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eureka!!!
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corner top left Previous Puzzles of the Month + Solutions  
December 2003-January 2004  

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logo puzzle of the month 1 Puzzle #93
Quiz/test #3 logo pzm 2
logo pzm 3 W-kammer #3
   Enjoy solving Archimedes' Lab™ Puzzles!

Solution
to puzzle #93
Send us 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 cross-shaped figure B puzzle 93
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francais/italiano

The curvilinear shape (A) is equidecomposable to 2 squares and the cross-shaped 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!
solution puzzle 93
See also the neat solution sent by Micheal Baldus.
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Previous puzzles of the month...

 

Quiz #3
Send us your comments on this
Test your math knowledges online
1. I buy a watch for 100 $, then I sell it at 120 $. I repurchase my watch for 140 $ and, finally, I sell it again at 160 $. How much did I earn? 2. The area of a square of 100 is equal to 2 smaller squares. The side of one is 1/2+1/4 the side of the other. Find the side of both squares... 3. 80% of 125% is...
a) 30 $
b) 10 $
c) 40 $
complete
a) 100%
b) 95%
c) 105%

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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!


Posted puzzles
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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

Wunderkammer #3
Puzzling facts

sangaku 1Wasan puzzles
During the Edo period (l603-1867), 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 hand-carved 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.

sangaku tablet
A sangaku tablet and some typical problems
sangaku 1b sangaku 2
sangaku 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!
•••
Month's Quote

"Expect the unexpected."
Heraclitus
•••

Math Gems

Any squared odd number is a multiple of 8 plus 1
•••
optical illusion

Vanishing egg

 

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