Math question re Pi

Speedwell

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Why is the convention to express Pi in terms of the diameter rather than the radius? Arbitrary? Some good reason?
The only reason I can think of is that the diameter of a circular object is a straight line thus more easily measurable and more likely to be known than the circumference.
 
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OldWiseGuy

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Why is the convention to express Pi in terms of the diameter rather than the radius? Arbitrary? Some good reason?

But seriously, from a practical point of view you generally need to first know the diameter in order to determine the radius.
 
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chevyontheriver

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I hope this isn't going to the controversy over the measurement of the laver in 1Kings. :doh:
What would be the creationist point of view regarding pi?
 
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The only reason I can think of is that the diameter of a circular object is a straight line thus more easily measurable and more likely to be known than the circumference.
I believe that the OP means, "Why diameter and not radius?"

I don't have a definitive answer, but I would guess that diameter was more important to builders, and was brought into analytical geometry a later time.

(Notice that radians are based on radius rather than diameter.)
 
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Lazarus Short

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bekkilyn

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My thought is that the formula uses in terms of diameter instead of radius because it is a less complex formula that eliminates the possibility of error. For example, if pi is the ratio of the circumference to the diameter, c/d, you could substitute numbers for c and d and get the same result.

However, if you instead used the ratio of the circumference to twice the radius and used c/2r, then you may risk not always getting the same result as someone could introduce an error by using (c/2)r instead of c/(2r).

The ratio of c/d is always clear.

(There may also be something in Archimedes proof that makes diameter a better choice than ratio, but I haven't studied it.)
 
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Knee V

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Convention has us express things in the simplest terms possible. We could say that Pi = C/2r, but since 2r = d, it is simpler to say that Pi = C/d. Similarly, we could say that A = Pi * (d/2)^2, but it is simpler to say that A = Pi * r^2.

In short, we express things as simply as possible. In some contexts that means we use r, and in some contexts we use d; whichever is simpler.
 
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durangodawood

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My thought is that the formula uses in terms of diameter instead of radius because it is a less complex formula that eliminates the possibility of error. For example, if pi is the ratio of the circumference to the diameter, c/d, you could substitute numbers for c and d and get the same result.

However, if you instead used the ratio of the circumference to twice the radius and used c/2r, then you may risk not always getting the same result as someone could introduce an error by using (c/2)r instead of c/(2r).

The ratio of c/d is always clear.

(There may also be something in Archimedes proof that makes diameter a better choice than ratio, but I haven't studied it.)
Forget the 2 factor. Pi would be c/r =6.28ish.
 
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