Graphic design
The importance of margins
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| Pierre de Fermat |
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Occasionally, the book's margins can be more important than the book itself. The mathematician Pierre de Fermat (1601-1655) used the margins of one of his
books to scribble a mathematical result known today as "Fermat's Last Theorem." He added
the he had found a wonderful proof for that result, but that there was not enough room in the margins to describe it.
For the next 300 years, many mathematicians tried to prove Fermat's theorem (a conjecture, really) without success. Only in 1995 did Andrew Wiles finally succeed in proving the theorem. If Fermat had enough space in the margins, the history of mathematics might have been different. So perhaps math books should be designed with
especially ample margins...
Fermat also made important contributions to the study of optimization problems, that is,
problems in which we seek the best among diferent options. The present task presents
optimization problems involving page design.
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This task asks that you design two books, both with
a margin area of 300 square centimeters.
Book 1:
The width of margins on all sides is 3 cm.
(The dynamic figure below shows different designs that satisfy the requirements of a margin area of 300 square cm and a margin width of 3 cm all around.)
Book 2:
The width of top, bottom, and outer margins is 2 cm.
The width of the inner margin is 4 cm.
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Investigate different options for design
For each book describe the
different design options that
satisfy the requirements for both the total margin area and the
margin widths.
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For each book find a design that makes the text area as large as possible. Show pictures of your designs (use the
Page Design tool to do it).
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Generalize the investigation to the case of any given margin area and any given margin widths. Find general expressions for page height and width that maximize the text area.
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