Gutenmacher / Vasilyev Lines and Curves

A Practical Geometry Handbook
Erscheinungsjahr 2013
ISBN: 978-1-4757-3809-4
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 156 Seiten, eBook

Originally written in Russian and used in the Gelfand Correspondence School, "Lines and Curves" has since become a classic: the exposition maintains mathematical rigor while balancing creative storytelling and unusual examples of geometric properties. One of the key strengths of the text is its reinterpretation of geometry in the context of motion, whereby curves are realized as trajectories of moving points instead of as stationary configurations in the plane. This novel approach, rooted in physics and kinematics, yields surprisingly intuitive and straightforward proofs of many otherwise difficult results. This newly revised and expanded edition includes more than 200 theoretical and practical problems in which formal geometry provides simple and elegant insight, including problems of maxima and minima and the construction of sets satisfying specific geometric constraints.  Hence Lines and Curves is well positioned for companion use with software packages like The Geometer’s Sketchpad ® , and it can serve as a guidebook for engineers.  Its deeper, interdisciplinary treatment is ideal for more theoretical readers, and the development from first principles makes the book accessible to undergraduates, advanced high school students, teachers, and puzzle enthusiasts alike.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Gutenmacher, Victor

Vasilyev, N. B.

Weitere Mitwirkende

Kundu, A.

Inhaltsverzeichnis

1 Sets of Points.- 2 The Alphabet.- 3 Logical Combinations.- 4 Maximum and Minimum.- 5 Level Curves.- 6 Quadratic Curves.- 7 Rotations and Trajectories.- 8 Drawings, Animation, and the Magic Triangle.- Answers, Hints, Solutions.- A Summary of Results from Analytic Geometry.- B Some Facts from School Geometry.- B.1 Proportional segments.- B.2 Distances, perpendiculars.- B.3 The circle.- B.4 Triangles.- C A Dozen Assignments.- C.1 Name the “letters”.- C.2 Transformations and constructions.- C.3 Rotating straight lines.- C.4 Straight lines and linear relations.- C.5 The tangency principle (conditional extremum).- C.6 Partitions.- C.7 Ellipses, hyperbolas, and parabolas.- C.8 Envelopes, infinite unions.- C.9 Tangents to cycloids.- C.1O Equations of curves.- C.11 Geometrical practical work.- C.12 Small investigations.- About Victor Gutenmacher.- About N. B. Vasilyev.