The Journal of the Indian Mathematical Society

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Semi-Inverse Simplexes


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1 Indian Institute of Technology, Kharagpur, India
     

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a. Let S(P)=P0 ... Pn (P=B,C) be a pair of semi-inverse simplexes for a hypersphere (M) in an n-space such that their corresponding vertices Pi-form pairs of inverse points for (M) and. are therefore collinear with its centre M. Their circum-hyperspheres (P) are inverse of each other w.r.t. (M), or (M) is a hypersphere of antisimilitude and M a centre of similitude of (P). The second hypersphere (M') of antisimilitude of (P), being orthogonal to (M) and coaxal with (P), has its centre M' at their second centre of similitude as the pole of their radical prime m w.r.t. (M) [cf. 4].
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  • Semi-Inverse Simplexes

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Authors

Sahib Ram Mandan
Indian Institute of Technology, Kharagpur, India

Abstract


a. Let S(P)=P0 ... Pn (P=B,C) be a pair of semi-inverse simplexes for a hypersphere (M) in an n-space such that their corresponding vertices Pi-form pairs of inverse points for (M) and. are therefore collinear with its centre M. Their circum-hyperspheres (P) are inverse of each other w.r.t. (M), or (M) is a hypersphere of antisimilitude and M a centre of similitude of (P). The second hypersphere (M') of antisimilitude of (P), being orthogonal to (M) and coaxal with (P), has its centre M' at their second centre of similitude as the pole of their radical prime m w.r.t. (M) [cf. 4].