Re: Challenge: Triangles puzzle

From: Raymond Martineau (bk039_at_freenet.carleton.ca)
Date: 10/17/04 

Date: Sat, 16 Oct 2004 21:47:02 -0400

On Sat, 16 Oct 2004 23:29:52 +0200, "Yogo" <n o s p a m> wrote:

>> Sorry, but i do not agree with your solution.
>> You missed many triangles.
>>
>> E.g., P0 -> P8 -> P5 -> P0 is a triangle of zero area.
>> but it is not counted in th solution of 27.
>
>hmm...
>
>What are you talking about?
>
>A triangle with an area equal to zero doesn't exist.

Not as far as a computer is concerned. Without any form of sanity
checking, the most intuitive (read: quickest for the programmer to
implement) definition of a triangle for a computer is a set of three
points.

The puzzle in question only considers triangles to be formed from a given
set of points, as well requiring a known line connecting between those
points. Although the puzzle didn't define triangle, the webpage now
includes an update that requires these traingle to have an area.

>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...

Using the "three angles" definition, the line given is valid. There are
three angles in the shape:

P5 -> P0 -> P8 : 0 degree angle
P0 -> P5 -> P8 : 180 degree angle
P0 -> P8 -> P5 : 0 degree angle.

0 degrees is still an angle, as is 180. These angles are generally
significant as they indicate parallel lines, but can be valid in figures.

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