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

## 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:- write a mathematical proof for the construction of a circle inscribed in a triangle;
- illustrate the proof with a dynamic figure created with the Geometry Applet.

## Credits

## Cite This Page

### MLA Style

*Science Buddies*. Science Buddies, 20 June 2014. Web. 24 July 2014 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/CompSci_p004.shtml>

### APA Style

*Combining Computer Science and Math: Inscribing a Circle in a Triangle Using the Geometry Applet.*Retrieved July 24, 2014 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/CompSci_p004.shtml

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.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.

This project has two objectives:

- write a mathematical proof for the construction of a circle inscribed in a triangle;
- 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

- The Math Forum at Drexel University has some good advice on how to build a mathematical proof:

http://mathforum.org/library/drmath/view/54693.html - There are many more examples in their FAQ section:

http://mathforum.org/dr.math/faq/faq.proof.html - For help with the programming the Geometry Applet, see:

Getting Started with the Geometry Applet - The Geometry Applet was kindly provided to Science Buddies by its author, Professor David Joyce, who wrote it for illustrating an amazing online edition of Euclid's
*Elements*:

http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

## 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.

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Experimental Procedure

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

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Variations

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

## Share your story with Science Buddies!

I Did This Project! Please log in and let us know how things went.## Ask an Expert

The Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.Ask an Expert

## Related Links

## If you like this project, you might enjoy exploring these related careers:

### Mathematician

Mathematicians are part of an ancient tradition of searching for patterns, conjecturing, and figuring out truths based on rigorous deduction. Some mathematicians focus on purely theoretical problems, with no obvious or immediate applications, except to advance our understanding of mathematics, while others focus on applied mathematics, where they try to solve problems in economics, business, science, physics, or engineering. Read more### Computer Programmer

Computers are essential tools in the modern world, handling everything from traffic control, car welding, movie animation, shipping, aircraft design, and social networking to book publishing, business management, music mixing, health care, agriculture, and online shopping. Computer programmers are the people who write the instructions that tell computers what to do. Read more### Math Teacher

Math teachers love mathematics and understand it well, but much more than that, they enjoy sharing their enthusiasm for the language of numbers with students. They use a variety of tools and techniques to help students grasp abstract concepts and show them that math describes the world around them. By helping students conquer fears and anxieties about math, teachers can open up many science and technology career possibilities for students. Teachers make a difference that lasts a lifetime! Read more## Looking for more science fun?

Try one of our science activities for quick, anytime science explorations. The perfect thing to liven up a rainy day, school vacation, or moment of boredom.

Find an Activity