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)"


Your example is three collinear points and the radius of the
circle is infinite!

--
Best wishes!

James Silverton
Potomac, Maryland

E-mail, with obvious alterations:
not.jim.silverton.at.verizon.not