Rade said:There are an infinite number of radii within any given circle, are there also an infinite number of circles within a circle as shown in the attached image ?
Rade said:There are an infinite number of radii within any given circle, are there also an infinite number of circles within a circle as shown in the attached image ?
I can see the attachment fine--are you still having problem ?radou said:Given a radius R, there is an infinite number of 0 < r < R, so the answer is yes. I can't see the attachment though, but there is no way to display that. Non-formally speaking, you could be talking about a shaded disk of radius R, I guess.![]()
berkeman said:Seems like an analogous question to "Are there an infinite number of discrete points between 0 and 1 on the number line?" Is there something special about the circle aspect of this question?
Rade said:I can see the attachment fine--are you still having problem ?
No it is not.berkeman said:BTW, is this a homework problem
Neither of these constraints apply--see the figure in post #1--perimeter has width, not a shaded disk.Gib Z said:There are an infinite number of circles if the perimeter has "no" width and the distances between the radii are zero. ie A Shaded Disk.
Rade said:Neither of these constraints apply--see the figure in post #1--perimeter has width, not a shaded disk.
Rade said:Neither of these constraints apply--see the figure in post #1--perimeter has width, not a shaded disk.
OK, but there would be an infinite number if the perimeter of added circles "has no width"--in the same way that there are an infinite number of radii (without width) in a circle--correct ?CRGreathouse said:I'm not entirely sure what you're saying, but if each of the 'circles' is actually an object with nonzero area (say, the set of all points within 0.001 units of a circle) then only finitely many can fit into the (large) circle without overlapping, since the area of a circle is finite.
Rade said:OK, but there would be an infinite number if the perimeter of added circles "has no width"--in the same way that there are an infinite number of radii (without width) in a circle--correct ?
A disk of some radius R≥0 can be thought of as {(x,y) : 0≤x2+y2≤R2}Rade said:OK, but there would be an infinite number if the perimeter of added circles "has no width"--in the same way that there are an infinite number of radii (without width) in a circle--correct ?