Advanced Geometric Constructions PDF Download
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Author: Alfred S. Posamentier
Publisher: Dale Seymour Publication
ISBN: 9780866514293
Category : Geometrical constructions
Languages : en
Pages : 102
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Book Description
19 basic straightedge and compass constructions and construction solutions to algebraic equations. Also explores triangle, circle, and non-compass constructions. Many proofs, exercises and problems.
Author: Alfred S. Posamentier
Publisher: Dale Seymour Publication
ISBN: 9780866514293
Category : Geometrical constructions
Languages : en
Pages : 102
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Book Description
19 basic straightedge and compass constructions and construction solutions to algebraic equations. Also explores triangle, circle, and non-compass constructions. Many proofs, exercises and problems.
Author: George E. Martin
Publisher: Springer Science & Business Media
ISBN: 1461206294
Category : Mathematics
Languages : en
Pages : 210
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Book Description
Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.
Author: Nicholas D. Kazarinoff
Publisher: Courier Corporation
ISBN: 0486143619
Category : Mathematics
Languages : en
Pages : 160
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Book Description
An intriguing look at the "impossible" geometric constructions (those that defy completion with just a ruler and a compass), this book covers angle trisection and circle division. 1970 edition.
Author: Roger A. Johnson
Publisher: Courier Corporation
ISBN: 048615498X
Category : Mathematics
Languages : en
Pages : 338
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Book Description
This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
Author: Christopher M. Freeman
Publisher: Routledge
ISBN: 100049330X
Category : Education
Languages : en
Pages : 101
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Book Description
Put compasses into your students' hands and behold the results! Hands-On Geometry teaches students to draw accurate constructions of equilateral triangles, squares, and regular hexagons, octagons, and dodecagons; to construct kites and use their diagonals to construct altitudes, angle bisectors, perpendicular bisectors, and the inscribed and circumscribed circles of any triangle; to construct perpendicular lines and rectangles, parallel lines, and parallelograms; and to construct a regular pentagon and a golden rectangle. Students will enjoy fulfilling high standards of precision with these hands-on activities. Hands-On Geometry provides the background students need to become exceptionally well prepared for a formal geometry class. The book provides an easy way to differentiate instruction: Because the lessons are self-explanatory, students can proceed at their own pace, and the finished constructions can be assessed at a glance. Grades 4-6
Author: Gerard A. Venema
Publisher: American Mathematical Soc.
ISBN: 0883857847
Category : Mathematics
Languages : en
Pages : 147
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Book Description
This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincare disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry. The text consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. First the ideas are explored at the computer and then those ideas are assembled into a proof of the result under investigation. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.
Author: Iris Mack Dayoub
Publisher:
ISBN: 9780866514996
Category : Geometry
Languages : en
Pages : 180
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Book Description
These more advanced Mira exercises explore basic geometric concepts, then constructions, transformations and problem solving. Students must create, observe, and conjecture about constructions, as well as analyze the properties of familiar geometric figures.
Author: Wendy Conklin
Publisher: Teacher Created Materials
ISBN: 1425878601
Category :
Languages : en
Pages : 11
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Book Description
This learning contract lesson allows learners to work at their own paces in a flexible learning environment. Written specifically for mathematics teachers, this lesson helps facilitate the understanding and process of writing learning contracts.
Author: Aad Goddijn
Publisher: Springer
ISBN: 9462098603
Category : Education
Languages : en
Pages : 327
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Book Description
This book shows how geometry can be learned by starting with real world problems which are solved by intuition, common sense reasoning and experiments. Gradually the more formal demands of mathematical proofs get their proper place and make it possible to explore new applications. This process helps students to feel the need for precise definitions and procedures, to contribute to the construction of an axiomatic system, and to experience the power of systematic reasoning. The course is designed for students in a Nature & Technology strand which prepares for studying the sciences or technology at university level. Its goal was basically to reintroduce ‘proof’ in a meaningful way in the late 1990s Dutch secondary education curriculum. Following the educational view of the Freudenthal Institute this is not done by stating Euclid’s axioms on page one, but rather a starting point is chosen in students’ intuitions and tentative solutions of problems that are experienced as real and relevant. The photograph on the cover shows students exploring one of the problems from the midpart of the course in the computerlab.
Author: Heinrich Dörrie
Publisher: Courier Corporation
ISBN: 0486318478
Category : Mathematics
Languages : en
Pages : 416
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Book Description
Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge, Steiner, and other great mathematical minds. Features squaring the circle, pi, and similar problems. No advanced math is required. Includes 100 problems with proofs.
