Cancer and Mathematics Module

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Conclusions and Extensions


A figure that appears more disorganized, star-like, or crab-like has a higher perimeter^2 to area ratio
Cancerous cells tend to appear more star-like, or crab-like as evidenced in breast x-ray images.
Studying the traits of images of cells we can make a fairly reasonable decision that more star-like cells, with a higher perimeter^2/area ratio are more likely to be cancerous cells.
Think: Try various ratios out with this figure to experiment with the topics you just learned?

Extensions for the Mathematics Classroom

Describe the ratio of many sided regular polygons....What does the ratio tend toward as the number of sides increases?
Describe the ratio of many sided irregualr polygons (like the star shape) What does this ratio tend toward as the number of sides increases? 
We have explored figures in 2-dimensions. We know that cells are 3-dimensional yet the 2-D image can give us very useful information.
If the ratio r = p^2/a works for 2 dimensional figures, is there an analog to three dimensional figures? Hint: Consider surface area and volume.Consider the shape of a soap bubble. Why do you think a soap bubble is a sphere and not spiky?

Extensions for the Science Classroom

Describe in a general sense what happens as cancer spreads, why are cacnerous cell clusters harmful to the body?
What are the most common forms of cancer? Is there a difference between cancer diagnoses in men and women? What kinds of differences?

Extensions for the Social Studies Classroom

  • What are harmful cancerous agents and how has our modern existence enhanced the possibility of exposure to cancerous agents?
  • Research the history of cancer discoveries. When was the first diagnosis of cancer?
  • Research more information about cancer on the internet and explain how genetics, society, and lifestyle contribute to the incidence of cancer.

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