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# Leonardo da Vinci

Leonardo da Vinci lived around 1500 in Italy. In the 15th and 16th century mathematicians were also painters. Leonardo made a living with what would nowadays be the work of a mathematician, painter, architect and engineer. He painted many beautiful and peaceful pictures, and at the same time he designed war machines.

The time of the 15th and 16th century is called Renaissance (rebirth) because the Europeans rediscovered the work of the Greeks. Scientists took over the Greek idea that the nature can be described best through mathematics. Their way of describing nature was to paint it in a way which gives the observer the same impression as the scene in real life does. This lead to a revolution in painting, to a new style in which the main tool was geometry. The mathematicians of the Renaissance created a whole new system, the system of perspective which is still taught in art school today.

The Renaissance painters decided to concentrate on what you can see with one eye. Our impression of depth comes through the slightly different point of view of our two eyes. The painters compensated this by shading and by using a gradual diminution in the intensity of colors depending on the distance.

The study of light was basic to their new technique. They imagined rays extending from the body they were observing toward one of their eyes. In their imagination they could put a piece of paper between the eye and the object. The rays would then pierce through the paper. Using this method they could get the important points for the proper perspective on the paper.

All the horizontal lines which are parallel to the imagined piece of paper have to be drawn parallel. Horizontal lines which are perpendicular to the immagined paper have to meet in a vanishing point. Lines which are further away from the observer have to be shortened. These rules seem common kowledge today, but they were revolutionary back then.

The new drawing technique was also important for other sciences like biology. Until about 1850, when photography was invented, drawing was the only way to record something you had seen.

Leonardo da Vinci thought that mathematics was an essential tool for painting. In one of his books he said that people who hadn't studied math shouldn't even start reading his work.