Euclidean geometry : a guided inquiry approach

Author(s)

• Clark, David M.

Bibliographic Information

Euclidean geometry : a guided inquiry approach

David M. Clark

（MSRI mathematical circles library, 9）

Mathematical Sciences Research Institute , American Mathematical Society, c2012

Note

Includes bibliographical references (p.123-124) and index

Description and Table of Contents

Description

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.

Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BB09801994
• ISBN:
  • 9780821889855
• LCCN: 2012016972
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berkeley, Calif.,Providence. R.I.
• Pages/Volumes: xxiv, 127 p.
• Size: 26 cm
• Classification:
  • LCC : QA451
  • DC23 : 516.2
• Subject Headings:
  • LCSH : Geometry, Plane
  • LCSH : Geometry, Solid
• Parent Bibliography ID:
  • BA88332392