Are my postulates true regarding circles?

AI Thread Summary
Knowing the exact radius of a circle prevents the determination of an exact circumference, and vice versa. The concept that exact values cannot be represented in finite decimal sequences is acknowledged, particularly with the example of a circle with a diameter of 1, where the circumference equals π. The discussion highlights that a circle cannot have both a rational circumference and a rational radius simultaneously. This understanding aligns with established mathematical principles dating back to ancient times. The postulates emphasize the limitations of precision in geometric measurements.
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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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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.
 

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