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From
the same authors of the article

Curiopticals,
ISBN 1847322298 
What
are you looking at,
ISBN 1847321836 
Eyetricks,
ISBN 1844427773 
Make
your own 3D illusions,
ISBN 1844426327 
Big
Book of Optical Illusions, ISBN 0764135201 
New
Optical Illusions, ISBN 1844423271 
Fantastic
Optical Illusions, ISBN 184442295X 
Puzzillusions,
ISBN 1844420647 
MateMagica,
ISBN 8889197560 
L'Almanach
du mathématicien en herbe, ISBN 2844690254 


Previous
Puzzles of the Month + Solutions


FebruaryMarch
2007 

Back to PuzzleoftheMonth
page  Home 
Difficulty
level: ,
basic geometry knowledge.
Puzzle # 110 Italiano Français
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!)



Someone
sent us this funny solution...
But,
more seriously, the solution isn't as difficult as
it appears... You have just to change your point
of view (fig. 1)...
...
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.archimedeslab.org
You can reuse 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. 

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