Proportionality and Similarity

  • Antonio Caminha Muniz Neto
Part of the Problem Books in Mathematics book series (PBM)


This chapter develops a set of tools which will allow us to start a systematic study of the metric aspects of Plane Euclidean Geometry; generally speaking, the central problem with which we shall be concerned here is that of comparing ratios of lengths of line segments. Among several interesting and important applications, the most prominent ones are the theorems of Thales and Pythagoras, which will reveal themselves to be almost indispensable hereafter. We also present a series of classical results, among which we highlight the study of the Apollonius circle and the solution of the Apollonius tangency problem, the collinearity and concurrence theorems of Ceva and Menelao, and some of the many theorems of Euler on the geometry of the triangle.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

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