Place 4 points in a plane so, that the 6 pointtopoint distances will be integers and at least 5 of them will be odd.
The law of cosines helps.
The following triangles have integer sides where the angle in degrees is the angle between the first two sides:
3, 8, 7 (60 degrees)
5, 8, 7 (60 degrees)
3, 5, 7 (120 degrees).
Consider the following layout:
A
B C
D
Where AB is 5; AC is 3; BC is 7; BD is 7; CD is 7; AD is 8.
Angle BAD is 60 degrees
Angle DAC is 60 degrees
Angle BAC is 120 degrees
Triangle BDC is equilateral, all sides being 7
Edited on April 20, 2014, 7:44 pm

Posted by Larry
on 20140420 19:42:36 