# Teaching Math with the KDE Interactive Geometry Program

I've written quite a bit about using Linux to help educate people. In the past, I've discussed using Linux to teach astronomy, programming and computer logic design. So today, I'm writing about using the KDE Interactive Geometry (Kig) program to teach mathematics. Kig allows you to use various tools to diagram and demonstrate different mathematical concepts. With Kig, you can draw points, lines, line segments, half lines, vectors, circles and various other conic sections. When Kig refers to a “half line”, it means what I was taught was a ray—essentially a line with one endpoint. Drawing hyperbolic curves on the computer sure beats getting dry-erase marker all over yourself or sneezing because of chalk dust. Even more important though, Kig diagrams are interactive, which means that once you create a diagram, you can move various elements around and see how they behave (more on that later).

Kig's user interface can be a bit deceptive at times. When you first start the program, you are presented with a grid and a group of tools used to create various diagram elements. At this point, you begin to think that the interface is intuitive and that you already “know” how to use it. Then, for a brief moment, you run into trouble. For example, if you try to use a tool to construct a circle given a center point and a line segment as a radius, the program is expecting that the line segment already has been created; you can't create the line segment as part of constructing the circle. After you've used the program for a few minutes, you begin to understand how it “thinks” and things go pretty smoothly.

Thankfully I read the documentation that came with Kig, otherwise, I would have missed out on some of its more powerful features. For example, if you select a curve, say a parabola, from your diagram, you can use the point tool to create a point on that curve. Later, you can drag that point around with the mouse, and it won't leave the curve to which it was constrained. Then, you can use that point to construct other curves, such as a tangent to the curve.

Without reading the documentation, I would have completely overlooked the Add Text Label function that is available by right-clicking on a curve. This function doesn't merely add text to your diagram; there's a text tool for that. The Add Text Label function lets you display information about a curve, such as slope, equation, focus and so on. Once the label has been added to the diagram, you can change various parts of the curve, and the label will reflect those changes.

For example, if you created a parabola through three points, you can add a label that displays the equation of that curve. You also can create a label that displays the coordinates of the points. Then, you can move the points around with your mouse, and see the labels change.

So, what can you do with Kig? Is it just a geometry teaching tool? Kig would be interesting if it were only for teaching geometry, but it can be used for much more. I can easily see how to use Kig to teach algebra, geometry, trigonometry, physics, analysis and calculus.

Let's start with algebra. Figure 1 shows two lines on the Cartesian (X,Y) coordinate plane. Each line is defined by two points, and the coordinates of those points are displayed nearby. The red point in the center is the intersection of the two lines. The equations of the lines also are displayed. By dragging the points around, you can change the lines and explore concepts such as slope, Y-intercept, the solution of an equation and the solution of a system of two equations.

I vaguely remember something from high-school geometry that said “the opposite interior angles formed by two parallel lines crossed by a third, are equivalent.” Figure 2 demonstrates this statement for the case where the angles happen to be 90 degrees. Kig makes it easy to construct two parallel lines. Then, you create a third line that crosses the other two. Finally, you tell Kig to label the angle formed by the various lines. Once this is done, you or your student can change the angles, the distance between the parallel lines and so on—the theorem still holds.

I also remember from when I was in school how obtuse mathematical statements tend to be (particularly those statements related to triangles and the size of their sides and angles), but quite often a picture easily much explains them. Kig would allow you to create an interactive demonstration of each the Euclidean geometry theorems.

Measurements of 30-60-90 do not make a very attractive super model, but they do make a great triangle (at least in Euclidean space, but let's not warp things too much here). Figure 3 demonstrates that the sum of all angles in a triangle is 180 degrees. Once this diagram is constructed, students can drag the angles around and explore any triangle they please.

This also would be a great way to demonstrate the various trigonometric ratios, such as sin, cos and tan. In this case, you simply would construct a right angle, and let the student manipulate the lengths of the sides. Kig could be asked to display the angles and lengths of the sides, and the student then could calculate and verify the various ratios.

But, this is where I found what I think to be one of the weaknesses of Kig. Perhaps I just don't know how, but I was unable to create a triangle and explicitly configure two of the angles. I could drag points to the approximate position I wanted, but I was unable to construct an exact 30-60-90 triangle. It seemed like Kig was keeping the lengths of the sides constant, and thus, when I tried to change the angles, they just didn't “fit”. I think this is important, so if it can be done, please let me know how.

