"James Silverton" schrieb :
> Michael wrote on Sun, 1 Jun 2008 17:01:45 +0200:
>
>
>> "James Silverton" schrieb :
>>> Michael wrote on Sun, 1 Jun 2008 15:46:26 +0200:
>>>
>>>> "James Silverton" schrieb :
>>>>> Michael wrote on Sat, 31 May 2008 17:24:16 +0200:
>>>>>
>>>>>> "James Silverton" schrieb :
>>>>>>> Michael wrote on Sat, 31 May 2008 15:50:44 +0200:
>>>>>>>
>>>>>>>> "Wayne Boatwright" schrieb :
>>>>>>>>> On Fri 30 May 2008 10:44:12p, sf told us...
>>>>>>>>>
>>>>>>>>>> On Fri, 30 May 2008 19:46:27 -0700, Leonard Blaisdell
>>>>>>>>>> > wrote:
>>>>>>>>>>
>>>>>>>>>>> Three dots make an ellipsis. No more. No less.
>>>>>>>>>>>
>>>>>>>>>>> leo
>>>>>>>>>>
>>>>>>>>>> Show off! All this time I thought three dots made a
>>>>>>>>>> triangle.
>>>>>>>>>>
>>>>>>>>> Only if you connect them! :-)
>>>>>>>>>
>>>>>>>> y = kx + d
>>>>>>>> Lot's of dots and no triangle ...
>>>>>>>
>>>>>>> Just for the hell of it! You can draw a circle thro' any
>>>>>>> three points (some might want to say non-collinear).
>>>>>>>
>>>>>> Nope. You can draw a circle through any _two_ points.
>>>>>> I didn't use the the formula for a line without reason ...
>>>>>
>>>>> Sorry Michael; strange it as it may seem, you will have to go back to your
>>>>> High School Geometry texts.
>>>>>
>>>> No, not really. You seem to confuse something here.
>>>> You can draw a circle through any two points so that the 3rd
>>>> point is inside the circle.
>>>> Let k = 0 and d = 0 in the formula above.
>>>> Let x = 0,1,2. That gives us the points 0/0, 1/1, 2/2.
>>>> Now try do draw a circle through these 3 points ...
>>>
>>> OK MIchael!
>>>
>>> You have three points, A, B and C.
>
>> A = (0/0). B = (1/1). C = (2/2).
>
>>> 1. Draw lines connecting AB and BC
>>> 2. Construct the line bisecting AB; all points on that line
>>> are equidistant from A and B. 3. Do the same thing for BC. 4.
>>> If the two bisecting lines intersect at D, D is equidistant
>>> from A, B and C. 5.Thus a circle centered on D can be drawn
>>> through A, B and C.
>>>
>> Nope. Not if A, B and C are on a line, as I've shown you.
>> Try it.
>
>>> I don't know if Euclid proved it this way but I can still
>>> remember it from 60 years ago!
>>>
>> I've given you a concrete example where your method doesn't
>> work.
>> That's why I objected to "You can draw a circle through every three points."
>
> I said,
> "Just for the hell of it! You can draw a circle thro' any
> three points (some might want to say non-collinear)"
>
Which you said _after_ I pointed out that connecting three points
don't always form a triangle (y = kx +d).
You can't draw a circle through any three points because it doesn't
work with collinear points.

>
> Your example is three collinear points and the radius of the circle is
> infinite!
>
Yes and no. Only if you allow the lines to converge in infinity ;-)


Cheers,

Michael Kuettner