chitspa wrote:I think that the easiest way to veiw an angle in 4-D would be to imagine a cone. Then to give the cone a 3-D coordinate system. The angles of the cone can be measured in the x and y directions. ie. the measurement of an angle in 4-D can be expressed as 30x,45y. Although this isn't a perfect cone since it has an oval base it is still an angle in 4-D.
elpenmaster wrote:if you took a regular tetrahedron and put the vertex in the center of it, the angle of one of the sides would be 90 degrees, for a cube it woud be 60 degrees. in a regular polytope, the center angle to one of the lines, or sides, or cells, would be 360 divided by number of sides.
right?
elpenmaster wrote:what are solid angles measured in? how many of them are the in a sphere?
elpenmaster wrote:why is it that in 2-d, the circumference of a circle divided by the diameter equals a very long number (3.14159265358979323846264338327950288419716939927510. . .)
but in 3-d space, the surface area of a sphere divided by the area of a great circle in it is a very simple "4"?
Aale de Winkel wrote:I gather this makes the circle stand out from the line the way it thus, question now rises given a line with length R, the circle relating to this line has length 2?R. When I take some line with length (2?)[sup]2[/sup]R let ends meat, does this object relate in the same way to the circle as the circle relates to the line, especially when we had a circular based number system?
elpenmaster wrote:why is it that in 2-d, the circumference of a circle divided by the diameter equals a very long number (3.14159265358979323846264338327950288419716939927510. . .)
but in 3-d space, the surface area of a sphere divided by the area of a great circle in it is a very simple "4"?
elpenmaster wrote:does that mean that the surface of a glome divided by a great sphere in the glome will be an irrational number?
What is this number?
:?
elpenmaster wrote:why is it that in 2-d, the circumference of a circle divided by the diameter equals a very long number (3.14159265358979323846264338327950288419716939927510. . .)
Aale de Winkel wrote:Note, I haven't the faintest clue how a non-linear number system looks like, Sci-fi freaks (like me) might remember the metamorph on moon-base alpha, she had an elliptical based number system and calculated things faster then the moonbase computer
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