All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Four points on a Plane (Posted on 2004-11-21)
How many ways can four points be arranged in a plane so that the six distances between pairs of points take on only two different values?

 See The Solution Submitted by Erik O. Rating: 4.1429 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): And three more | Comment 8 of 15 |

The "point on the near side" would not form an equilateral triangle with the two nearest points.  The whole is more a kite shape than a rhombus.  Consider the fourth point, after the three that make up the equilateral triangle, to be on a circle centered on one of those three points, and on the extended median or altitude from that point.  It's distance from the nearer two points is less than the side of one of the equilateral triangles.  For the rhombus, the different distance would be that to the far point on the triangle.
 Posted by Charlie on 2004-11-22 00:02:49

 Search: Search body:
Forums (0)