10: Geometric Symmetry and the Golden Ratio — Read

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Patterns and geometry occur in nature and humans have been noticing these patterns since the dawn of humanity. In this chapter, topics in geometry will be examined. These topics include transformation and symmetry of geometric shapes, similar figures, gnomons, Fibonacci numbers, and the Golden Ratio.

10.1: Transformations Using Rigid Motions
In this section we will learn about isometry or rigid motions. An isometry is a transformation that preserves the distances between the vertices of a shape. A rigid motion does not affect the overall shape of an object but moves an object from a starting location to an ending location. The resultant figure is congruent to the original figure.
10.2: Connecting Transformations and Symmetry
Humans have long associated symmetry with beauty and art. In this section, we define symmetry and connect it to rigid motions.
10.3: Transformations that Change Size and Similar Figures
10.4: Fibonacci Numbers and the Golden Ratio
A famous and important sequence is the Fibonacci sequence, named after the Italian mathematician known as Leonardo Pisano, whose nickname was Fibonacci, and who lived from 1170 to 1230. This sequence is: {1,1,2,3,5,8,13,21,34,55,………}
10.5: Exercises

Thumbnail: Golden spirals are self-similar. The shape is infinitely repeated when magnified. (Public Domain; Jahobr via Wikipedia)

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