A rectangle ABCD is circumscribed around a
rhombus AECF. The long sides of the rectangle coincide with two sides of the rhombus. Also, the rhombus and the rectangle share a common diagonal AC.
B E A
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C F D
What are the smallest dimensions when all the lengths AB, BC, AE, AC and EF are integers?
Find a parameterization of all such integral rectangle/rhombus pairs.
(In reply to
Computer aided. by brianjn)
In looking at Charlie's data I did feel a little unnerved at first until I realised how we had approached the problem.
My values "a" + "c" = AB, or more precisely "a"+"d", but "c" = "d" anyway.
What might be noted when looking down my "a" column under "Partial Result Listing" is that the multiple of 7 suddenly goes awry, but that is not to be unexpected when one has a multiplicity of creating Pythagorean triangles. Naturally that suggests that there are other solutions for which a Pythagorean triple is lowest valued base for a set of related figures.

Posted by brianjn
on 20080415 01:22:10 