Euclidean geometry : a guided inquiry approach
著者
書誌事項
Euclidean geometry : a guided inquiry approach
（MSRI mathematical circles library, 9）
Mathematical Sciences Research Institute , American Mathematical Society, c2012
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注記
Includes bibliographical references (p.123-124) and index
内容説明・目次
内容説明
Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation.
Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry.
The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority.
This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Math Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
目次
Introduction to the student
Congruent figures
Axioms, theorems and proofs
Area measure
Angle measure
Similar figures
Trigonometric ratios
Circle measure
Perspective geometry
The axioms
Guidelines for the instructor
Hilbert's axioms
Bibliography
Index
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