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Magic Triangles, or the Area Paradox (solutions 1)

 
by Gianni A. Sarcone
 
Pages: | 1 || 2 || 3 |
When we place side by side two right triangles of Circea's puzzle, a small one to a large one, we obtain another larger triangle which seems to be a right triangle. But in reality, according to the measures of the illustration 1.a), the angle a can not be equal to 90 degrees. In fact,
a = arctan 7/6 + arctan 5/6 = approx. 89.2 degrees

So, the inscribed rectangle of the squares 2.a) and 2.b) is actually a parallelogram (see fig. 1.b), and according to the way this one is oriented, it changes the square into an irregular octagon (fig. 3)! The fig. 4) is a visual way to demonstrate that the polygon in the fig. 2.b) can not be a square. We understand it at a glance!

visual explanation 1
visual explanation 2
visual explanation 3

Continues on page 3
Back to page 1

 

 

 
© 1992-2007 G. Sarcone, www.archimedes-lab.org
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.
 
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