000			03344nam a22003855i 4500
001			978-0-387-78131-0
003			DE-He213
005			20251006084418.0
007			cr nn 008mamaa
008			100301s2008 xxu| s |||| 0|eng d
020			_a9780387781310
020			_a99780387781310
024	7		_a10.1007/978-0-387-78131-0 _2doi
100	1		_aBottema, O. _eauthor.
245	1	0	_aTopics in Elementary Geometry _h[electronic resource] / _cby O. Bottema.
264		1	_aNew York, NY : _bSpringer New York, _c2008.
300			_bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aThe Pythagorean Theorem -- Ceva's Theorem -- Perpendicular Bisectors; Concurrence -- The Nine-Point Circle and Euler Line -- The Taylor Circle -- Coordinate Systems with Respect to a Triangle -- The Area of a Triangle as a Function of the Barycentric Coordinates of Its Vertices -- The Distances from a Point to the Vertices of a Triangle -- The Simson Line -- Morley's Triangle -- Inequalities in a Triangle -- The Mixed Area of Two Parallel Polygons -- The Isoperimetric Inequality -- Poncelet Polygons -- A Closure Problem for Triangles -- A Class of Special Triangles -- Two Unusual Conditions for a Triangle -- A Counterpart for the Euler Line -- Menelaus's Theorem; Cross-Ratios and Reciprocation -- The Theorems of Desargues, Pappus, and Pascal -- Inversion -- The Theorems of Ptolemy and Casey -- Pedal Triangles; Brocard Points -- Isogonal Conjugation; the Symmedian Point -- Isotomic Conjugation -- Triangles with Two Equal Angle Bisectors -- The Inscribed Triangle with the Smallest Perimeter; the Fermat Point.
520			_aThis small book has for a long time been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, Poncelet's polygons, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained in this classical field over the past years. There are 27 independent chapters on a wide range of topics in elementary plane Euclidean geometry, at a level just beyond what is usually taught in a good high school or college geometry course. The selection of topics is intelligent, varied, and stimulating. In a small space the author provides many thought-provoking ideas. This book will fit in well with the increasing interest for geometry in research and education. This book was originally published in Dutch, and this will be the first English translation. This translation also includes a new foreword by Robin Hartshorne. "This highly entertaining book will broaden the reader's historical perspective in an enlightening manner and it provides attractive topics for classroom discussion." -Hendrik Lenstra, Universiteit Leiden
650		0	_aMATHEMATICS.
650		0	_aGEOMETRY.
650	1	4	_aMATHEMATICS.
650	2	4	_aGEOMETRY.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387781303
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-78131-0 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59043 _d59043