Gems of Geometry

1. Front Matter

   Pages i-xiii

   PDF

2. The Golden Number

   • John Barnes

   Pages 1-26

3. Shapes and Solids

   • John Barnes

   Pages 27-62

4. The Fourth Dimension

   • John Barnes

   Pages 63-87

5. Projective Geometry

   • John Barnes

   Pages 89-111

6. Topology

   • John Barnes

   Pages 113-135

7. Bubbles

   • John Barnes

   Pages 137-155

8. Harmony of the Spheres

   • John Barnes

   Pages 157-178

9. Chaos and Fractals

   • John Barnes

   Pages 179-204

10. Relativity

    • John Barnes

    Pages 205-229

11. Finale

    • John Barnes

    Pages 231-246

12. Back Matter

    Pages 247-325

    PDF

Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on a geometrical journey via Shapes and Solids, through the Fourth Dimension, finishing up with Einstein's Theories of Relativity.

 

Equally suitable as a gift for a youngster or as a nostalgic journey back into the world of mathematics for older readers, John Barnes' book is the perfect antidote for anyone whose maths lessons at school are a source of painful memories. Where once geometry was a source of confusion and frustration, Barnes brings enlightenment and entertainment.

 

In this second edition, stimulated by recent lectures at Oxford, further material and extra illustrations have been added on many topics including Coloured Cubes, Chaos and Crystals.

• geometry
• geometry and crystals
• relativity
• topology

• John Barnes Informatics, Reading, United Kingdom

  John Barnes

Mr Barnes' principal achievements have been in the area of computer programming language design. He designed the language RTL/2 whilst with ICI. This was widely used in the 1970s and 80s for process control in the UK, the Netherlands and South Africa. It still lingers in use in a number of systems (eg the Thames Barrier). He was a member of the Ada language design teams. Ada is widely used in safety critical applications such as those found in defence systems generally, avionics, air traffic control and railroad signalling. He has published eight books: RTL/2 Design and Philosophy, Heyden, 1976. Programming in Ada, Addison-Wesley, 1982. Programming in Ada 95, Addison-Wesley, 1996. High Integrity Ada, Addison-Wesley, 1997. Ada 95 Rationale, Springer-Verlag, 1997. High Integrity Software, Addison-Wesley, 2003. Programming in Ada 2005, Addison-Wesley, 2006. Ada 2005 Rationale, Springer-Verlag, 2008. Programming in Ada went through four editions and was translated into six other languages. Revised versions are entitled Programming in Ada 95 and Programming in Ada 2005. Combined total sales of these books are over 150,000. Mr Barnes has given many lectures and tutorials on various aspects of programming. Although moving towards retirement he still gives occasional lectures including lectures for postgraduate courses at the University of York. He has published many papers, this list gives just two from his early career in ICI, a milestone paper when Ada emerged, and a pair of recent reflective papers. An algorithm for solving non-linear equations based on the secant method, The Computer Journal, vol 8, no 1 (April 1965). A KDF9 Algol list-processing scheme, The Computer Journal, vol 8, no 2 (July 1965). An overview of Ada, Software Practice and Experience, vol 10, pp851-887 (1980). Half a century of programming and not much progress, Software Focus, vol 2, no 1 (2001). Half a century of programming and a spark of light, Software Focus, vol 2, no 2 (2001). Recently, he has rediscovered an interest in mathematics and has given a number of courses at the University of Reading as part of their Continuing Education program.

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