Arc de Triomphe

A parabola passing through a square’s bottom vertices and tangent to its top side. What fraction is blue?

Scroll down for a solution to this problem.


The blue fraction is 2/3.

Solution by John Michael.

Strictly speaking, the parabola could also be slanted as shown below, such that the tangency point is not exactly at the top. Due to the Archimedes Theorem, however, the fraction still remains 2/3. It says that the area of the parabolic segment equals 4/3 of the inscribed triangle, which is 1/2 of the square.


The Arc de Triomphe
Is wrapped
A temporary work,
To dream, imagine
For a fantastic contemporary creation
The packaging is silvery blue
And red rope will attach the panels, an unique view
A collage supported by the Center Pompidou
The Eternel Flame still burns and remembers you


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