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Hearty Pattern!

Image Credit: VollherzigHerzgeometrie Image Credit: VollherzigHerzgeometrie

Mai's friends and lovers were all invited for the Valentine's Day party. After enjoying the wonderful love music and meal, she believed that it's the great idea to play the heart-counting game. The dialogue started:

Mai: The shape is counted as one heart if:

  • Two adjacent sectors in a heart are either tangential or intersecting.
  • The projected lines are tangent to the sectors.

Yugi: That seems quite interesting.

Tea: I am not even good in discrete mathematics, so I am SO bad in counting. Since I believe you are so good in mathematics, you should figure out the best method to answer Mai's problem! There isn't any reason why I would find another man to love! :)

Mai: The couple who arrives with the correct answer first wins the game and earns a grand prize! The time starts now!

[Mai revealed the image as shown above. After few seconds..]

Yugi: I have the answer, and I am very sure it's correct! [Answer hidden]

Mai: We have a winner!

Tea: Wow! What a versed skill you have here! You are the true Valentine mathematician!

How many hearts in all did he find?

Note: Assume that the common circular sectors have same area, and that the 14-sided polygon is regular.

This is the fifth chapter of the story. Check the following chapter directory if you are interested:

First - Second - Third - Fourth - Fifth


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