Conclusions and Extensions

Conclusions:

• 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.