|
%I #16 Nov 07 2018 03:53:46
%S 1,3,6,8,1,5,5,7,1,2,8,9,1,5,5,9,1,4,7,8,2,5,5,8,2,5,5,10,3,5,5,9,2,4,
%T 7,11,3,5,5,11,4,5,5,10,2,6,7,9,4,5,5,12,3,4,8,11,4,5,7,10,2,5,10,11,
%U 1,7,8,14,1,8,9,12,3,7,9,11,1,6,10,15,2,7,9,14,1,7,11,13,6,7,8,11,1,10,10,13,2,9,11,12,3,6,13,14,3,8,10,15
%N Primitive cyclic quadrilaterals with integer area.
%C Entries are listed as quadruples: (a,b,c,d). They are ordered first by perimeter, second by area, then 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 It appears that the number of odd sidelengths in any quadruple is always 0, 2, or 4.
%e We list here the early quadruplets, in parentheses, augmented by the associated perimeter and area to justify the ordering of the quadruplets:
%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 (2, 6, 7, 9) 24 30
%e etc.
%Y Cf. A298860, A297790, A210250, A230136, A131020, A218431, A219225, A233315, A242778, A273691, A273890.
%K nonn,tabf
%O 1,2
%A _Gregory Gerard Wojnar_, Jan 28 2018
|
