7: Mathematics and the Arts
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- 7.1: Projective Geometry
- Before drawing a 3-dimensional object on a flat surface, such as a sketch book or a canvas, one needs to learn some principles of perspective. This skill, based on projective geometry and developed during the Renaissance, allows the artist to draw things more realistically. All of us have seen, for instance, pictures of railroad tracks and straight highways where the two lines, though parallel in space, appear to converge to a point, referred to as the principal vanishing point.
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- 7.2: The Golden Ratio and Fibonacci Sequence
- In this section, we will discuss a very special number called the Golden Ratio. It is an irrational number, slightly bigger than 1.6, and it has (somewhat surprisingly) had huge significance in the world of science, art and music. It was also discovered that this number has an amazing connection with what is called the Fibonacci Sequence, originally studied in the context of biology centuries ago. This link among algebra, biology, and the arts suggests the mathematical unity of the world.
Thumbnail: Golden spirals are self-similar. The shape is infinitely repeated when magnified. (Public Domain; Jahobr via Wikipedia )
Contributors and Attributions
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Saburo Matsumoto
CC-BY-4.0