Shortcuts
 
sitemap
 SiteMap
shop
 Shop
books
 Books
syndication
 Print Syndication
galleries
 Galleries
Archimedes Journal
 A'Journal
e-cards
 E-cards
games
 Games
newsletter
 N'Letter
email
 E-mail

eureka!!!
corner

corner top left

Magic Triangles, or the Area Paradox

 
by Gianni A. Sarcone
 

"La sapienza è figliola della sperienza. Fuggi i precetti di quelli speculatori, che le loro ragioni non son confermate dalla isperienza"
Leonardo da Vinci


Pages: | 1 || 2 || 3 |
Cut out a square of 12 units per side into 8 triangular pieces, as shown below (fig.1). We can rearrange these 8 right triangles together to form some square variants. Further below you will find 4 possible configurations. The first configuration is a real square (fig. 2.a); the second one (fig. 2.b), though it seems to be a square is not a square at all! Can you say why this is so? The last examples (fig. 2.c and 2.d) are squares but with extra protruding triangular elements! Compare them to the square of the fig. 2.a). What is wrong?

fig.1Circea puzzle
The 8 triangles of the Circea's Puzzle
Circea triangles
The 4 possible configurations
examples
(This 8-piece puzzle, called Circea's puzzle and created
by G. Sarcone, is copyrighted: © 1992-2007)

arrow  solution + more exciting vanishing area paradoxes

 

 
You can re-use content from Archimedes’ Lab on the ONLY condition that you provide credit to the authors (© G. Sarcone and/or M.-J. Waeber) and a link back to our site. You CANNOT reproduce the content of this page for commercial purposes.  
transparent gif
recommend Suggest this page to a friend | facebook Follow us on Facebook | comment Report any error, misspelling or dead link
Archimedes' Laboratory™ | How to contact us
| italian flag Come contattarci | francais flag Comment nous contacter
line
About Us | Sponsorship | Press-clippings | Cont@ct | ©opyrights | Tell-a-friend | Link2us | Sitemap
© Archimedes' Lab | Privacy & Terms | The web's best resource for puzzling and mental activities
spacer spacer corner right bottom