id: 05899945
dt: b
an: 2011f.00518
au: Yaglom, I.M.
ti: Geometric transformations IV: circular transformations.
so: Anneli Lax new mathematical library44. Washington, DC: Mathematical
Association of America (MAA) (ISBN 978-0-88385-648-2/pbk). 296~p.
(2009).
py: 2009
pu: Washington, DC: Mathematical Association of America (MAA)
la: EN
cc: G54 G55 G94 G95
ut: transformation geometry; circular transformations; conformal mappings
ci:
li:
ab: Publisherâ€™s description: This book, which concludes a four-part Geometric
Transformations series, can be studied independently of Parts I, II,
and III. It develops the geometry of transformations of the plane that
map circles to circles (conformal or anallagmatic geometry). The notion
of inversion, or reflection in a circle, is the key tool employed. The
plane geometry of secondary school - figures composed of lines and
circles - takes on a new life when it is viewed as the study of
properties that are preserved by special groups of transformations. No
longer is there a single, universal geometry: different sets of
transformations of the plane correspond to intriguing, disparate
geometries. Applications include ruler-and-compass constructions and
the PoincarÃ© model of hyperbolic geometry. The presentation assumes
background only in elementary geometry and trigonometry.
rv: