Фигуры четвёртого измерения \ Figures of the fourth dimension
- Thread starter macyk
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treugolnik
The Force is Strong With This One
Очень крутое видео, спасибо большое)
Here what he is talking about :
He says that in order to make 4D object we should add one more line of coordinates.(we have 3)
He begin with making a 2D object from 3D one. How it will look like.
In order To see a 4-dimensional object we need 3-dimensional vision. We live in 3-dimensional space, but with our eyes we see a 2-dimensional picture, but we can determine the distance to the object, he says.
Then he shows how 3D object would look like for 2D resident (Cylinder).
A cylinder that passes through 2-dimensional space is seen as a circle, if you put it on its side, it will be a rectangle. Further he leads to the fact that having seen several slices of a 3-dimensional object, the inhabitant of 2-dimensional space will probably be able to guess what this object is and will be able to suggest how it looks like in 3D space approximately.
In the similar way he suggests us to look at a 4-dimensional object. (How 4d object would look like in 3d)
Then he talks about how the object rotates in 2.3.4 dimensional spaces. A 2-dimensional object rotates in the one plane. A 3-dimensional object can be rotated in 3 planes. To rotate a 4-dimensional object we need 6 parameters he say.
And then he shows different 4-dimensional shapes that intersect our 3-dimensional space and suggests what they would look like to us.
He also makes examples of how a particular shape looks in 2D, so that it would be clearer why we would see a 4-dimensional shape in this way.
While editing a video, he came across a strange figurine in wikipedia that resembled a 4-dimensional object. Dürer's polyhedron
en.wikipedia.org
Then he continue with different objects.
He also talks about the animation of the rotation of the Quadratic Hypercube, which can be found is in wikipedia. He is trying to do the same thing, but he has a different picture due to the fact that he shows the object in a slice, only that piece of the figure that passes through our space, but this animation of the rotation of the Four-Dimensional Hypercube is a projection of the whole object.
And then he plays with drawing and rotating objects.
He says that in order to make 4D object we should add one more line of coordinates.(we have 3)
He begin with making a 2D object from 3D one. How it will look like.
In order To see a 4-dimensional object we need 3-dimensional vision. We live in 3-dimensional space, but with our eyes we see a 2-dimensional picture, but we can determine the distance to the object, he says.
Then he shows how 3D object would look like for 2D resident (Cylinder).
A cylinder that passes through 2-dimensional space is seen as a circle, if you put it on its side, it will be a rectangle. Further he leads to the fact that having seen several slices of a 3-dimensional object, the inhabitant of 2-dimensional space will probably be able to guess what this object is and will be able to suggest how it looks like in 3D space approximately.
In the similar way he suggests us to look at a 4-dimensional object. (How 4d object would look like in 3d)
Then he talks about how the object rotates in 2.3.4 dimensional spaces. A 2-dimensional object rotates in the one plane. A 3-dimensional object can be rotated in 3 planes. To rotate a 4-dimensional object we need 6 parameters he say.
And then he shows different 4-dimensional shapes that intersect our 3-dimensional space and suggests what they would look like to us.
He also makes examples of how a particular shape looks in 2D, so that it would be clearer why we would see a 4-dimensional shape in this way.
While editing a video, he came across a strange figurine in wikipedia that resembled a 4-dimensional object. Dürer's polyhedron
Truncated triangular trapezohedron - Wikipedia
Then he continue with different objects.
He also talks about the animation of the rotation of the Quadratic Hypercube, which can be found is in wikipedia. He is trying to do the same thing, but he has a different picture due to the fact that he shows the object in a slice, only that piece of the figure that passes through our space, but this animation of the rotation of the Four-Dimensional Hypercube is a projection of the whole object.
And then he plays with drawing and rotating objects.