Can a Circle have an infinite diameter?

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hecd2 said:
Yes, if it has an infinite radius and diameter.
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Which results in the same answer: no.

Because by its very definition, a circle is a CLOSED area, the graph of which defined as a set of points (x,y) on a cartesian plane, centered around coordinates (h,k) at a distance r that satisfy the equation

(x - h)^2 + (y - k)^2 = r^2

If r were of an infinite value, then no values x and y will ever satisfy the equation, so no circle graphing such an equation could ever exist.
 
While all of that is true, as a limit the math does work out: If r is infinite, then the curvature or 1/r is equal to 0, and the circle becomes a straight line.

ICXC NIKA
 
porthos11 said:
Which results in the same answer: no.

Because by its very definition, a circle is a CLOSED area, the graph of which defined as a set of points (x,y) on a cartesian plane, centered around coordinates (h,k) at a distance r that satisfy the equation

(x - h)^2 + (y - k)^2 = r^2

If r were of an infinite value, then no values x and y will ever satisfy the equation, so no circle graphing such an equation could ever exist.
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Does a circle of infinite circumference have a diameter?
I would think so…
And would the diameter be finite?
I would think not.
Which means the diameter must then be infinite.

Which contradicts your conclusion.
Where is the flaw?
 
Blue_Horizon said:
Does a circle of infinite circumference have a diameter?
I would think so…
And would the diameter be finite?
I would think not.
Which means the diameter must then be infinite.

Which contradicts your conclusion.
Where is the flaw?
Click to expand...
If the circumference is infinite, there can be no curvature at all, else it would close.

Again, the result is a straight line.
 
IWantGod said:
Can a Circle have an infinite diameter?
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Defining or identifying something as a circle requires that thing to be of finite dimensions.

An infinite thing cannot exist in reality.

In an imaginary world, you can have an infinite sized anything you want.
 
reggieM said:
Defining or identifying something as a circle requires that thing to be of finite dimensions.

An infinite thing cannot exist in reality.

In an imaginary world, you can have an infinite sized anything you want.
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Pretty much what I thought.
 
Blue_Horizon said:
I am not sure that is coercive logic.
How would you prove that?
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Curvature is the inverse of the radius. The smaller the radius the larger the curvature. The inverse of an infinite radius is zero curvature. A zero radius would give infinite curvature.

rossum
 
Blue_Horizon said:
Does a circle of infinite circumference have a diameter?
I would think so…
And would the diameter be finite?
I would think not.
Which means the diameter must then be infinite.

Which contradicts your conclusion.
Where is the flaw?
Click to expand...
There is no such thing as an infinite circumference. It cannot satisfy the equation of a circle.

A circumference is by its nature, closed, as a triangle, by definition, is a closed, three-sided polygon.
 
rossum said:
Curvature is the inverse of the radius. The smaller the radius the larger the curvature. The inverse of an infinite radius is zero curvature. A zero radius would give infinite curvature.

rossum
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By that reasoning the slope of the horizontal component of an infinitely long 1/x curve would be 0. But it never does, thats the very definitional logic of an asymptote. It never turns into a perfectly straight line though it tends to.

The very definition of a circle is that the bigger the diameter the smaller the slope (curvature) of the circumference at any given point. I really cannot see the difference in logic bewteen the two examples.

What I believe we have is in fact a word game that is ultimately internally contradictory and does not symbolise anything that can exist in reality. Like irresistable forces meeting immovable objects.

Essentially its asking the question whether two infinite values can exist in a ratio of PI to each other. Its a flawed question. Just as an asymptote meeting its limit by definition cannot exist…so too an infinite circle cannot exist…for the definition of the word infinite essentially contradicts the definition of the word circle.

So the answer it seems is not no based on some sort of inductive or deductive reasoning.
It is no because the question itself is nonsensical.

I think there is a subtle difference between these two approaches to solving the question.

If we think of the word infinite in a dynamic, ever getting bigger sense a fixed ratio bewtween two infinitely inflating values may be more logical.
An expanding shockwave from a point explosion. If we compare the ratio of the force field strength at any two fixed points at different distances from the point the vales will be getting increasingly bigger at a fixed cubic ratio.
 
The explosion would have to be infinitely powerful of course.
 
hecd2 said:
Yes, if it has an infinite radius and diameter.
Click to expand...
A circle by definition is finite. As soon as you have an infinite diameter you lose that which makes it a circle in the first place. The center of a circle always has to be a finite distance away from its circumference…
 
porthos11 said:
Which results in the same answer: no.

Because by its very definition, a circle is a CLOSED area, the graph of which defined as a set of points (x,y) on a cartesian plane, centered around coordinates (h,k) at a distance r that satisfy the equation

(x - h)^2 + (y - k)^2 = r^2

If r were of an infinite value, then no values x and y will ever satisfy the equation, so no circle graphing such an equation could ever exist.
Click to expand...
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