Heads reproduction in Hercules and hidras battles

Abstract

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Hercules killed the Hydra of Lerna in a bloody battle-the second of the labor tasks imposed upon him in atonement for his hideous crimes. The Hydra was a horrible, aggressive mythological monster with many heads and poisonous blood, whose heads multiplied each time one of them was severed. This paper explores some mathematical methods about this interesting epic battle. A generalization of the original Kirby & Paris model is proposed, concerning a general heads reproduction pattern. We also study the connection of this model with Goodstein ultra-growing and recursive sequences. As an interesting application, we next analyze the inevitable death of another huge monster of our modern era: the Internet.