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Exploring Classical Greek Construction Problems with Interactive Geometry Software

Ad Meskens, Paul Tytgat (Autoren)

Buch | Softcover

XII, 185 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-42862-8 (ISBN)

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In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves.
By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers.

1 Introduction.- 2 The Genesis of Geometry.- 3 Straightedge and compass constructions.- 4 The Delian Problem.- 5 Trisecting an angle.- 6 Squaring the circle.- 7 Constructible numbers.- 8 The Cinderella of regular polygons.- Afterthoughts.- Solutions.- Index.

"This book provides historical sketches to accompany the problems. This places the activity in context, and will motivate some students to look more closely at the culture and history of mathematics. I thoroughly enjoyed the opportunity to review this book, and recommend it to anyone interested in this area of mathematics. ... The book is clearly written while remaining brief and is excellently illustrated. The exercises are interesting and in my view well-judged for undergraduate students." (Chris Sangwin, International Journal of Research in Undergraduate Mathematics Education, Vol. 4, 2018)

“This book provides historical sketches to accompany the problems. This places the activity in context, and will motivate some students to look more closely at the culture and history of mathematics. I thoroughly enjoyed the opportunity to review this book, and recommend it to anyone interested in this area of mathematics. … The book is clearly written while remaining brief and is excellently illustrated. The exercises are interesting and in my view well-judged for undergraduate students.” (Chris Sangwin, International Journal of Research in Undergraduate Mathematics Education, Vol. 4, 2018)

Erscheinungsdatum	25.02.2017
Reihe/Serie	Compact Textbooks in Mathematics
Zusatzinfo	XII, 185 p. 160 illus., 10 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
	Sozialwissenschaften ► Pädagogik
Schlagworte	circle quadrature • Delian problem • doubling the cube • duplication of the cube • enquiry based learning • Euclid • GeoGebra • Geometry • heptagon • History of mathematical sciences • interactive geometry • mathematics and statistics • mathematics education • neusis • ruler and compass • straightedge and compass • trisection
ISBN-10	3-319-42862-4 / 3319428624
ISBN-13	978-3-319-42862-8 / 9783319428628
Zustand	Neuware