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TheEquator |
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TheEquator is an application for plotting graphs of mathematical functions, and is a useful tool for
helping students (or those who are interested in maths in general) to investigate the properties of various
functions visually: Just enter an equation, in the correct syntax, and observe the graph it produces. TheEquator v1.4 (available for download) now allows the user to plot functions in 3D, so that 'y' can be plotted as a function of 'x' and 'z', and the screenshots further down the page show the results from some of these attractive functions. Essentially, TheEquator is a simple 'graph plotter', but work is planned for future versions with a 'fit to data' mode, which means that you will be able to load in an array of points (perhaps from real-life data, ie. experimental results, retail sales, Website stats etc.) and TheEquator will suggest the equation which most closely fits. The eventual result may or may not be informative in every case, but the function is interesting nonetheless. 
Equation Syntax The equation syntax of TheEquator is slightly unusual, but doesn't take long to get used to. The 'basic unit' is the generally accepted line-equation form 'y = mxb + c', where m = gradient, b = power of x, and c = y-intercept (the following equations are all valid: 'x', '2x', '2x^3', '2x+4', '2x^3+4'), but any equation which cannot be expressed in this form must be constructed from brackets. If any brackets are present, then everything needs to go inside brackets which correctly identify the hierarchy of the equation. For example, if you wanted to see the graph 'y = (4x2 + 3)2' you might reasonably type '(4x^2+3)^2' but this will cause an error because of the 'loose' 2. Since everything needs to be described by the 'basic unit', and everything needs to be bracketed if any brackets are present, we need to put a bracket round the 2 (which, in essence, is stored as '2x0+0') and get the correct graph displayed via '(4x^2+3)^(2)'. Other functions can be applied also, such as sin, cos, tan, ln, log, exp and sqrt, and the syntax for these is rather simply 'sin(x)', 'tan(2x)+(3x)', 'sqrt(exp(-x)/cos(4x^3+2))', '(ln((2x)/(3.2x^-3)))^(4)' etc. You do not need to put any brackets before the function declaration (even if you did it wouldn't matter - 'sin(x)' gives identical results to '(sin(x))', '((sin(x)))' etc.), just ensure that the function declaration is placed just before the opening bracket of the intended equation. NOTE: The equation you see written on the graph (ie. 'y=2x^4x') may not actually be the graph that is displayed; due to the way the program understands equations, as previously explained, the graph you see will actually be the graph of 'y=2x^4', ignoring the second 'x', but it will still display the equation string you typed in. Be doubly sure that you use the correct syntax at all times, and remember - if in doubt, stick it in brackets. If you are not 100% sure of your syntax, you cannot be completely confident that the graph is what it says it is. Also note that the equation will still plot successfully if you miss out the final closing bracket - since the program interprets 'no more data' as the close of the last bracket - so '((4x^2)*ln(x)' will execute just as successfully as the correct form '((4x^2)*ln(x))'. As a mild obsessive compulsive, however, I would ask that you close the equations properly so that the graph corresponds correctly to the displayed equation. TheEquator v1.1 Additional Notes A 'z' variable has been included for this latest version, and the same rules apply to 'z' as to 'x' (ie. any 'z'-component of the equation is of the form 'y = mzb + c'). The most important thing to note is that you cannot mix 'x' and 'z' equations inside the same bracket. Again, if in doubt, you can't have too many brackets; separate your equations out into logical sections, and avoid any confusion. 
You can also toggle between 2D and 3D display modes, so if you're only interested in a simple equation like 'y = sin(x)', where the entire z-axis is irrelevant, you don't need to see superfluous parallel plotting of this planar equation. TheEquator v1.4 Additional Notes Versions 1.2 and 1.3 were skipped as new functionality kept being added, so we've gone straight to v1.4 with TheEquator. You are now able to apply filters to the functions (simple filters - where one is multiplied, point by point, by the other - as well as convolution and differentiation filters), and if you include the variable 't' in your equations, you will be able to flick through a series of graphs plotted for the various values of 't'. |
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