Hi,Which of the following steps do you believe needs more proof in order to be satisfactory:
Claim #1: What is the furthest apart that two points on a circular arc can possibly be? Diametrically opposed.
Claim #2: Thus if the distance between two points, d, is greater than the diameter, D, of the circular arc, it is impossible to draw a circular arc that passes through both points.
Claim #3: Therefore we have the requirement that the arc is impossible is
D < d
Claim #4: If R is the radius of the arc, the diameter is D = 2R.
Claim #5: What is the distance between the point <X1,Y2> and <X2,Y2>?
d = sqrt( (X2 - X1)² + (Y2 - Y1)² )
Claim #6: Substituting in we have
D < d
2R < sqrt( (X2 - X1)² + (Y2 - Y1)² )
Claim #7: Squaring both sides we have
(2R)² < sqrt²( (X2 - X1)² + (Y2 - Y1)² )
4·R² < (X2 - X1)² + (Y2 - Y1)²
What specific problem do you have with which specific step?
How, in your mind, does this qualify as just posting the same equation and claiming that doing so is a proof?
The only possible claim that I can imagine you taking issue with is Claim #1. Fine. I asked you to show what YOU would consider an adequate proof of that claim and you've declined to do so. Yet you are saying that it is perfectly reasonable to accept Claim #5 without an substantiation.
Thanks for the reply.
Oh in your previous post you were talking about some vector operations so i thought you could show that work.
I would really like to see this other approach as it differs from mine.
I understand your most recent approach and the explanation is better than before i think.
I'll try to post mine either tonight or tomorrow sometime. I've been busy watching the judge confirmation hearings today so didnt do much else.
For a quick explanation though, the logic is that if we have two points and some radius, no matter what that radius is we have two possible centers which could in the degenerate case be the same but in the more general case are not the same, and because the radius is a maximum constraint that means the the two centers can not be farther apart then 2*R. The result of this approach has been very interesting and with a surprise twist which i will show. The main point i was trying to make though is that this constitutes a verbal description while the mathematical proof would be more towards a set of equations that automatically spit out the result. I'll be sure to post this very soon.