
05694773
j
2010b.00476
Persson, Ulf
Triangles with given inscribed and circumscribed circles. (Trianglar med givna omskrivna och inskrivna cirklar.)
Normat. 57, No. 3, 129140 (2009).
2009
Nationellt Centrum f\"or Matematikutbildning (NCM), G\"oteborgs Universitet, G\"oteborg
SV
G90
G50
G70
Poncelet's theorem
elliptic curves
geometric group structures
Zbl 1188.51007
ME 2009f.00485
Summary: This is a second article [for a review of the first one see ibid. 57, No. 1, 1021 (2009; Zbl 1188.51007; ME 2009f.00485)] in a series of three, concerning 1dimensional families of triangles. In this case those with given circumscribed and inscribed radii $R,r$ are presented. The construction of such families is a special case of Poncelet's theorem, exploiting the approach via elliptic curves, initiated by Jacobi.