"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."

Cheers,

Michael Kuettner