- #36
archaic
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Like this?fresh_42 said:Yes and no. Yes, as this is part of the question, and no, since this procedure has to be done with any second point. We have a fixed single point ##P## and a set ##\mathbb{S}^2##. Then we consider all lines ##\overline{PQ}## from ##P## to ##Q## to another point ##Q## on the sphere. This line has a center ##M_Q##. The problem asks for ##\{\,M_Q\in \overline{PQ}\,|\,Q\in \mathbb{S}^2\,\}\,.##
Supposing that ##P=(x,y,z)##, the set of all midpoints between ##P## and ##Q## by varying ##Q## would be ##\{(\frac{x+x_Q}{2},\frac{y+y_Q}{2},\frac{z+z_Q}{2})|(x_Q,y_Q,z_Q)\in\mathbb{S}^2\}##.