Engaging Geometry Challenges to Spark Your Curiosity
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Chapter 1 Fun with Geometry Puzzles
With my Norms, Metrics, and Topology exam approaching tomorrow, I find myself overwhelmed by the numerous proofs in my notes. Honestly, I could use a little cosmic luck for the test! Who among us can truly recall what a Hausdorff topological space entails?
In the meantime, let’s dive into a fun geometry puzzle!
I encourage you to pause this article, grab a pen and paper, and give it a shot. Once you feel ready, continue reading for the solution!
Solution to the Puzzle
To solve the puzzle, we define several variables: let "s" represent the side length of the square, "w" denote the width of the paintbrush, and "x" indicate the leg length of one of the congruent unpainted isosceles right triangles. Since half of the square is painted, the other half remains unpainted. Thus, there are four unpainted triangles, each constituting 1/8 of the square's total area.
From this, we can derive the following mathematical relationship:
This leads us to the conclusion that x equals 1/2s.
Next, we recall that "w" is the width of the paintbrush. By examining the equation 1/2w + x + 1/2w = x + w, we can see that this expression equals half the square's diagonal.
Thus, we can further simplify our findings:
Substituting x = 1/2s into our equation, we arrive at:
And there we have it—our solution!
Photo by Andreas M on Unsplash
What a fascinating challenge! I’d love to hear your thought process on this puzzle. Please share your insights in the comments below!
Math Puzzles Worth Sharing
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Happy Solving, Bella 😊
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