An equilateral triangle inscribed in a square. What’s the proportion of the red to the blue area?

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## Solution

The proportion blue : red is 1.

First we recognize that the blue triangles are right triangles with top angle 15°, whereas the red triangle is isosceles with top angle 90°. Then we fit the two blue triangles together to form an isosceles triangle with top angle 30°.

If for convenience we set the equilateral triangle sides to √2, the blue area is √2*√2*sin(30)/2=1/2. The red area is 1*1*sin(90)/2=1/2.

## Visual solution

## Poem

May be just a stained glass window of a cathedral

Which lets the light shot through

Goethe said ” poems are like stained glasses “

Pieces put together

With ideas, words, sentences ,

They hold all our emotions

Our dreams

Our thoughts

A poem illuminates

Spirit and soul

The meaning spreads like light

Through us

And connects us

To heaven

To the moon

To the stars

Van Gogh said

“Poetry surrounds us everywhere “