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Forget the 2 factor. Pi would be c/r =6.28ish.
???Pi x r/squared is the formula for the area of a circle.
Pi x D is the formula for the circumference of a circle.
Two entirely different measurements.
Because D is precisely equal to 2r. The conversion could not be more simple.And how would you mathematically prove that Pi is really the ratio of the circumference to the radius instead of the ratio of the circumference to the diameter?....
In terms of r Pi =6.28... is exactly as simple as Pi =3.14... in terms of D. The complexity either way is identical.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.
Because D is precisely equal to 2r. The conversion could not be more simple.
In terms of r Pi =6.28... is exactly as simple as Pi =3.14... in terms of D. The complexity either way is identical.
I see what you're saying now.In terms of r Pi =6.28... is exactly as simple as Pi =3.14... in terms of D. The complexity either way is identical.
Not entirely different, since D = 2r.
It would be, if you knew where A = pi x r^2 came from.For instance the circumference of a barrel isn't necessary to calculate it's volume.
That is where A = pi x r^2 came from. It riffs on circumference. (Knowing that, we just commit it to memory.)Why make it more complicated than it needs to be?
Why is the convention to express Pi in terms of the diameter rather than the radius? Arbitrary? Some good reason?
I meant the measurements have different purposes. For instance the circumference of a barrel isn't necessary to calculate it's volume.
How can you calculate the volume of a barrel without using the circumference?
OB
Pi comes from c/d.Volume = height x Pi x r squared.
No circumference (Pi x D) needed.
Pi comes from c/d.
Without pi, volume = height x (circumference/diameter) x (radius, squared)
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