Degree Distasnce

[Rincewind]

Originally Posted by Robust

Yes, that's what I'm saying (using the irrational pi); using the rational pi value of 256/81(earliest known) the distance would be 0.07901234567 ad infinitum. I hold to the latter, yet consider the finite of 3.1640625.

Yes, but 0.07901234567 of what units? Inches? Metres? Miles? Angstroms? Light years?

Without a unit, a distance is meaningless. That's like saying, "Phew, I just walked forty-seven, and I'm pooped!"

[Robust]

Originally Posted by Rincewind

Yes, but 0.07901234567 of what units? Inches? Metres? Miles? Angstroms? Light years?

Without a unit, a distance is meaningless. That's like saying, "Phew, I just walked forty-seven, and I'm pooped!"

I don't understand the question, Rincewind. It would be whatever units you use to describe the diameter.

[Rincewind]

Originally Posted by Robust

I don't understand the question, Rincewind. It would be whatever units you use to describe the diameter.

So if I choose to describe the diameter in metres, then you're saying that the least possible distance between 2 adjacent angular degrees on the circumference is 0.07901234567 m, or 7.901234567 cm -- the equivalent of approximately 3.11 inches. Is that right?

If it is right, then explain why it can't be 5 cm or 1 cm. If it's wrong, then please explain why it's wrong and what you actually mean.

[Robust]

Originally Posted by Rincewind

So if I choose to describe the diameter in metres, then you're saying that the least possible distance between 2 adjacent angular degrees on the circumference is 0.07901234567 m, or 7.901234567 cm -- the equivalent of approximately 3.11 inches. Is that right?

If it is right, then explain why it can't be 5 cm or 1 cm. If it's wrong, then please explain why it's wrong and what you actually mean.

Whatever units you use, Rincewind, it is simply radius/radian or,if you prefer, pi/40, the latter referencing the Base 10 number system.

[Rincewind]

Originally Posted by Robust

Whatever units you use, Rincewind, it is simply radius/radian or,if you prefer, pi/40, the latter referencing the Base 10 number system.

So explain why you think the least distance can't be as small as 5 cm or 1 cm, then. I still don't understand.

[Robust]

Originally Posted by Rincewind

So explain why you think the least distance can't be as small as 5 cm or 1 cm, then. I still don't understand.

Simply because, Rincewind, radius/radian doesn't give those figures There can only be one figure defining the minimal distance between each adjacent angular degree. It is necessary to understand - and I find not emphasized enough in the general curriculum that the radian is the same distance on the arc as the line of the radius subtending it . Thus: radius/radian giving the least distance possible between 2 adjacent angular degrees on the circumference. I personally prefer the formula of pi/40....but that's only perhaps 'cause I'm an advocate of Pythagoras and the Base 10 number system.

"All things number and harmony." - Pythagoras

[C1ay]

Originally Posted by Robust

Simply because, Rincewind, radius/radian doesn't give those figures There can only be one figure defining the minimal distance between each adjacent angular degree. It is necessary to understand - and I find not emphasized enough in the general curriculum that the radian is the same distance on the arc as the line of the radius subtending it . Thus: radius/radian giving the least distance possible between 2 adjacent angular degrees on the circumference. I personally prefer the formula of pi/40....but that's only perhaps 'cause I'm an advocate of Pythagoras and the Base 10 number system.

"All things number and harmony." - Pythagoras

You leave no choice. Your claim is strange and frivolous and without the mathematical proof that's been requested to support it. Thus, this junk math has been moved to the strange claims forum.

[Robust]

Originally Posted by C1ay

You leave no choice. Your claim is strange and frivolous and without the mathematical proof that's been requested to support it. Thus, this junk math has been moved to the strange claims forum.

Clay, You are denying then that the formulae radius/radian and pi/40 give the least possible distance between 2 angular degrees? On what determination? I have given the maths proof quite thoroughly. On the other hand you do not come up with any figures to show otherwise. I'm going to have to appeal this personal and preemptive decision of yours.

[C1ay]

Originally Posted by Robust

Clay, You are denying then that the formulae radius/radian and pi/40 give the least possible distance between 2 angular degrees? On what determination? I have given the maths proof quite thoroughly. On the other hand you do not come up with any figures to show otherwise. I'm going to have to appeal this personal and preemptive decision of yours.

You've given nothing that qualifies as a mathematical proof. FWIW, MathWorld and my Handbook of Mathematics clearly state that the Arc length equals arc radius times the angle in radians, something I have known since high school. Here's plenty more for you to peruse. Appeal all you want.