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 Sphere Intersections (Posted on 2015-11-11)

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: My thinking on it. Comment 4 of 4 |
(In reply to My thinking on it. by Charlie)

P_1 is defined as being a member of E^n not equal to E^n.
Likewise, for the following - member of not equal to.

 Posted by Bractals on 2015-11-11 16:05:27

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