Download e-book for iPad: Dissections: Plane and Fancy by Greg N. Frederickson

By Greg N. Frederickson

ISBN-10: 0521525829

ISBN-13: 9780521525824

ISBN-10: 0521571979

ISBN-13: 9780521571975

Are you able to reduce an octagon into 5 items and rearrange them right into a sq.? How approximately turning a celebrity right into a pentagon? those are only of the countless demanding situations of geometric dissections, the mathematical paintings of slicing figures into items that may be rearranged to shape different figures, utilizing as few items as attainable. during the a while, geometric dissections have interested puzzle lovers and nice mathematicians alike. listed below are dissections identified to Plato and interesting new discoveries alike. Greg Frederickson explains answer tools rigorously, assuming just a easy wisdom of highschool geometry. This superbly illustrated ebook presents hours of delight for each mathematical puzzle fanatic.

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Extra info for Dissections: Plane and Fancy

Example text

20: Three squares: w = x + y 36 4 . 22. We place the y-square in the upper left corner of the u/-square, and the x-square beneath it. Imagine the remaining part of the u>-square partitioned into three rectangles: an (x x w-x-y)-rectangle below the x-square, a {y x w-y)rectangie to the right of the y-square, and a (u> - x x w -y)-rectangle. 5), then we can change the first two rectangles via P-slides into rectangles that together with the ( w - x x w -y)-rectangle fill in the z-square. 6). 2 twice, first to convert the v^-square and 2-squarc to a vB-square, and then to convert the V3-square and resulting vC-squarc to a 3-square.

5). 2), when z - y, I have found three cases. If x >. 10. Place the two equal triangles (lush against each other and slide them flush against the x-triangle. This gives an irregularshaped piece that we can view as a triangle perched atop a trapezoid. Applying a Q-slide to the trapezoid compresses it to form a base for the triangle. 12. y-triangle. 11, the remaining portion would look like a trapezoid with a small triangle perched on top. 9. If we form a quadrilateral whose boundary coincides with the slide line of the Q-slide, we save a piece, giving the 6-piece dissection.

Then I convert the y-triangle to this quadrilateral in four pieces, using the TT2-strip technique, which we will see in Chapter 12, near the end of the discussion of the triangle-to-square dissection. 9. 9: Three unequal triangles to one: II For three triangles, as for three squares, there are special relationships that facilitate more economical dissections. 5). 2), when z - y, I have found three cases. If x >. 10. Place the two equal triangles (lush against each other and slide them flush against the x-triangle.

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Dissections: Plane and Fancy by Greg N. Frederickson


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