1. The picture below shows a variant of a famous paradoxical puzzle. On the left, we take two rectangles of area 60, and cut each one into two pieces. On the right, we rearrange the four pieces, and put them together into a single rectangle of area 119. How could this be? 11 (a) Explain what's wrong. (Similar paradoxes can be found under names such as "Chessboard paradox" or "Missing square puzzle". It's fine to look at a source that explains such a paradox, provided you cite it and explain it in your own words.) (b) Although two 5 x 12 rectangles cannot really be rearranged into a 7 x 17 rectangle, it is possible to take two a × b rectangles and cut them as shown in the picture above to make a cxd rectangle, with no paradox. What should the lengths a, b, c, d be (up to scaling, of course)? (c) It is also possible to take three congruent rectangles, cut each one into two pieces, and rearrange them to form a single rectangle similar to the original three. How can we do this? Try to find an answer that lets you create a paradoxical decomposition of your own!

1. The picture below shows a variant of a famous paradoxical puzzle. On the left, we take two rectangles of area 60, and cut each one into two pieces. On the right, we rearrange the four pieces, and put them together into a single rectangle of area 119. How could this be? 11 (a) Explain what's wrong. (Similar paradoxes can be found under names such as "Chessboard paradox" or "Missing square puzzle". It's fine to look at a source that explains such a paradox, provided you cite it and explain it in your own words.) (b) Although two 5 x 12 rectangles cannot really be rearranged into a 7 x 17 rectangle, it is possible to take two a × b rectangles and cut them as shown in the picture above to make a cxd rectangle, with no paradox. What should the lengths a, b, c, d be (up to scaling, of course)? (c) It is also possible to take three congruent rectangles, cut each one into two pieces, and rearrange them to form a single rectangle similar to the original three. How can we do this? Try to find an answer that lets you create a paradoxical decomposition of your own!

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.CR: Review Problem Set

Problem 35CR

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