¶ Fourth Dimension: Regular Tetrahedron as Fourth Dimension Model (1)
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Index Entry
Since the outset of humanity’s preoccupation exclusively with the XYZ coordinate system mathematicians have been accustomed to figuring the altitude of a triangle as a product of the base times one-third of its perpendicular altitude. And the volume of tetrahedra are arrived at by multiplying one-quarter of the height of the perpendicular to the base times the area of the base. But the tetrahedron has four uniquely symmetrical enclosing planes and its dimensions may be arrived at by the use of perpendicular heights above its four possible bases. That’s what the fourth dimension system is: it is produced by the angular and size data arrived at by measuring the four perpendicular distances in respect to the centers of area of the four faces of a tetrahedron. As with the triangle, the perpendicular from the center of the tetrahedron’s base triangle goes right through the tetrahedron’s apex. The central angles converge at 109° 28’.
The area of a triangle is arrived at by multiplying the length of the base line times one-third of the triangle’s apex altitude. This is four dimensionality. A tetrahedron of a"
