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The Fourth Dimension

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Sam Ballard

on 1 April 2011

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Transcript of The Fourth Dimension

The Fourth Dimension What is the fourth dimension? the fourth dimension is all space that one can get to by travelling perpendicular to three dimensional space the fourth dimension is indestinguishable from the other three; it's just another axis for points, lines, shapes, etc. to follow as far as this presentation goes, the fourth dimension does not refer to time, as has been theorized possible by physicists this is the spatial fourth dimension, unlike time, this can be understood and measured in a Euclidean fashion, the fourth dimension of time requires far more complex math studied by Einstein and his ilk... First, a little history... the idea that there were more than three dimensions was first studied by mathemeticians in the 19th century not a bunch of artists in Emeryville in 1827, August Ferdinand Mobius first realized that a three dimensional shape, rotated in four dimensions, would create its mirror image he was ecstatic from here, you have Ludwig Schläfli and his discovery of many higer dimensional polytopes a polytope is a geometric object with flat sides, which exists in any general number of dimensions his findings were not published until after his death so, less ecstatic by Sam Ballard and German p Bernard Riemann gave higher dimensions a firm footing in 1854 with his book Über die Hypothesen welche der Geometrie zu Grunde liegen in which he considered a "point" to be any sequence of coordinates (x1, ..., xn) the possibility of geometry in higher dimensions was established Geometry of the Fourth Dimension in order to understand the shapes of the fourth dimension, we must consider the shapes of previous dimensions first, the point the point has no length, width, or depth
it's zero dimensional next, we have an object from the first dimension, the line a line has length, but no depth or width now it's time for the second dimension the square it has width and length but no depth the third dimension it provides depth is all around us like in the cube length width depth length length and finally... the fourth dimension it provides a fourth measurement, w
(length, width, and depth being x,y,z) in a three dimensional plane, the divisions made by x,y,z provide 6 cardianl directions up, down, east, west, north, and south the extra dimension adds two more cardinal directions: ana and kata Greek for Up Toward Greek for down from our best representation for one of the four dimensional objects is this it's known as a tesseract this is not what it actually looks like, only our best way to understand it the tesseract is actually composed of eight equal cubes

it may not look like it from the diagram (what is known as a Schlegel Diagram)

we live in a three-dimensional world, therefore it is virtually impossible to accurately depict a four dimensional object we can try, though Four Dimensionality is merely a theoretical idea... or for all we know, we could be a three dimensional world hanging on the wall of a four dimensional house but that's a topic best left for philosophers questions? the tesseract is actually part of a group of six four dimensional objects known as the regular convex polychora these are analagous to the platonic shapes in the three dimensional world they include the following:
the pentachoron, made of 5 tetrahedra

the tesseract, made of 8 cubes

the hexadecachoron, made of 16 tetrahedra

the icositetrachoron, made of 24 octahedra

the hecatonicosachoron, made of 120 dodecahedra

the hexacosichoron, made of 600 tetrahedra
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