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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.
Don't know, that is why I ask. Consider that 0 and 1 that serve as limits in your example are similar limits in that they are both integers, but in the circle example it is not clear to me that both limits are similar.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 ?
The formula for finding the number of circles within a circle is n = r², where n represents the number of circles that can fit within the larger circle and r represents the radius of the circles.
The radius of the smaller circles is equal to half the radius of the larger circle. This means that the diameter of the smaller circles will be equal to the radius of the larger circle.
If the radius of the smaller circles is not given, the number of circles within a circle can still be calculated by using the formula n = r² and substituting the diameter of the smaller circles for the radius.
No, there is no limit to the number of circles that can fit within a circle. As the radius of the smaller circles decreases, the number of circles that can fit within the larger circle increases.
Knowing the number of circles within a circle can be useful in various fields such as mathematics, engineering, and design. It can help in calculating the distribution of objects within a given space, designing patterns, and understanding geometric relationships.