So, after 10 years of wanting to study the book that Ramanujan relied upon for a lot of his early strides in mathematics, it's 2012, and the book is finally online.
To celebrate, I want to go through each of the propositions using my command line, finding a way to interact with each one.
octave syntax, first one is
a^2 - b^2 = (a-b) * (a+b)
That's familiar from algebra, of course.
For now, I just want to be able to make a picture of this difference of squares.
I've looked at gnuplot, and it doesn't seem to be designed to do simple geometric shapes.
NB: I don't want to plot the function
f(x, y) = x^2 - y^2. I want to draw two squares of a given size in different colors, one inside the other, to illustrate the difference of squares graphically.
What I'd like to be able to do is type something like
$plotsquare --center origin --colors=black,gray black=8x8 gray=3x3 -q -o plot.png
'black' being an 8x8 square, 9 being a 9x9 square; the gray square inside the black square illustrates the difference of squares.
Does anything like that exist?