Riddle me this, circumference of a circle

[Brad Johnson]

Calling all resident math genii... why is the formyuler for calculating circumference of a circle 2πR and not simply Dπ? Apologies, the pi symbol doesn't seem to be representing well.

Why is the formula made overly complex by half? Diameter times pi gives the same answer with half the calculations and is relatively easy to mentally generalize on the fly. Why the unnecessary step? Why not pare it down to the simplest possible formula? I thought one of math's goals was making sense of the world by distilling things down, eliminating the fluff.

I've always wondered why. Had a reminder this morning so figured I'd ask you bozos.

(Yes, I could likely find out by Googling it, but I'm feeling extra lazy this morning.)

Brad

[dogmush]

It IS πD.   Or rather π is defined as the ratio of a circle's circumference to it's diameter.

Back in the day I was told that it's commonly written 2πR because the REST of the normal formulas (πR², 4πr², (4/3)πr³, etc.) for circles and spheres are radius based and math books though to  would be easier to remember everything in terms of R.  No idea if true or an old wives math teacher's tale, but that's what they told me.

[zxcvbob]

I'm pretty sure dogmush got it right.

The area of a circle is πr².  The circumference 2πr is the first derivative of the formula for the area.  (and to take it a little farther, the volume of a sphere is 4/3πr³, the first derivative of that is the area of its circle and the second derivative is the circumference.)

That's assuming I still remember the difference between a derivative and an integral 

[MechAg94]

And maybe students have a talent for getting units and dimensions mixed up so using radius for everything might cut down on errors.  I imagine in spreadsheets and programming referencing one variable instead of two is easier.

I first learned it as Pi*D. 

[Tuco]

Why?
I'll tell you "Why"
The formula is wrote up that way because it's easier to measure a circle's diameter than it is to measure it's radius.
That's why.
Damn pinheads..

[Hawkmoon]

It IS πD.   Or rather π is defined as the ratio of a circle's circumference to it's diameter.

Back in the day I was told that it's commonly written 2πR because the REST of the normal formulas (πR², 4πr², (4/3)πr³, etc.) for circles and spheres are radius based and math books though to  would be easier to remember everything in terms of R.  No idea if true or an old wives math teacher's tale, but that's what they told me.

I guess I was born and edumacated before "the day," because until this thread I never heard of the formula for circumference being anything other than πD.

[230RN]

And even on Rigel 4, where they have eight fingers on each upper appendage, radians (from "radius") would be universally understood rather than degrees or grads or artillery degrees.

Why?
I'll tell you "Why"
The formula is wrote up that way because it's easier to measure a circle's diameter than it is to measure it's radius.
That's why.
Damn pinheads..

I differ.  It's easier to find the exact center of a circle by erecting perpendiculars from the tangents at any two random (not opposing) points on the circumference.  The intersection of those perpendicular lines is the exact geometrically accurate center of the circle.

From that point back to the circumference will be the exact geometrically accurate radius.

This is axiomatic, that is, no "proof" is necessary.

This, as opposed to screwing around trying to find the greatest distance between two points on the circumference, which would still only be an estimate, however "accurate" it might be.

As opposed, also, to measuring the circumference and then dividing by 2 times  3.14159265358979323846264338327950288419716939937510
  58209749445923078164062862089986280348253421170679
  82148086513282306647093844609550582231725359408128
  48111745028410270193852110555964462294895493038196
  44288109756659334461284756482337867831652712019091
  45648566923460348610454326648213393607260249141273
  72458700660631558817488152092096282925409171536436
  78925903600113305305488204665213841469519415116094
  33057270365759591953092186117381932611793105118548
  07446237996274956735188575272489122793818301194912
  98336733624406566430860213949463952247371907021798
  60943702770539217176293176752384674818467669405132
  00056812714526356082778577134275778960917363717872
  14684409012249534301465495853710507922796892589235
  42019956112129021960864034418159813629774771309960
  51870721134999999837297804995105973173281609631859
  50244594553469083026425223082533446850352619311881
  71010003137838752886587533208381420617177669147303
  59825349042875546873115956286388235378759375195778
  18577805321712268066130019278766111959092164201989, which itself, is only an estimate since I read it off my slide rule.



Terry, 230RN

[dogmush]

I guess I was born and edumacated before "the day," because until this thread I never heard of the formula for circumference being anything other than πD.

I thought you were born and educated before Euclidean Geometry? 

[Hawkmoon]

I thought you were born and educated before Euclidean Geometry? 

I was born and edumacated before dirt.

[230RN]

I was born and edumacated before dirt.

Lucky you.  That was before the edumication system got loaded with bullshit artists, do-gooders, communist propagandists, and people who use rising inflections on every declarative clause --in the Valley Girl manner.

Terry, 230RN

[Perd Hapley]

I don't remember being taught 2πr.

When I think of it, it's always πD.
The EB seems to agree.

https://www.britannica.com/science/pi-mathematics

Pi, in mathematics, the ratio of the circumference of a circle to its diameter.

[Nick1911]

This, as opposed to screwing around trying to find the greatest distance between two points on the circumference, which would still only be an estimate, however "accurate" it might be.

I suppose that depends on what one is doing.  I find diameters easier...

[zahc]

If you want to complain about something, you shouldn't complain about using R instead of D, because R is a better. R is basically better and more fundamental than D in general. Rather, the problem is with Pi itself being defined in terms of D, the worse of the two metrics. This results in Pi being half the size that it should be, so the majority of places that Pi shows up, which are usually formulated in terms of radius, it always shows up with a factor of 2. So the dimension that you always seem to be dealing with is not Pi, but 2Pi. 2pi is so common there should be a single symbol for it (actually that should have been pi instead of pi being pi).

[230RN]

A circle is a line formed by a point radiating from (moving a certain constant distance from another fixed point.

That is, the radius defines a circle.

The fact that as an engineering and practical matter the diameter is more often used than the radius does not change that definition.  The fact that it is easier to find and use the diameter on solid objects does not change that definition.... although my tri-squares (try-squares) all came with a center finder.

     

It's that doohickey on the right.

I'm going to draw a circle of 3" in diameter.

I don't set my drawing compass to 3 inches.

I set it to 1.5 inches.  The radius.

So there. Nyah-nyah-nyah!

[Hawkmoon]

If you want to complain about something, you shouldn't complain about using R instead of D, because R is a better. R is basically better and more fundamental than D in general. Rather, the problem is with Pi itself being defined in terms of D, the worse of the two metrics. This results in Pi being half the size that it should be, so the majority of places that Pi shows up, which are usually formulated in terms of radius, it always shows up with a factor of 2. So the dimension that you always seem to be dealing with is not Pi, but 2Pi. 2pi is so common there should be a single symbol for it (actually that should have been pi instead of pi being pi).

But this does not result in Pi being multiplied by a factor of 2. For circumference, Pi is Pi and D Oor 2R) is to the first power. For the area of a circle, Pi is still to the first power (no factor applied to Pi) butR is squared -- not multiplied by a factor of anything, but raised to the second power.