caa a22 4500 388092467 CHVBK 20180307125255.0 cr unu---uuuuu 161130e199904 xx s 000 0 eng 10.1017/S0004972700032883 doi S0004972700032883 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700032883 Heron quadrilaterals with sides in arithmetic or geometric progression [Elektronische Daten] We study triangles and cyclic quadrilaterals which have rational area and whose sides form geometric or arithmetic progressions. A complete characterisation is given for the infinite family of triangles with sides in arithmetic progression. We show that there are no triangles with sides in geometric progression. We also show that apart from the square there are no cyclic quadrilaterals whose sides form either a geometric or an arithmetic progression. The solution of both quadrilateral cases involves searching for rational points on certain elliptic curves. Copyright © Australian Mathematical Society 1999 Buchholz R.H. Department of Defence, Locked Bag 5076, Kingston ACT 2605 Australia e-mail: ralph@defcen.gov.au MacDougall J.A. Department of Mathematics, University of Newcastle, Callaghan NSW 2308 e-mail: mmjam@cc.newcastle.edu.au Bulletin of the Australian Mathematical Society Cambridge University Press 59/2(1999-04), 263-269 0004-9727 59:2<263 1999 59 BAZ https://doi.org/10.1017/S0004972700032883 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700032883 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Buchholz R.H. Department of Defence, Locked Bag 5076, Kingston ACT 2605 Australia e-mail: ralph@defcen.gov.au NATIONALLICENCE 700 1- MacDougall J.A. Department of Mathematics, University of Newcastle, Callaghan NSW 2308 e-mail: mmjam@cc.newcastle.edu.au NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 59/2(1999-04), 263-269 0004-9727 59:2<263 1999 59 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge