Are my postulates true regarding circles?

In summary, the conversation discusses the relationship between the exact radius and circumference of a circle. It is stated that if one is known, the other cannot be known exactly. This concept has been known since ancient times and it is not possible for a circle to have both a rational circumference and radius.
  • #1
student34
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If we know the exact radius of a circle, then we can't have an exact circumference, and if we know the exact circumference, then we can't know the exact radius.

If these postulates are true, then I realize that this idea is not original but probably known since B.C.
 
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  • #2
Exact isn't the right word to use. If I have a circle with diameter 1, I know that the circumference is exactly ##\pi##, I just can't represent ##\pi## by a finite decimal sequence.

However you are right in your idea, a circle cannot simultaneously have a rational circumference and a rational radius.
 

1. Are circles always perfectly round?

Circles are defined as a shape with a continuous and even curvature, so they are generally considered to be perfectly round. However, in reality, there may be slight variations in the roundness of a circle due to imperfections in its construction or measurement.

2. Can a circle have a radius of zero?

No, a circle cannot have a radius of zero. A radius is defined as the distance from the center of a circle to its edge, so if the radius were zero, the circle would essentially be a single point.

3. Are all points on the circumference of a circle equidistant from the center?

Yes, by definition, all points on the circumference of a circle are equidistant from the center. This is what makes a circle a unique and distinct shape.

4. Do circles have infinite sides?

No, circles do not have sides. Unlike polygons, which have a finite number of sides, a circle is a continuous curve with no distinct edges or sides.

5. Can a circle have a negative radius?

No, a circle cannot have a negative radius. A radius is a measure of distance and therefore cannot be negative. However, a circle can have a negative curvature, which would result in an inverted or "inside-out" circle.

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