Onmatu- General Math Learning Article

The three squares math problem


       So I went to a job fair some time ago and I found there a new math challenge which is called "the three squares problem" or the "the three squares puzzle". So you have three squares like in the image of this article and you need to find the sum of the three angles A, B and C. Now this math problem can be solved with or without trigonometry and most challenging part is to solve it without trigonometry. The beauty of this math puzzle is that it can be solved in many ways applying different simple concepts of basic geometry and trigonometry.  I think I found 5 or 6 different ways of solving it so far. I have spent some time thinking about this math puzzle like 3-4 days or more and I don't regret anything. You should try to solve it also.  Of course you can find many of the solutions online, but this is not the goal of my article and of this challenge. 
       This is by far one of the most interesting math puzzle I met so far in my life. If you will be able to solve it in more than one way and I fully recommend you to do so you will be delighted with the results and the struggle will improve your imagination, creative and critical thinking and the ability to think out of the box. Finding as many solutions as you can will improve also your perseverance habit, motivation and self study habit. You can have many benefits from solving this one. It can be extended also for four squares, five squares and so on and see what results do you get and if this rule stays the same. Concepts involved here are angles formed by parallel lines cut by a transversal line, congruent and similar triangles, right angle triangles and their properties, the elementary trigonometric functions and their reciprocals and so on, even the properties of angles inscribed in a circle and the properties of arcs of circle. But i am sure you can find many more.  
        For the math lovers of all ages the puzzle can be an exciting one. Try it. Thank you for reading this article.    
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