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"The School of Athens" by Raphael
The School of Athens was painted by Raphael Sanzio or Raffaello Santi (1483-1520) for Pope Julius II (1503-1513) as a part of Raphael's commission to decorate with frescoes the rooms that are now known as the Stanze di Raffaello, in the Apostolic Palace in the Vatican. In this fresco, Raphael depicts the great philosophers and mathematicians of ancient Greece as colleagues in a timeless academy:
Plato is in the center pointing his finger to the heavens while holding the Timaeus, his treatise on the origin of the world. Next to him, his younger pupil Aristotle holds a copy of his Ethics while describing the earth and the wide realm of moral teaching with his extended hand in an elegant horizontal gesture, Pythagoras contemplates his system of proportions at the lower left and Euclid draws a circle on a slate at the lower right.
To the Greeks mathematics was essentially geometry, and it
was in Elements, Euclid's treatise on the subject, that the
notion of an axiomatic system was first laid out In this
system certain self-evident statements called axioms are
assumed to be true and new statements called theorems are
derived from them using the Aristotelian rules of inference.
Kaleidoscope
A kaleidoscope is a tube of mirrors containing loose coloured beads, pebbles, or other small coloured objects. The viewer looks in one end and light enters the other end, reflecting off the mirrors. For a 2D symmetry group, a kaleidoscopic point is a point of intersection of two or more lines of reflection symmetry. In the case of a discrete group the angle between consecutive lines is 180°/n for an integer n≥2. At this point there are n lines of reflection symmetry, and the point is a center of n-fold rotational symmetry. Source:
Wikipedia,
Kaleidoscope.
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