martes, 17 de enero de 2017

1193. To fly!

    Teacher, thanks for teaching me how to fly.

    I gave him back the compliment... I tell Pepe Chapuzas that it was very easy to teach to fly to children who were born with wings...
    Pepe said goodbye with a gift: a Geometry problem...

    Dear Teacher:
    The orange area is 10 m2, and the green area is...
    Nina Guindilla was born with wings too...
  
    Dear Teacher:
    There are 10 orange circles, so, one circle area is  1 m, and its radius measures  1/π .
    The radius of the blue decagon measures  csc 18° / π . I have no calculator but I have here a chart of cosecants...
csc 15°  =  6 + 2
csc 18°  =  5 + 1
csc 30°  =  2
csc 45°  =  2
csc 54°  =  − 1
csc 60°  =  √12 / 3
csc 75°  =  − 2
csc 90°  =  1

    So, the radius of the blue decagon measures

(5 + 1) / π .

    And the radius of the green circle measures

(√5 + 1) / π  −  1 / π  =  π .

    And the green area is... half the orange area

π · (π)2  =  5 m2 .

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