This link at wikipedia about Rational trigonometry is interesting as it is more sensible than correlating circles to triangles, but it still leaves something to be desired. It have considered how to get rid of sqrt(-1) and I have found no solution yet. I did think of something that is useful that I will take advantage of in my program.
The idea is to graph functions like Ω or' Big O' notation on a scale that is the inverse of functions. If y=f(n) and f(n) is x2 , then the x axis is sqrt(n) and as a result the graph can be displayed as a line and where it curves up and down shows that it is outside the bounds of the function. I imagine I could use a color to indicate it had wandered outside a specific reasonable error range. I could even do a piped least squares channel. There are log10 graphs and why not show something that relates information. What information do you get from a graph that wiggles all over the place and represents no usable solution to the complexity of the data. I think it is a much better way to represent data in a human usable form.
I know XKCD and others have a jokes about complex graphs, but I am too lazy to link to them. I thought of one while I was typing this, : A salesman is showing the sales figures for the month and the graph is in the shape of a fish. PHB senses something fishy about the results.
It seems to make more sense than when I started thinking about it. A log graph of a data set shows that it conforms to log and that is not evident in any other graph. In that same way, would you be able to tell if a function was bounded in or x2 or x3, unless it was plotted against its inverse? I doubt that many people are able to plot the derivative of all the points of a curve and determine if they lie out side some standard deviation by just looking at a curve.
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