2 with four 3 d hypersections equation 1 implies a

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Unformatted text preview: together with four others that complete the symmetry. To build the Tolerance-Map for the position of the axis of either hole in Fig. 1(a), choose $1, $2, $3, $4, and $5 to be five basis-lines that define the space of the fourdimensional set of lines in the tolerance-zone of Fig. 1(b). These lines are mapped to five corresponding basis-points in a hypothetical Euclidean four-dimensional point space which points are arranged to be the vertices $1, $2, $3, $4, and $5 of a 4-simplex (simplest polyhedron in a 4-D point-space). One of the basis-lines in the tolerance-zone is assigned to a corresponding vertex in the four-dimensional T-Map point space. Our choices for locating the basis-points are shown in Fig. 2. The geometry for the simplex causes every angle at apex $1 to be 90° so that $1 can be regarded as the origin of a 4-D Cartesian frame of reference that is overlain on the T-Map. The four edges of the 4-simplex that are joined at 48 S. Bhide et al. $1 become Cartesian axes corresponding to four of the Plück...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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