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1981•The Arithmetic TeacherRequires access

Putting an Old Puzzle to Work

Joseph P. Donegan, John D. Pricken

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Abstract

Many teachers are familiar with the mathematical puzzle that consists of cutting apart an 8-by-8 square piece of paper and rearranging the pieces into another rectangular shape that has a different area. This puzzle is demonstrated in figure l. It seems the area of the square is 64 square units while the area of the rectangle is 65 square units. The question is, Where does this extra square unit come from?

About this research paper

What this paper is about

Many teachers are familiar with the mathematical puzzle that consists of cutting apart an 8-by-8 square piece of paper and rearranging the pieces into another rectangular shape that has a different area. This puzzle is demonstrated in figure l. It seems the area of the square is 64 square units while the area of the rectangle is 65 square units. The question is, Where does this extra square unit come from?

Why it matters

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Key contribution

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Method / approach

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Available abstract

Many teachers are familiar with the mathematical puzzle that consists of cutting apart an 8-by-8 square piece of paper and rearranging the pieces into another rectangular shape that has a different area. This puzzle is demonstrated in figure l. It seems the area of the square is 64 square units while the area of the rectangle is 65 square units. The question is, Where does this extra square unit come from?

Key concepts: Square (algebra), Rectangle, Unit square, Mathematics education, Unit (ring theory), Mathematics, Arithmetic, Work (physics)

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