Results 1 -
6 of
6
Möbius transformations and ellipses
- The Pi Mu Epsilon Journal
, 2007
"... This expository article considers non-circular ellipses in the Riemann
sphere, and the action of the group of Mobius transformations. In
particular, we find which Mobius transformations are symmetries of an
ellipse, and which take one ellipse to another. We also survey some
of the ``special plane ..."
Abstract
-
Cited by 2 (2 self)
- Add to MetaCart
This expository article considers non-circular ellipses in the Riemann
sphere, and the action of the group of Mobius transformations. In
particular, we find which Mobius transformations are symmetries of an
ellipse, and which take one ellipse to another. We also survey some
of the ``special plane curves'' which appear as inversive images of
the ellipse.
Ellipses in the inversive plane
"... This expository article considers non-circular ellipses in the Riemann
sphere, and the action of the group of Mobius transformations. In
particular, we find which Mobius transformations are symmetries of an
ellipse, and which take one ellipse to another. We also survey some
of the ``special plane ..."
Abstract
- Add to MetaCart
This expository article considers non-circular ellipses in the Riemann
sphere, and the action of the group of Mobius transformations. In
particular, we find which Mobius transformations are symmetries of an
ellipse, and which take one ellipse to another. We also survey some
of the ``special plane curves'' which appear as inversive images of
the ellipse.
ARISTOTELIAN REALISM
"... Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as rat ..."
Abstract
- Add to MetaCart
Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity,
Indirect proofs and proofs from assumptions
"... In his valuable book on mathematics and its philosophy in the ..."
