searching_and_sorting.nb

A bit about ListPlot[] and Fit[]

Just so you see how to collect and display results, the ListPlot function generates the pictures.
It takes as data {x,y} points in the form { {x1,y1}, {x2,y2}, ... }. Everything else is an option.

{AspectRatio1/GoldenRatio, AxesAutomatic, AxesLabelNone, AxesOrigin ... , Prolog {}, RotateLabelTrue, TextStyle$TextStyle, TicksAutomatic}

Here's how you might generate a bunch of numbers to plot.

( 1 1 ) 2 3 3 5 4 7 5 ... 9 6 11 7 13 8 15 9 17 10 19

Or, if you have all the x's and then all the y's, you can flip them around.

Generating the plot is just

[Graphics:../HTMLFiles/index_156.gif]

Though there are many options you can apply.

RowBox[{pointPlot, =, RowBox[{ListPlot, [, RowBox[{data, ,, , AxesLabel {" ... owBox[{RowBox[{PointSize, [, 0.02, ]}], ,, RGBColor[1, 0, 0]}], }}]}]}], , , ]}]}]

[Graphics:../HTMLFiles/index_159.gif]

To find an equation that matches the points, you can use Fit[], which also has a bunch of variations. For a polynomial fit,

$Fit[data, {1, x, x^2, x^3}, {x}]$

$RowBox[{RowBox[{-, 1.}], +, RowBox[{2., , x}], +, RowBox[{1.78569*10^-16, , x^2}], +, RowBox[{1.01033*10^-17, , x^3}]}]$

which gives some tiny numbers due to round-off errors. But we can get rid of them with Chop.

$bestFit = Chop[Fit[data, {1, x, x^2, x^3}, {x}]]$

Here's what that function looks like.

[Graphics:../HTMLFiles/index_166.gif]

And here are both plots shown together with a label.

Show[pointPlot, linePlot, Graphics[Text["Dots and a line.", ... PlotRange {{0, 12}, {0, 20}}, PlotLabel->"Cool, eh?"]

[Graphics:../HTMLFiles/index_169.gif]

Created by Mathematica (September 29, 2004)