The School of Euclid

The image from Raphael's School of Athens expresses of spirit of this web site

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This detail, taken from the lower right section of Raphael’s School of Athens, represents, in a single grouping, the painter’s ideas about different stages of learning. The master Euclid, himself bent over in the shape of a triangle, demonstrates a proof from his Elements. Each of his students represents a stage of the learning process:


Lower left (kneeling): The young man is engrossed in the unfolding of the theorem’s proof and visual representation. The fingers of his left hand form an enumerated triangle.


Upper right: “I think I’ve got it!” This man is following the argument, and expresses his dawning comprehension with the cupped hands facing downward. Perhaps they are even moving slightly in rhythm to express the process of dawning comprehension.


In the middle: “Huh? I don’t get it!” This student, with an expression of dismay or plea for help, looks over his shoulder to his friend, who might explain the proof; but...


Upper left: With his right hand on the back of the man who already comprehends, this man (in green, like his confused friend) proceeds to point out (his left index finger already aimed at Euclid) the solution to the problem.