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From the same authors of the article
Sarcone and Waeber
Curiopticals
Curiopticals, ISBN 1847322298
What are you looking at?
What are you looking at, ISBN 1847321836
Eyetricks
Eyetricks, ISBN 1844427773
Make your own 3D illusions
Make your own 3D illusions, ISBN 1844426327
Big Book of Optical Illusions
Big Book of Optical Illusions, ISBN 0764135201
New Optical Illusions
New Optical Illusions, ISBN 1844423271
Fantastic Optical Illusions
Fantastic Optical Illusions, ISBN 184442295X
Dazzling Optical Illusions
Puzzillusions, ISBN 1844420647
MateMagica book
MateMagica, ISBN 8889197560
Almanach book
L'Almanach du mathématicien en herbe, ISBN 2844690254

 

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Previous Puzzles of the Month + Solutions

 
February-March 2007  
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Difficulty level: bulbbulb, basic geometry knowledge.
Puzzle # 110
 Italiano italiano Français francais
Prof. Gibbus' Angle
 
Help Prof. Gibbus find the angle a in the diagram below (solve this puzzle using just basic geometry, no sines or cosines allowed!)

puzzle 110

solution

Someone sent us this funny solution...

fake solution

But, more seriously, the solution isn't as difficult as it appears... You have just to change your point of view (fig. 1)...

puzzle solution

... and look beyond the boundaries of the problem (fig. 2), as suggested in our tips to puzzle solving. Actually, you can find the solution without any calculation! Just extend the grid and draw two lines as shown in the picture, and you'll form a right isosceles triangle having two opposite angles of 45 degrees. The base (or the hypothenuse) of the triangle is parallel to the diagonal (the red line in fig. 2) of the previous 1x3 rectangle. One leg of the right triangle 'intersects' both parallels. A transversal line which intersects a pair of parallel lines produces pairs of alternate interior angles which are EQUALS. So, angle a worths 45 degrees.

The winner of the puzzle of the month is: John REIDY, Australia. Congratulations John!

 

© 2002 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.

You're encouraged to expand and/or improve this article. Send your comments, feedback or suggestions to Gianni A. Sarcone.


Previous puzzles of the month...
contents+solutions
puzzle solver
Puzzle Archive
Jan 07:
triangles to square

Aug-Sept 06:
balance problem

June-July 06:
squared strip

Apr-May 06:
intriguing probabilities

Febr-March 06:
cows & chickens

Dec 05-Jan 06:
red monad

Sept-Oct 05:
magic star

July-Aug 05:
cheese!

May 05:
stairs to square

Febr 05:
same pieces
Sept-Oct 04:
odd triangles

June 04:
pizza's pitfalls

May 04:
Pacioli puzzle...

April 04:
inscribed rectangle

March 04:
magic 4-T's

Febr 04:
a special box

Dec-Jan 04:
curvilinear shape...

Oct-Nov 03:
same area? well...

Sept 03:
square vs rectangle

June 03:
magic bagel

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