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A sheet of A4 paper (which is used commonly outside of the USA) has the following interesting property: when folded in half along its longest dimension, the smaller rectangle is mathematically similar to the original rectangle.
What fraction of a sheet of A4 paper lies inside the largest circle that can be drawn on that sheet of paper? |
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Follow-up ChallengesIf the original piece of paper is a square, what fraction of the paper lies inside the largest circle that can be drawn on the paper?
What if the original piece of paper is a golden rectangle? Describe the dimensions of a sheet of paper such that exactly one-third of the paper is inside the largest circle that can be drawn. Can you find a real piece of paper that (approximately) fits your description? A correspondent from Austin, Texas wondered whether it is possible to construct an "A4 rectangle" with compass and straightedge. What do you think? |
Response VideosMarissa's response video
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