## The octagon in Leonardo’s drawings.(English)Zbl 1155.01002

Summary: Mark Reynolds presents a study on Leonardo’s abundant use of the octagon in his drawings and architectural renderings. Specifically, he focuses on Leonardo’s applications of the octagon: in his studies and sketches of the centralized church, and for which we can find influences specifically from Brunelleschi, as well as from other fifteenth-century architects working with this type of religious structure; in his almost obsessive and frequently repetitious drawing of octagonal shapes and forms in his notebooks throughout his career; in his project for a pavilion while with the Sforzas in the last part of his period in Milan. Also examined are ways to develop the modules to accommodate $$\sqrt2$$ and the $$\theta$$ rectangles. The application of the modular units, so far, have been within the square and its gridwork, but as the octagon has traditionally been used in the development of both the circle and the square, this shape is an interesting challenge in terms of linking the two-dimensional surface to the three-dimensional forms we are planning to generate. The object is to provide us with more insight as to why the octagon held so much fascination for Leonardo as one of the ultimate geometric expressions of grandeur and practicality in spatial organization, design, and development. Often in Leonardo’s drawings of octagons, precise geometric constructions were lacking; the master’s approach was freehand. The author seeks to learn if Leonardo’s sketches can be put to the rigors of strict geometric construction, and still be viable as accurate renderings of octagonal geometric spaces with his own geometric constructions of those same spaces.

### MSC:

 01A40 History of mathematics in the 15th and 16th centuries, Renaissance

### Keywords:

Leonardo da Vinci; octagons; geometric constructions

### Biographic References:

Leonardo da Vinci
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