Harmony of the Spheres

  • John Barnes


IN THE LECTURE on Bubbles we saw how the centres of bubbles, the centres of curvature of dividing films, and points on tangents formed various harmonic ranges. In this lecture we will start by looking at some other pretty properties of circles and spheres. But first a brief explanation of the title of this lecture.


Outer Circle Parabolic Point Inverted System Equal Circle Fixed Circle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • John Barnes
    • 1
  1. 1.CavershamEngland

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