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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.

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 “

Bella

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