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7 - First Steps

Published online by Cambridge University Press:  05 August 2012

Greg N. Frederickson
Affiliation:
Purdue University, Indiana
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Summary

Down two levels in the sub-basement, the librarian unlocks first the door to the special collection and then the cabinet door. Retrieved from within is a substantial leather-bound volume, the third in the collected works of Girolamo Cardano, containing De Rerum Varietate. The thick pages are in good condition, sa ve for the bleedthrough of the print. The volume has survived for over three centuries, outlasting so many, many people. And before its printing in 1663, its contents had survived a century from their penning in 1557. Cached amidst a variety of things is an illustration of how to cut a (2a × 3b)-rectangle into just two pieces that rearrange into a (3a × 2b)-rectangle. The Latin text now obscures an explanation. Written by a man who embraced the then-new notion of shared knowledge, his contribution has endured to lie buried in a basement, locked within a room, within a cabinet, within a now-dead language.

The dissection Cardano (1663) described is an example of the step technique, so named because of the resemblance to stair steps. In its simplest form, the step technique cuts a rectangle in a zigzag pattern, alternating horizontal cuts of one length with vertical cuts of another. By shifting the two resulting pieces by one step relative to each other, we form a different rectangle. Figure 7.1 illustrates the case for converting a (3a × 4b)-rectangle to a (4a × 3b)-rectangle.

Type
Chapter
Information
Dissections
Plane and Fancy
, pp. 60 - 70
Publisher: Cambridge University Press
Print publication year: 1997

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  • First Steps
  • Greg N. Frederickson, Purdue University, Indiana
  • Book: Dissections
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511574917.008
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  • First Steps
  • Greg N. Frederickson, Purdue University, Indiana
  • Book: Dissections
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511574917.008
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • First Steps
  • Greg N. Frederickson, Purdue University, Indiana
  • Book: Dissections
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511574917.008
Available formats
×