represented by (x,y) coordinates, so S^2-{p} is equals to R^2 locally... and complete sphere cannot be represented by any flat surface... but two flat sufaces work... there is a difference between homeomorphism and homotopy... using homeomorphism, u cannot collapse points, because if u do, u loose the isomorphism... but u can using homotopy.
jjsantos81 2 years ago
random
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HumanMedia 4 years ago
Your videos are very nice, I suggest to add some soft music otherwise one thinks are too slow videos. What about "la vita e bella"? thanks
joliteal 4 years ago
We used to have musik to these videos, but removed them due to copy right problems. Sorry.
bothmer 4 years ago
so?
AlgeKalipso 5 years ago
Looks trivial? Compare it to "Gluing a Torus", then you'll get the drift, dear tuber.
leporidus 5 years ago