Skip to main content
SpringerLink
Log in

Topics in Elementary Geometry

  • Textbook
  • © 2008

Overview

Authors:
  1. O. Bottema
    View author publications

    You can also search for this author in PubMed   Google Scholar

  • A unique place to find classical results in geometry, along with more theorems

  • Contains a foreword by Robin Hartshorne

  • Covers a wide range of topics in elementary plane Euclidean geometry

  • Translator has added historical references and an updated bibliography

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (27 chapters)

  1. Front Matter

    Pages 1-8
    Download chapter PDF

  2. The Pythagorean Theorem

    • O. Bottema, Reinie Erne
    Pages 1-6

  3. Ceva’s Theorem

    • O. Bottema, Reinie Erne
    Pages 1-5

  4. Perpendicular Bisectors; Concurrence

    • O. Bottema, Reinie Erne
    Pages 1-6

  5. The Nine-Point Circle and Euler Line

    • O. Bottema, Reinie Erne
    Pages 1-3

  6. The Taylor Circle

    • O. Bottema, Reinie Erne
    Pages 1-2

  7. Coordinate Systems with Respect to a Triangle

    • O. Bottema, Reinie Erne
    Pages 1-4

  8. The Area of a Triangle as a Function of the Barycentric Coordinates of Its Vertices

    • O. Bottema, Reinie Erne
    Pages 1-4

  9. The Distances from a Point to the Vertices of a Triangle

    • O. Bottema, Reinie Erne
    Pages 1-5

  10. The Simson Line

    • O. Bottema, Reinie Erne
    Pages 1-3

  11. Morley’s Triangle

    • O. Bottema, Reinie Erne
    Pages 1-3

  12. Inequalities in a Triangle

    • O. Bottema, Reinie Erne
    Pages 1-4

  13. The Mixed Area of Two Parallel Polygons

    • O. Bottema, Reinie Erne
    Pages 1-5

  14. The Isoperimetric Inequality

    • O. Bottema, Reinie Erne
    Pages 1-7

  15. Poncelet Polygons

    • O. Bottema, Reinie Erne
    Pages 1-7

  16. A Closure Problem for Triangles

    • O. Bottema, Reinie Erne
    Pages 1-3

  17. A Class of Special Triangles

    • O. Bottema, Reinie Erne
    Pages 1-4

  18. Two Unusual Conditions for a Triangle

    • O. Bottema, Reinie Erne
    Pages 1-2

  19. A Counterpart for the Euler Line

    • O. Bottema, Reinie Erne
    Pages 1-2

  20. Menelaus’s Theorem; Cross-Ratios and Reciprocation

    • O. Bottema, Reinie Erne
    Pages 1-5
Back to top

Keywords

About this book

Oene Bottema (1901–1992) may not be so well known abroad, but in his own country he is ”the great geometer”. He graduated from the University of Groningen in 1924 and obtained his doctor’s degree from Leiden University in 1927. He spent his early years as a high school teacher and administrator. He published extensively, and as his ability became known, he was made professor at the Technical University of Delft in 1941, and later rector of thatuniversity(1951–1959). Withhisencyclopedicknowledgeof19th-century geometry and his training in 20th-century rigor, he was able to make many contributions to elementary geometry, even as that subject was eclipsed by the modern emphasis on abstract mathematical structures. He also had a fruitful collaboration with engineers and made substantial contributions to kinematics, culminating in the book Theoretical Kinematics,withBernard Roth, in 1979. Throughout his life he was inspired by geometry and poetry, and favored elegant succinct proofs. This little book, ?rst published in 1944,then in a secondexpanded edition in 1987, gives us a glimpse into his way of thinking. It is a series of vignettes, each crafted with elegance and economy. See, for example, his proof of the Pythagorean theorem (1. 2), which requires only one additional line to be drawn. And who can imagine a simpler proof of the nine-point circle (4. 1)? There is ample coverage of the modern geometry of the triangle: the Simson line, Morley’s theorem, isogonal conjugates, the symmedian point, and so forth.

Reviews

From the reviews of the second edition:

"This small book includes Ceva’s and Menelaus’s theorems, the nine-point circle and Euler line, configuration theorems, Morley’s triangle, inequalities for elements in a triangle … . The arguments are not only geometric or trigonometric ones but also different coordinate systems are considered such as barycentric or trilinear coordinates in relation to a given triangle. … The book is very useful for teachers and teacher students who want to be inspired by the results of elementary geometry." (Herbert Hotje, Zentralblatt MATH, Vol. 1159, 2009)

Bibliographic Information

  • Book Title: Topics in Elementary Geometry

  • Authors: O. Bottema

  • DOI: https://doi.org/10.1007/978-0-387-78131-0

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag New York 2008

  • Softcover ISBN: 978-0-387-78130-3Published: 20 August 2008

  • eBook ISBN: 978-0-387-78131-0Published: 10 December 2008

  • Edition Number: 2

  • Number of Pages: XII, 142

  • Number of Illustrations: 76 b/w illustrations

  • Additional Information: Original Dutch editions published by Mathematics Institute, University of Utrecht, The Netherlands

  • Topics: Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation