#7**+13 **

Have you heard of the story of the red indian chief who had three squaws (wives) ?

They were allowed to choose the bedding on which they slept, each according to her own preference. The first chose to sleep on a hippopotamus skin, the second on a lion skin and the third on a tiger skin. (And yes I know what you are going to say, but this was long ago when there were hippopotami and tigers in North America.)

In the fullness of time, the first wife bore triplets, the second wife had twins, but the third could only manage a single baby.

The moral of the story is that "The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides".

Bertie
May 21, 2014

#3**+5 **

Proof of Pythagorean Theorem using similar triangles:

Let ABC be a right triangle with altitude BD

Then by similar triangles,

ABD ≈ ACB ⇒ (AD/AB = AB/AC) ⇒ ( AB^{2} = AD*AC)

DBC ≈ BAC ⇒ (DC/CB = CB/AC) ⇒ ( CB^{2} = DC*AC)

Adding the expressions in the parentheses we have,

AB^{2} + BC^{2} = AD*AC + AC*DC

AB^{2} + BC^{2} = AC(AD + DC)

AB^{2} + BC^{2} = AC(AC)

AB^{2} + BC^{2} = AC^{2 }

BTW.....There is little historical evidence that Pythagoras ever had much to do with his own "Theorem" ......

CPhill
May 21, 2014

#4**+10 **

Very impressive CPhill.

My turn

A pythagorean formula is one that satisfies Pythagoras' Theorem.

Pythagoras' Theorem states that in any right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

If the hypotenuse is h and the other 2 sides are a and b then $$h^2=a^2+b^2$$

Melody
May 21, 2014

#5**+8 **

And for those who paid close attention........

In "The Wizard of Oz," the scarecrow - after getting a "brain" from the Wizard - states:

"The sum of the square roots of any two sides of an* isosceles* triangle is equal to the square root of the remaining side."

It sounds convincing when he says it......but it's wrong.......

CPhill
May 21, 2014

#7**+13 **

Best Answer

Have you heard of the story of the red indian chief who had three squaws (wives) ?

They were allowed to choose the bedding on which they slept, each according to her own preference. The first chose to sleep on a hippopotamus skin, the second on a lion skin and the third on a tiger skin. (And yes I know what you are going to say, but this was long ago when there were hippopotami and tigers in North America.)

In the fullness of time, the first wife bore triplets, the second wife had twins, but the third could only manage a single baby.

The moral of the story is that "The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides".

Bertie
May 21, 2014