Distance and Angle; Triangles and Quadrilaterals

  • Basil Gordon
Part of the Heidelberg Science Library book series (HSL)

Abstract

We shall now systematically study Galilean geometry, i.e., the geometry of the plane xOy whose motions are given by the equations This means that we shall be interested solely in those properties of figures in the plane xOy that are invariant under the transformations (1) (or, equivalently, under the shears
$$\begin{array}{*{20}c} {x' = \,x,} \\ \end{array} $$
(1a)
and the translations
$$\begin{array}{*{20}c} {x = \,x + a,} \\ \end{array} $$
(1b)
cf. p. 25 above);it is only these properties of figures that have geometric significance in this unusual geometry. Also, we shall bear in mind that our geometry arose naturally out of mechanical considerations connected with Galileo’s principle of relativity. This implies that, in our case, properties of geometric significance are really properties of mechanical significance; more specifically, facts of one-dimensional kinematics.

Keywords

Sine Italicize Assertion 

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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Basil Gordon

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