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A348143 Areas of integer-sided cyclic quadrilaterals whose area equals their perimeter. 0
16, 18, 20, 30 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There are no further terms. Note that without the condition "integer-sided" there are other solutions, such as (1, 17/2, 17/2, 16) which has perimeter and area 34.
LINKS
Ralph H. Buchholz and James A. MacDougall, Cyclic Polygons with Rational Sides and Area, 2001.
EXAMPLE
The areas or perimeters 16, 18, 20, 30 pertain respectively to cyclic quadrilaterals with sides (4, 4, 4, 4), (3, 3, 6, 6), (2, 5, 5, 8), (5, 5, 6, 14).
MATHEMATICA
lst={}; Do[s=(a+b+c+d)/2; If[s>a, (K=Sqrt[(s-a)(s-b)(s-c)(s-d)]; If[IntegerQ[K]&&K==2s, AppendTo[lst, Sort@{a, b, c, d}]])], {a, 1, 15}, {b, 1, a}, {c, 1, b}, {d, 1, c}]; lst
CROSSREFS
Cf. A098030, A290451. First four terms of A161874.
Sequence in context: A273543 A274127 A328736 * A161874 A095953 A084800
KEYWORD
fini,full,nonn
AUTHOR
Frank M Jackson, Oct 02 2021
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)