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BioLab 2
Exercise 2
Insect Mathematicians
Objectives:
- To explore how insects display mathematical principles.
- To utilize the Internet as a tool to learn more about mathematics in the insect world.
- To examine and analyze mathematical principles in ants and beetles.
- To submit answers in writing to your instructor based on your observations and calculations.
Materials:
- A computer.
- Internet access through an Internet service provider (ISP),
and a browser such as Netscape Navigator.®
- A calculator.
- Pen and paper.
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Background:
- There are many mathematical concepts that appear in biological systems. Two of these concepts will be explored in this exercise: Buffon's Needle Algorithm and Voronoi Diagrams.
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Methods:
- Comte de Buffon (1707-1788) was a mathematician who is known for two major contributions: translating into French Newton's Methods of Fluxions and the "Buffon's Needle Problem" in the theory of probability. (A History of Mathematics, Carl. B. Boyer, 1968, John Wiley & Sons, Inc., New York)
The Buffon's Needle Algorithm provides an estimate for the value of Pi, the ratio of a circle's circumference to its diameter (Pi=C/d). In biology, ants of the species Leptothorax albipennis follow this algorithm to assess potential new nest sites. Go to the following two web sites to read
and learn about the Buffon's Needle Algorithm and its application to ants. Then return to this page to continue.
Buffon's
Needling Ants
Based on what you have read, you now know the theory behind the Buffon's Needle Problem and its application to ants.
Go back to the
Buffon's Needling Ants web site. Select the needle simulation exercise, and work the problem.
Submit your work to your instructor via email.
- A Voronoi Diagram of a set of points is a collection of regions that divide up a plane. Each region is associated with one of the points. All the points in one region are closer to the associated point than to any other point.
Voronoi diagrams can be applied to studying animal territories, in particular, beetle entrance points into the bark of a tree. Go to the
Voronoi Diagrams in Biology
web site to read and learn more about these mathematical diagrams and their application to a biological system of beetles. Then return to this page to continue.
Now that you have read Jeremic Zdravko's paper, what do you think? Do you agree with his ideas on the application of Voronoi Diagrams to beetles? Answer in essay form and submit your work to your instructor via email.
Additional Links:
- Mathematics in Biology
- Math in Medicine and Biology Problems
- Society for Mathematical Biology
- Topics in Mathematical Biology
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