Plane Intersecting a Sphere

Aristarchan

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Feb 13, 2020
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I was thinking this morning of X,Y and Z axes, visualizing a plane intersecting a sphere at varying depths from it's surface. Would the movement of that plane in a direction perpendicular to it's two dimensions, so that a circle indicating where the sphere intersects with the plane changes diameter but stays centered on the same point in that plane, be always referred to as movement along a Z axis?
 

lev888

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Jan 16, 2018
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Not sure I understand the question. How exactly is the coordinate system defined? In any case, a plane moving in the direction of its normal will intersect any sphere in the way you describe.
 

pka

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Jan 29, 2005
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I was thinking this morning of X,Y and Z axes, visualizing a plane intersecting a sphere at varying depths from it's surface. Would the movement of that plane in a direction perpendicular to it's two dimensions, so that a circle indicating where the sphere intersects with the plane changes diameter but stays centered on the same point in that plane, be always referred to as movement along a Z axis?
Consider the sphere \(x^2+y^2+z^2=25\) see here.
Now the points \(P_1: (5,0,0),~P_2,~(0,5,0)~\&~P_3,~(0,0,5)\) are on that sphere.
Thus the plane determined by those points is \(x+y+z=5\) SEE HERE
Now we have a model for your question. Please re-frame your question.
 

LCKurtz

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May 3, 2019
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I had a little time to kill, so here's an animation showing a plane passing through a sphere, intersecting in various size of circles:
sphereanimation.gif
Not sure what the OP's question is, but the plane can cut the sphere at any angle.
 
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