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Mikael Brockman wrote:

> Jim Newton <> writes:
>
>> > hmm...
>> > What are you talking about?
>> > A triangle with an area equal to zero doesn't exist. A triangle has
>> > three angles and none of them may be equal to zero, otherwise you
>> > just don't have a triangle.
>> > What you describe with P0 -> P8 -> P5 -> P0 is a segment of a line
>> > not a triangle...
>> >
>>
>> no, you are wrong. an angle may have zero degrees, or less than zero
>> degrees or more than zero degrees.
>>
>> the sum of the angles in a triangle is 180 degrees. and a 0, 0, 180
>> triangle is still a triangle.
>
> You're wrong. The triangle inequality states that the sum of two
> triangles sides exceeds the other side.

Actually, it is "equals or exceeds". A three-sided polygon with sides 3, 4
and 7 is a degenerate triangle, but it is a triangle.

http://www.fact-index.com/t/tr/triangle_inequality.html

"In mathematics, the triangle inequality is a statement which states roughly
that the distance from A to B to C is never shorter than going directly
from A to C. "

Note that it says "never shorter than ...". Not "always longer than ...".

> Zero is not a side in any
> triangle.

True, but not the present issue. The problem appears to be the case of
angles of 0,0,180 and nonzero sides a + b = c.

--
Paul Lutus
http://www.arachnoid.com