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Sphere Intersections (Posted on 2015-11-11) Difficulty: 3 of 5

  
SPHERE INTERSECTIONS IN En (n≥1)

   K = H(P1,a1) ∩ H(P2,a2) ∩ ... ∩ H(Pn,an)

               where

        ai ≥ ai+1 > 0        for i = 1, 2, ... , n-1.

               and

        P1En  and

        PiH(P1,a1) ∩ H(P2,a2) ∩ ... ∩ H(Pi-1,ai-1)
                                   for i = 2, 3, ... , n.

DEFINITIONS

     • En denotes Euclidean n-space. The set of n-tuples of
             real numbers.

     • If P ∈ En and r is a real number greater than zero, then
                      H(P,r) = { Q ∈ En | δ(P,Q) = r }.
       A "sphere" with center P and radius r.

     • δ(P,Q) denotes the distance between points P and Q in En.

QUESTION

     Is K empty ?
  

No Solution Yet Submitted by Bractals    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: analytical solution | Comment 3 of 4 |
(In reply to analytical solution by Daniel)


But, we are given that a_i greater than or equal a_i+1
for all i greater than or equal to 1 and less than n. 

  Posted by Bractals on 2015-11-11 15:57:31
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