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%I #21 Nov 07 2018 03:53:08
%S 1,3,6,8,18,12,1,5,5,7,18,16,1,2,8,9,20,12,1,5,5,9,20,15,1,4,7,8,20,
%T 18,2,5,5,8,20,20,2,5,5,10,22,18,3,5,5,9,22,24,2,4,7,11,24,20,3,5,5,
%U 11,24,21,4,5,5,10,24,28,2,6,7,9,24,30,4,5,5,12,26,24,3,4,8,11,26,30,4,5,7,10,26,36,2,5,10,11,28,36,1,7,8,14,30,28,1,8,9,12,30,42
%N Primitive cyclic quadrilaterals with integer area.
%C Entries are listed as sextuples: (a,b,c,d), Perimeter, Area. They are ordered first by perimeter, second by area, third by a, then b, then c, then d. Rectangles and kites with two right angles are not listed; thus a < b <= c <= d. By "primitive" we mean (a,b,c,d) is not a multiple of any earlier quadruple.
%C We observe that the number of odd integers in any quadruple is always an even number.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclicQuadrilateral.html">Cyclic Quadrilateral</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cyclic_quadrilateral">Cyclic quadrilateral</a>
%e The first row of the table gives sidelengths (a,b,c,d)=(1,3,6,8) with perimeter=18 and area=12. Thus:
%e a b c d Perim Area
%e = = = == ===== ====
%e 1 3 6 8 18 12
%e 1 5 5 7 18 16
%e 1 2 8 9 20 12
%e 1 5 5 9 20 15
%e 1 4 7 8 20 18
%e 2 5 5 8 20 20
%e 2 5 5 10 22 18
%e 3 5 5 9 22 24
%e 2 4 7 11 24 20
%e 3 5 5 11 24 21
%e 4 5 5 10 24 28
%e etc.
%Y Cf. A298907, A297790, A210250, A230136, A131020, A218431, A219225, A233315, A242778, A273691, A273890.
%K nonn,tabf
%O 1,2
%A _Gregory Gerard Wojnar_, Jan 27 2018
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