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

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## Solution

The blue fraction is 2/3.

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.

## Poem

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