No Wonder a^{2}+b^{2}=c^{2}
was Greek to me !

**—In
a right triangle, the square of the hypotenuse is
equal to the sum of the squares of the other two
sides.**

** ****(the
Pythagorean theorem)**

**My plan is to go to
Calabria**, the town of Crotone (the map, below,
shows the province of Crotone. Find the 'e' at the end
and walk down to the town. It's at water's edge).
Specifically, I want the high school, the *Liceo
Ginnasio Classico Pitagora* at piazza Umberto I,
15. I intend to offer to teach their English classes for
a whole week just so I can teach the kids one of the
world's most complicated pun-stories, one that bears
directly on their own town, indeed one that connects
their town and themselves to every kid in the world who
has ever studied geometry. And they won't have to pay
me. I can drive it from Naples in a few hours, and I 'll
cover my own expenses because I've got this great idea
for a t-shirt.

**T**his is the
story. It was my high-school geometry teacher's
favorite. We were grade-bound to laugh long and loud (no
groaning, please) every time he told it. We wound up
with pretty good grades and really sore diaphragms. For
the politically correct, I realize that the use of the
S-word is potentially offensive. I do know that the word
*squaw* derives from the eastern Algonquian
languages and appears in various spellings to mean
'woman' and has often been generalized incorrectly and
unfairly. I remind you that this is just a joke, for
Pete's sake. For the zoologically correct, I do know
that there are no hippopotamuseseses in North America. I
remind you that this is just a joke, for Pete's sake.
For the Ethical-Treatment-of Animally-correct —please
get a life; I got the hides from Teddy Roosevelt. This
is just a joke, for Pete's sake.

**Once
upon a time, there were three pregnant Indian
squaws. The first squaw was sitting on a buffalo
hide, the second squaw on an antelope hide, and
the third squaw on a hippopotamus hide. The
first squaw gave birth to a baby boy, as did the
second squaw; but the third squaw—the one on the
hippo hide—had twin boys. So, what's the moral
of this story? ***The squaw... on the
hippopotamus... is equal to the... sons of the
squaws... on the other two hides!*

** **

** ****(He always spoke the last line
slowly, dots and all, just to make sure we got it.
He also leaned to the side a bit to show the
italics.)**

**Crotone is a great little town**
that you should visit even if you hate math; it has
great beaches, a harbor and a current population of
about 60,000. As long as you're there, however, know
that it had a glorious presence as part of Magna Grecia. They had
great athletes, famous philosophers, fine doctors and,
best of all, this is where Pythagoras (image, above
right) had his academy, founded in 510 BC. It was a
monastic-like, ascetic order, dedicated to
numbers—especially the relationships *between *numbers.
It all led eventually to the science of mathematics, the
powerful tool for describing and predicting natural
phenomena. They were so intent on serious study that
they got steamed at nearby Sybaris, the citizens of
which were notoriously luxuriant, flabby and given to
good times. Pythagoreans sent Crotone's great wrestler,
Milo, over with an army of goons and wiped out the weak
and meek Sybarites.

**W**e can forgive them.
The *-naissance* part of * renaissance *was
Greek: Thales, Anaximandros, Heraclitos and a legion of
others were worthy of the name "scientist," as we
understand that word today: one who knows from
observation and investigation. "Science" is related to
the word "scissors"; a scientist therefore cuts and
divides. The Greeks were the first who tried to cut and
divide, figure out and label the universe on a natural
rather than supernatural basis. Pythagoras was right in
the middle of them, and of all the figures of early
Ionian science, none had more influence on future
generations than did he.

**T**he Pythagoreans were
fascinated, for example, by the mathematical
relationship between the frequencies of musical tones.
The interval of an octave (from a C to the next C above
it=1:2) and that of a fifth (C to the next G=2:3) were
considered the most harmonious and pleasing. The fact
that a cube has 6 faces, 8 corners and 12 edges, numbers
which are in the same relationship as those musical
intervals, conferred "geometrical harmony" on the cube
and made it special. They loved "perfect" numbers: those
which were equal to their separate factors added
together. For example, 6 (because 6=1+2+3). 28 is
another (1+2+4+7+14=28). (Quick! What is the next such
number? If you can figure that one out, see if you are
still in time to catch the night train to Crotone—some
of the old gang might still be around.) Then, they found
"amicable" numbers: two numbers, each of which is equal
to the factors of the other. 220 and 284, for example,
(because the factors of 284 are 1, 2, 4, 71 and 142,
which add up to 220, the factors of which—1, 2, 4, 5,
10, 11, 20, 22, 44, 55 and 110—equal 284!) Pythagoras,
himself, is said to have discovered those two numbers.
(If you have others of your own, by all means go
first-class. But be careful: as might be expected, they
play a mean game of Blackjack down there. No matter what
Pythagoras does, don't *you* take a hit on 17!)

**Pythagoras, of course**,
is most famous for the geometry theorem which bears his
name and which was the foundation of the groaner at the
beginning of this brief discourse. Of all the
mathematical knowledge attributed to the Pythagoreans,
the most important was the realization that not every
quantity can be expressed in whole numbers. True, if the
shorter sides of a right triangle are 3 and 4, then the
hypotenuse is 5 (3^{2}+4^{2}=5^{2};
that is, 9+16=25), a fact that delighted the
Pythagoreans. But, if the shorter sides are, say, 4 and
5, then the hypotenuse is not a whole number, but winds
up as 6.4031242... , an unwhole number if ever there was
one. This bothered the Pythagoreans and later
generations of mathematicians no end. It doesn't bother
me. Their love of beauty and symmetry and their love of
numbers led members of the Pythagorean school to some
important views about the nature of the universe. One
disciple of Pythagoras, Philolaos, even suggested that
the earth was a planet and, like all other planets, was
in orbit around a "central fire" in the middle of the
universe.

**A** thousand years were
to pass before the fires of knowledge kindled by the
Greeks would be reignited, this time by Arab
astronomers. My big regret is that the Arabs, the
inventors of *al* (the) *jabr*
(reunion of broken parts) did not leave a good story, so
I might have done better in high-school *algebra*.
Maybe I can get some tips from the kids in Crotone. So,
about these t-shirts...

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