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Solution
to puzzle #92 

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Prove
empirically (without measuring or cutting)
that Area of square A = Area of rectangle
B 


Report rectangle B on
a vertex of square A as
shown, and draw lines to extend the
sides of both quadrilaterals to form
a larger rectangle R whose
height is the sum of the heights of A and B,
and whose width is the sum of the widths
of A and B.
If the diagonal connecting the corners
of R that are not touched
by A and B goes
through the point where A and B meet,
they have the same area.
For more info see "Visual
proof", April 2001. 


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Quiz
#2 

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Puzzle
#3, logic, by Kh.
Guili 
Why
is it very common to have a 9 minute
snooze interval on alarm clocks and not 10 instead? 
Rate: •••• 
Solution
#3 

Puzzle
#4, logic, by Augusto
P. 
50
ants are dropped on a 2meter stick. Each
one of them is traveling either to the
left or to the right with constant speed
of 1 meter per 1/2 minute. When 2 ants
meet, they bounce off each other and reverse
direction. When an ant reaches an end of
the stick, it falls off. What is the longest
amount of time to wait that the stick has
no more ants? 
Rate: •• 
Solution
#4 




The
Radical Symbol
A square root of x is
a number r such that r^{2} =
x. Square roots are also called radicals or surds.
Any positive real number has two square
roots: one positive and one negative. For
example, the square roots of 9 are 3 or
3.
Before
symbols, the words "roots" or "side" were
commonly used for the square root of a
number. Arab writers thought of a square
number as growing out of a root, so Arabs
often used the word radix, "extracting",
or pulling out, the root. Latin writers
thought of it as "finding" the latus,
or side of a square.
Late medieval Latin writers turned radix
into a single symbol R_{x}. This
symbol was introduced by Leonardo Fibonacci
(1170) and was used for more than two hundred
years. The French writer Nicolas Chuquet
(1484) sometimes used R_{x}^{2} for
R_{x}, R_{x}^{3} and
R_{x}^{4} for cube and
fourth roots, respectively.
The symbol was
introduced by Christoff Rudolff in 1525
in his book Die Coss (the reason
for this strange book title is that cosa,
an Italian word, is a thing which
was used for the unknown. Algebraists were
called "cossists", and algebra
the "cossic art", for many years!).
It is believed this symbol was used because
it resembled a small r (radix) at the time.
Rudolff's symbol was not immediately used.
The letter l (latus, "side")
was often used. For example the square
root of 4 was l4 and the third
root of 5 was lc5. By the seventeenth
century, the square root symbol was being
used regularly even though there were many
ways the indices were written for higher
roots.
To conclude, here are some abbreviations
in use in the XVth century for the various
powers of the unknown, namely:
"cosa" = r (= x),
"censo" = c (= x^{2}),
"cubo" = b (= x^{3}),
"censo di censo" = cc (= x^{4}),
"cubo relato cosa" = br (= x^{5}),
and "cubo di cubo cosa" = bb (= x^{6}).

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•••
Month's Quotes
Life
looks like 2 locked boxes, each containing the others
key...
•••
"Always
live within your income, even if you
have to borrow money to do so."
Josh Billings
•••
Math Gems
(1+5)/2
=1.618...
Golden number
••• 

Vanishing
egg 
