"The square of the hypotenuse (i.e. longest side) is equal to the sums of the squares of the two (other) sides." There you have it...the Pythagorean Theorem. AxA=(BxB)+(CxC)
(The following, wonderful story was told in class by my high school math teacher over 30 years ago. I have never heard it in any other context, and I have made the retelling of it my own since I only remember the "high points" & the "punch line.")
(May the native Americans who are reading this accept my gratitude for the wonderful heritage that provides the backdrop for this story. You have my respect and I will tell the story with all the historical correctness that I can recall. This apocryphal story takes place in the American West in the mid-1800's.)
THE SQUAW OF THE HIPPOPOTAMUS! (A Mathematical Concept in Word Pictures)
Since it is customary for the eldest son to begin his leadership of a tribe at the death of his father, an aging chief with no sons is a great cause for concern.
Yet, that was the very case in the tribe of Pythagoras, chief & wise man. Though Pythagoras was very proud of the two daughters of his youth (both born in his early twenties) and the daughter of his old age (born the day he turned forty,) there were no rules in place to govern this situation.
Wise Pythagoras chose the occasion of his eightieth birthday to name a grandson as his successor. The son of the eldest daughter was the obvious choice, but the youngest daughter made a challenge on the basis of youthful vigor to breathe new life & hope into the tribe.
That is right! The youngest daughter thought she had as much right to be chief as her two nephews.
After thinking about his answer for a day, Pythagoras finally had a solution.
"The chief of this tribe must be brave, strong, vigorous, cunning, and wise. These two strong braves and one strong squaw must present a tribal gift of food and clothing at the door to the chief's tent by sundown tomorrow. The soul with the greatest gift will be chief."
The tribe was pleased, "Yes, we agree to that!"
Two brave figures on horseback rode off into the dark find the best quarry. Both shook their heads as their youthful aunt went to bed...unaware that she was already confident of victory.
At the time appointed the first youth presented a flawless pelt and succulent venison never before tasted in its richness. Second brought a twenty-point moose head, a huge pelt, and food enough for two tribes.
"Where is my youngest daughter?" intoned the chief. "Does she dare to challenge and then fail to deliver?"
As he spoke the silhouette of his youngest daughter crested the hill riding to his amazement...a hippopotamus.
"Daughter, I am incredulous that you have captured such a profound creature, let alone tamed it enough to be your mount, but you were instructed to bring a gift of food & clothing. This creature is alive.
"Please, tell me why I should not disqualify you?"
"Father, the deer and the moose may feed us but once for they no longer live, but the hippopotamus being a mammal may provide us with milk many days hence. That should certainly outlive the need for the pelts during the long, hot days of summer."
"You have well spoken, Daughter! All of you, Leave me now! Come in the morning for my decision."
At first light the trio listened to the wisdom of their chief.
"You have all done well in providing much for the tribe you wish to lead. The two pelts will provide clothing for many. The venison & moose will feed us for many days. The hippopotamus will continue to feed us after that.
"You three are family with varied strengths & weaknesses. You three will lead our tribe better together than one of you would alone.
"With your love for family & tribe we will create a new three-branch government like the United States to check your strengths & balance your weaknesses."
The tribe cheered, "We are agreed!"
Therefore, the moral of this story is that "The squaw of the hippopotamus is equal to the sons of the squaws of the two hides."