Slightly OT...four points on a plane. - Printable Version +- HP Forums ( https://archived.hpcalc.org/museumforum)+-- Forum: HP Museum Forums ( https://archived.hpcalc.org/museumforum/forum-1.html)+--- Forum: Old HP Forum Archives ( https://archived.hpcalc.org/museumforum/forum-2.html)+--- Thread: Slightly OT...four points on a plane. ( /thread-129109.html) |

Slightly OT...four points on a plane. - Hal Bitton in Boise - 12-03-2007
Good evening everyone.
2. One point on each vertice of an equilateral triangle, and one point in the center of the triangle.
3. One point on each corner of a rhombus which has one diagonal congruent to it's sides. (can also be thought of as 2 equilateral triangles sharing a common side).
4. An equilateral triangle, with a fourth point centered on an arc drawn between two point of the triangle, the arc center (radius point) being the remaining point of the triangle.
Any other solutions completely elude me. I'll wait (with baited breath) to see what other solutions the brilliant minds that frequent this forum can come up with.
Re: Slightly OT...four points on a plane. - Meenzer - 12-03-2007
Aren't 1 and 4 special cases of 3?
Re: Slightly OT...four points on a plane. - Arnaud Amiel - 12-03-2007
All 4 points on top of each other?
Re: Slightly OT...four points on a plane. - Bram - 12-03-2007
I was thinking of a trapezium, almost immediately. Re: Slightly OT...four points on a plane. - Meenzer - 12-03-2007
Quote: When I construct this - not being sure if I get it right - I allways get a third length: (1) base=sides, (2) other parallel, (3) the distance between points A and C diagonally.
Re: Slightly OT...four points on a plane. - Bram - 12-03-2007
I have a picture to make clear, but unfortunately I cannot post it right now. Re: Slightly OT...four points on a plane. - Dave Shaffer (Arizona) - 12-03-2007
Quote:
Unless you've been eating fishing worms, you are waiting with "bated" breath!
Re: Slightly OT...four points on a plane. - Hal Bitton in Boise - 12-03-2007
Thanks Dave...
Re: Slightly OT...four points on a plane. - Dave Shaffer (Arizona) - 12-03-2007
I think that if you make the interior angle between the long top and either of the (shorter) sides to be 72 degrees, you will find that the sides and the short base are all the same length. If alpha is this top interior angle, then the relationship between side and bottom lengths (x) and the top length (t) is
cos(alpha) = (x/2)/t
Re: Slightly OT...four points on a plane. - Hal Bitton in Boise - 12-03-2007
Thanks for the responses everyone.
Best regards, Hal
Re: Slightly OT...four points on a plane. - BruceH - 12-03-2007
4 points on top of each other fails the "one of 2 possible lengths test": since they are all zero distance away from each other there is only one length involved. Two dots on one point and 2 dots on another would satisfy the problem.
Re: Slightly OT...four points on a plane. - Werner - 12-04-2007
There's a sixth (apart from your 4 and the trapezium): Re: Slightly OT...four points on a plane. - Hal Bitton in Boise - 12-04-2007
Of course...if I would have just taken my circle "full circle". |