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Solution
to puzzle #93 

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your comments on this puzzle 



Prove
empirically (without measuring or superimposing
any shape on the other one) that Area of curvilinear
shape A = Area of crossshaped
figure B 
click to
enlarge 

The curvilinear shape (A) is equidecomposable to
2 squares and the crossshaped figure (B) to
a larger square. We can then demonstrate thanks
to the Pythagorean
Theorem that they are of the same area,
as shown in the figure below. During this operation
no pieces are superimposed nor placed side
by side! 

See
also the neat
solution sent by Micheal
Baldus. 

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Previous
puzzles of the month...






Quiz
#3 

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Everyone
has at least one logic or math puzzle that
is his or her favorite. Send
us yours and let all our readers enjoy them!


Puzzle
#1, logic, by G. Kan 
Is
it cheaper to invite (assuming you are
paying...) one friend to the movies twice,
or two friends to the movie at the same
time? 
Rate: ••• 
Solution
#1 

Puzzle
#2, logic, by Theresa Walt 
During
a racing, you passes the runner who is
in the second place. Then, what is now
your current rank? 
Rate: •• 
Solution
#2 




Wasan
puzzles
During the Edo period (l6031867), when Japan was almost
completely cut off from the western world, a distinctive
style of mathematics, called Wasan (和算; "native
Japanese mathematics" in contrast to yosan, "Western
mathematics"), was developed.
Results and theorems were originally displayed in the
form of problems, sometimes with answers but with no
solutions, inscribed on wooden boards and accompanied
by beautiful coloured figures. These problems dealt
predominantly with Euclidian geometry and, true to
wasan preferences, mostly dealt with circles and ellipses. These
boards (see an example below), known as Sangaku
(算額; "mathematical tablet"),
were hung under the eaves in shrines and temples. Later,
books appeared, either handwritten or printed from
handcarved wooden blocks, containing collections of
sangaku problems with solutions. The earliest known
Sangaku tablet was created in 1683.
The samurai remained the dominant creators of sangaku,
consistent with their status of the educated and artistic
caste in Japan. A majority of sangaku are inscribed
in Kambun (漢文), an archaic Japanese
dialect related to Chinese. Kambun was the equivalent
of Latin in
Europe, used during the Edo period for scientific works
and
known predominantly by only the most educated castes.
A
sangaku tablet and some typical
problems 




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ORIGINAL Wunderkammer fact 



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•••
Month's Quote
"Expect
the unexpected."
Heraclitus
•••
Math Gems
Any
squared odd number is a multiple of 8 plus 1
••• 


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