Many concepts in physics can be expressed with what's known as a “vector”. Such things as position, velocity and acceleration can all be expressed as a vector. Kig has rudimentary support for vectors, including vector addition. Figure 4 shows a hypothetical physics problem expressed as the sum of two vectors. Here we have an object moving along a given vector. This object also is being affected by a force, expressed as another vector—gravity in this case. The resulting motion is found by adding the two vectors, as shown.

In analysis, the student begins to learn the features of various curves. Figure 5 gives an example of a hyperbolic curve. I've also included the calculated asymptotes as well as the equation of the curve in both the Cartesian and Polar coordinate systems. Of course, this diagram is completely interactive. Finally, Figure 6 shows a parabola and a tangent line. You also can see the equation of the tangent and watch the equation change as you move the tangent point along the parabola. This could be a nice way to introduce the concept of the differential and, eventually, the derivative in calculus.

Despite a few weaknesses, Kig is a very powerful tool for teaching upper-level mathematics. After climbing a little bit of a learning curve (yes, it's all about curves), both students and teachers can use Kig to have fun learning and teaching mathematics.

Attachment | Size |
---|---|

kig1.png | 13.86 KB |

kig2.png | 6.57 KB |

kig3.png | 11.54 KB |

kig4.png | 7.79 KB |

kig5.png | 15.11 KB |

kig6.png | 7.23 KB |

Mike Diehl is a freelance Computer Nerd specializing in Linux administration, programing, and VoIP. Mike lives in Albuquerque, NM. with his wife and 3 sons. He can be reached at mdiehl@diehlnet.com

## Trending Topics

## Webinar

### Practical Task Scheduling Deployment

July 20, 2016 12:00 pm CDT

One of the best things about the UNIX environment (aside from being stable and efficient) is the vast array of software tools available to help you do your job. Traditionally, a UNIX tool does only one thing, but does that one thing very well. For example, grep is very easy to use and can search vast amounts of data quickly. The find tool can find a particular file or files based on all kinds of criteria. It's pretty easy to string these tools together to build even more powerful tools, such as a tool that finds all of the .log files in the /home directory and searches each one for a particular entry. This erector-set mentality allows UNIX system administrators to seem to always have the right tool for the job.

Cron traditionally has been considered another such a tool for job scheduling, but is it enough? This webinar considers that very question. The first part builds on a previous Geek Guide, Beyond Cron, and briefly describes how to know when it might be time to consider upgrading your job scheduling infrastructure. The second part presents an actual planning and implementation framework.

Join *Linux Journal*'s Mike Diehl and Pat Cameron of Help Systems.

Free to *Linux Journal* readers.

Stunnel Security for Oracle | Jul 28, 2016 |

SUSE LLC's SUSE Manager | Jul 21, 2016 |

My +1 Sword of Productivity | Jul 20, 2016 |

Non-Linux FOSS: Caffeine! | Jul 19, 2016 |

Murat Yener and Onur Dundar's Expert Android Studio (Wrox) | Jul 18, 2016 |

Rogue Wave Software's Zend Server | Jul 14, 2016 |

- Stunnel Security for Oracle
- SourceClear Open
- Murat Yener and Onur Dundar's Expert Android Studio (Wrox)
- SUSE LLC's SUSE Manager
- My +1 Sword of Productivity
- Managing Linux Using Puppet
- Google's SwiftShader Released
- Non-Linux FOSS: Caffeine!
- Parsing an RSS News Feed with a Bash Script
- Doing for User Space What We Did for Kernel Space

## Geek Guides

With all the industry talk about the benefits of Linux on Power and all the performance advantages offered by its open architecture, you may be considering a move in that direction. If you are thinking about analytics, big data and cloud computing, you would be right to evaluate Power. The idea of using commodity x86 hardware and replacing it every three years is an outdated cost model. It doesn’t consider the total cost of ownership, and it doesn’t consider the advantage of real processing power, high-availability and multithreading like a demon.

This ebook takes a look at some of the practical applications of the Linux on Power platform and ways you might bring all the performance power of this open architecture to bear for your organization. There are no smoke and mirrors here—just hard, cold, empirical evidence provided by independent sources. I also consider some innovative ways Linux on Power will be used in the future.

Get the Guide
## Comments

## Sounds like Dr. Geo II

It sounds like this tool is a nice companion to another open source application, Dr. Geo II.

Unlike KIG, DrGeoII seems more suited to elementary geometry, but the diagrams are also fully interactive, and could even be animated.

Perhaps both packages have something they can learn from each other. Thanks for the article.

http://wiki.laptop.org/go/DrGeo

## Thanks Mike! Very

Thanks Mike! Very interesting and useful.