matematicas visuales visual math


Durer was a painter and also a mathematician. He lived between 1471 and 1528. He was a representative of the German Renaissance. This was the time of the Reformation. He lived in Nuremberg and traveled to Italy and the Netherlands. He spreads the new techniques of perspective.

He wrote two books in German of particular interest to us. A treatise on descriptive geometry (Underweysung ...) with ruler and compass constructions and "The four Books of Human Proportions". In the third book he describes methods for changing the proportions of the figures. It is based on geometric transformations of different types. Some of these changes are affine transformations (preserving parallelism).

You can browse several pages of this book on U.S. National Library of Medicine.

Durero en National Library of Medicine |Albrecht Durer: Vier Bücher von menschlicher Proportion

By moving the points, the image is transformed by a "picewise affinity". These affinities are dilatations, shears, translations ...

Clicking on the faces in the control area you can choose between three different faces.

Clicking on the applet with the right mouse button and dragging you can move the canvas.


Dan Pedoe - The Gentle Art of Mathematics
D'Arcy Thompson - On Growth and Form


Los Embajadores de Holbein el Joven
In this painting we can see, among lots of interesting things, an anamorphosis of a skull. (In Spanish)