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Combining Computer Science and Math: Inscribing a Circle in a Triangle Using the Geometry Applet

Difficulty
Time Required Short (2-5 days)
Prerequisites Must understand the concept and method of a mathematical proof
Material Availability Readily available (laptop computer helpful for live demonstration)
Cost Very Low (under $20)
Safety No issues

Abstract

Here is a project that combines Computer Science and Mathematics. Prove a method for inscribing a circle within a triangle (as shown). You'll also learn how to create an interactive diagram to illustrate your proof, using an applet that runs in your Web browser. If you like solving problems and thinking logically, you'll like this project.

Objective

This project has two objectives:
  1. write a mathematical proof for the construction of a circle inscribed in a triangle;
  2. illustrate the proof with a dynamic figure created with the Geometry Applet.

Credits

Andrew Olson, Ph.D., Science Buddies

Cite This Page

MLA Style

Science Buddies Staff. "Combining Computer Science and Math: Inscribing a Circle in a Triangle Using the Geometry Applet" Science Buddies. Science Buddies, 20 June 2014. Web. 2 Sep. 2014 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/CompSci_p004.shtml>

APA Style

Science Buddies Staff. (2014, June 20). Combining Computer Science and Math: Inscribing a Circle in a Triangle Using the Geometry Applet. Retrieved September 2, 2014 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/CompSci_p004.shtml

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Last edit date: 2014-06-20

Introduction

The illustration below shows a circle, with center at point D, inscribed within triangle ABC. By definition, an inscribed circle is tangent to the three sides of the triangle.
image of a circle, with center point at D, inscribed within triangle ABC

This project has two objectives:
  1. write a mathematical proof for the construction of a circle inscribed in a triangle;
  2. illustrate the proof with a dynamic figure created with the Geometry Applet.

What is the Geometry Applet? It is a very cool program written by Professor David Joyce to illustrate an online version of Euclid's Elements. The applet creates dynamic diagrams in which you can manipulate the geometric figures by clicking and dragging on points. You program the applet much like creating a geometrical construction by hand, so as the points are dragged, all of the essential relationships in the diagram remain intact. It is an engaging and intuitive way to illustrate the generality of your proof. To see an example of the Geometry Applet in action, see any of these three projects:
Throwing You Some Curves: Is Red or Blue Longer?
Thinking in (Semi-)Circles: The Area of the Arbelos
Chain Reaction: Inversion and the Pappus Chain Theorem

To learn how to use the Geometry Applet to create your own dynamic diagrams, see:
Getting Started with the Geometry Applet

Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:
  • the concept of a tangent point,
  • congruent triangles,
  • bisection of an angle.

Bibliography

Materials and Equipment

  • For completing the proof manually, all you'll need is:
    • pencil,
    • paper,
    • compass, and
    • straightedge.
  • For creating a dynamic diagram of the proof using the Geometry Applet, you will also need:
    • a computer,
    • a text editor (Notepad will work fine),
    • a Web browser program (e.g., Internet Explorer or Firefox).
  • For a live demonstration along as part of your display, a laptop computer is recommended.

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Experimental Procedure

  1. Do your background research,
  2. organize your known facts, and
  3. spend some time thinking about the problem and you should be able to come up with the proof.

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Variations

  • Corollary: prove that the lines bisecting the three vertex angles of a triangle share a common intersection point.

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