da Vinci states his intention to write a book on the transformations of geometric shapes

As an artist, da Vinci’s interest in geometry was rooted in the subject's application to aesthetics. It is for this reason that da Vinci was more invested in learning the “continuous” mathematics of shape as opposed to the “discrete” math of arithmetic. Since da Vinci viewed shapes as continuous, he found himself especially interested in the transformations of one shape to another. One can find evidence of this interest in da Vinci’s sketches of elevated polyhedra, where a polyhedron essentially explodes into another one. da Vinci also explored this idea of transformation in the plane through the task of squaring the circle, which is the task of creating a square with the same area as a given circle. His notebooks show a fixation with the task, eventually displaying 169 ways to do the procedure. In 1505 da Vinci set out to make a publication on the transformation of shapes; unfortunately, this publication never came to fruition, but this idea remained an obsession of him throughout the rest of his life.


Isaacson, Walter. Leonardo Da Vinci. Simon & Schuster Paperbacks, 2018. 

The image is from Wikimedia Commons and in the public domain. 

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