# Gabriele Gelatti

Despite the mystery on the nature of the human thought, still mind and
nature share something: numbers. The primitive aspect of numbers as
figures and patterns creates “sense” to the mind, and even
“beauty”.

Any creation of human thought faces the idea of beauty, even to refuse
it. If a universal definition of beauty is still missing, it remains
the most effective link between art and mathematics, demonstrating
that “true is beautiful”.

Golden Ratio and related Fibonacci numbers express the convergence of
both mathematical and symbolic thoughts: the beauty of their contents
can be experienced by the two points of view.

The research of Gabriele Gelatti explores the archetypes of the
symbolic thought to find new mathematical objects.

“... the one which we maintain to be the most beautiful of all the
many triangles (...) is that of which the double forms a third
triangle which is equilateral (...) the triangle always having the
square of the longer side equal to three times the square of the
lesser side...” [Timaeus, 54 b].

Defining the “most beautiful” triangle Plato refers to Pythagorean
theorem, that proofs the Golden Ratio construction in the
image.

We pose: φ = √(5/4) – (1/2). Let ABC be an half-equilateral
triangle with |BC| = 1; |AB| = 2|BC| = 2; |AC| = √3. Then, by
Pythagorean theorem we have: |FB| = |AC| = √3; |BE| = |BD| = √8;
so that |FE| = √5. With |FA| = |BC| = 1, then |AE| = √5 – 1 = 2φ
that is the Golden Ratio of |AB|.

This work of art is based on Golden Ratio and is composed by two
images. The red and green painting is derived from a construction
that has an aesthetic appeal in it's simplicity. Moreover, there
is an important cultural content in this unexpected discovery of
Golden Ratio, as it is based on a passage of platonic Timaeus
mysteriously discussing the “most beautiful triangle”. The red and
green colours create an high contrast vision effect, emphasised by
the use of red and green glasses giving movement to the pattern
and 3D experience. The purpose is to underline the psychic meaning
of Golden Ratio in the research of beauty.

The Golden Ratio construction is presented on a clay tile as a
tribute to ancient mathematics.