Graphing equations using free software GraphCalc
Posted by Greten on 07 Jan 2012 under Free Instructional Applications
There's arithmetic calculator and there is scientific calculator. When I started taking-up calculus classes during college, I was surprised to find out that there's an even higher level of calculator, the graphing calculator.
A graphing calculator allows you to type down equation and it will plot the graph of the said equation. Some of the exercises in our calculus textbook explicitly instruct the use of graphing calculator but our professor never required us to buy one. She is content with just having us plot the graph on paper manually, which I think can be more helpful in the learning process. However, having the means of quickly showing how the graph of certain familiar forms of equations can help the students to be more familiar with them.
You can download it here: GraphCalc - graphing calculator.
GraphCalc is a free open source software (FOSS) that replicates the function of graphing calculator and even more. Aside from presenting graphs based on the inputted function, you can also import the graph as bitmap files. For teachers and instructional designers, it means they could easily sketch a graph with accuracy that truly reflects the equation, which they can use in lesson plans, visual aids, exams, courseware modules and educational games.
- graph functions in 2 dimension (x and y, with y as dependent variable) or in 3 dimensions (x, y, and z, with z as dependent variable)
- put up to 10 function graphs in 2D and up to 6 function graphs in 3D
- change the maximum and minimum range of the graph that is visible at standard zoom
- change the thickness of the graph and of the axis
- show or hide the numbers along the axes
- show or hide grid lines
- option to control the spacing of gridlines e.g., every integer, every even number, every tens, etc.
- both graphs can be zoomed-in or zoomed-out
- the 3D graph can be rotated and viewed from different directions
- save the graph as BMP image file
So far, these are the features that I find useful, in particular in making graphs for mathematics lessons and quizzes.
Limitations and ways to cirumvent them
There are certain features that teachers and instructional designers might need in creating graphs that are not readily available, but can still be used with some little clever tricks:
The equation must be in form y = f(x)
The textbox wherein you could type the equations readily starts with "y =" (appearing as y1: to y10:) and you have to encode only what's on the other side of the equal sign. This calculator will not graph 2x + y = 1. You need to transpose it to y = 1 + 2x. For 3D graph, the equations must be in the form of z = f(x,y).
Graphs only function
As a consequence of having to rewrite equations in terms of y = f(x) or z = f(x,y), we cannot have scenario wherein there are two possible values of dependent variable for just one independent variable (or two independent variables in 3D). That is, all our equations must be functions.
This will make it seem impossible for us to graph equations that are not functions, such as a hyperbola. The solution is to split such equation into two equations that can be considered functions. Using hyperbola again as an example, it's equation can be written in the form of:
If we manipulate this equation to arrive in the form of y = f(x), we will end up with this:
Suppose a = b = 1, we can reduce the equation as:
Since every extraction of square root has two possible results, one positive and one negative, we could split the equations into two:
You can then encode these equations as:
y1: sqrt (x^2 + 1)
y2: -sqrt (x^2 + 1)
To enforce the idea that it is just one graph of one equation, you could make the graphs with the same color by going to 2D Graph --> Equations. Then click the drop down arrow on the far right side of each equation and pick the same color. The result is shown below:
Exports only BMP files
This can be problematic for those teachers who intend to put up their own websites or courseware developers that are into web-based learning modules.
This limitation can be easily remedied by opening it on GIMP (free software), Photoshop or any similar image editing software, Then, use "Save As" or "Export" to save it as JPG, PNG, GIF or whatever format that suits you needs.
Notes in using 3D graph
The range option of the graphs works differently in 2D and 3D Graphs. If you set -10, 10, -10 and 10 as the values of x min, x max, y min and y max (in 2D Graph --> Equations --> Range & Precision), you will only see these as the maximum values visible in the standard view of the graph. When you zoom-out the view, you will still see the graph extending beyond these predefined ranges.
However, in 3D graphs, the generated surface does not go beyond the defined range. The surface generated on the figure above is actually surface of a hemisphere with radius of 10 units. However, the values of x min, x max, y min and y max here are -5, 5, -5 and 5 respectively. Thus, the part of the surface that lies outside the box defind by this range was abruptly cut.
For some unknown reason, in generating hemisphere, the surface appears to be missing some piece, like some sort of broken glass near the x-y plain, as shown in the picture above. I do not know what's causing this, if there's anyway to fix this, or if the programmers of this software, Mike and Brendan, did this on purpose. Maybe they do not want to totally hide the grid?
GraphCalc is a quite old software and its official website shows that it latest version was on November 2003. I was still working on my college thesis during that time. I'm not sure if it is still receiving any support from its programmers but maybe they still do, judging from the fact that the website is still up. Someone must be paying for the hosting.
While the software was last updated in 2003, I just installed in in Windows 7 and it is still working just fine. I was suppose to download the Linux version but when I noticed that it is still in version 0.0.1 with with 53KB installer (compare to Window's version 4.0.1 with 856KB installer), I decided not to try it. Instead, if you are using Ubuntu, one of the well-known forks of GNU/Linux, I would recommend that you use KAlgebra instead.
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