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Delving Deeper: Enumeration of Rectangles in a Tableau Shape
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The Mathematics Teacher article “Keep Counting Those Boxes—There's More” (Grassl and Mingus 1998) illustrated the ways a problem can be extended to create further problems to explore. In analyzing the question “How many squares of all sizes does a checkerboard contain?” the authors tackled the fairly natural extension “How many rectangles does a checkerboard contain?” and then, finally, the question “How many rectangles does a subdivided rectangular m-by-n grid contain?” The authors were able to show that the answer is given by.
National Council of Teachers of Mathematics
Title: Delving Deeper: Enumeration of Rectangles in a Tableau Shape
Description:
The Mathematics Teacher article “Keep Counting Those Boxes—There's More” (Grassl and Mingus 1998) illustrated the ways a problem can be extended to create further problems to explore.
In analyzing the question “How many squares of all sizes does a checkerboard contain?” the authors tackled the fairly natural extension “How many rectangles does a checkerboard contain?” and then, finally, the question “How many rectangles does a subdivided rectangular m-by-n grid contain?” The authors were able to show that the answer is given by.
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