The Importance of Margins - Task
Occasionally, the book's margins can be more important than the book itself. The mathematician Fermat 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.
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.
Book 2:The width of top, bottom, and outer margins is 2 cm. The width of the inner margin is 4 cm
- For each book describe the different design options that satisfy all requirements.
- For each book find a design that makes the text area as large as possible.
- 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.