Science Buddies will be down while making upgrades, beginning Thursday July 30, 2015 at 9:00PM PST for a few hours.
We apologize for any inconvenience!

Combining Computer Science and Math: Circumscribing a Circle about 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 circumscribing a circle about 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 that circumscribes a triangle;
2. illustrate the proof with a dynamic figure created with the Geometry Applet.

Credits

Andrew Olson, Ph.D., Science Buddies

MLA Style

Science Buddies Staff. "Combining Computer Science and Math: Circumscribing a Circle about a Triangle Using the Geometry Applet" Science Buddies. Science Buddies, 20 June 2014. Web. 29 July 2015 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/CompSci_p007.shtml>

APA Style

Science Buddies Staff. (2014, June 20). Combining Computer Science and Math: Circumscribing a Circle about a Triangle Using the Geometry Applet. Retrieved July 29, 2015 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/CompSci_p007.shtml

Share your story with Science Buddies!

Last edit date: 2014-06-20

Introduction

The illustration below shows a circle, with center at point D, circumscribed about triangle ABC. This is the circumcircle of the triangle, and point D is the circumcenter of the triangle. By definition, the points A, B, and C all fall on the circumference of the circle.
This project has two objectives:
1. write a mathematical proof for the construction of a circle circumscribed about 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:
• circumcircle,
• circumcenter,
• congruent triangles,
• bisection of a line segment.
Question:
• In general, there are three possible positions for the circumcenter of a triangle, relative to the triangle itself. What are the three positions? What property of the triangle is associated with each position of the circumcenter?

News Feed on This Topic

, ,
Note: A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed

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.

Experimental Procedure

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.

Share your story with Science Buddies!

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.

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

News Feed on This Topic

, ,
Note: A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed

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.