How do I plot a 2d curve and label lattice points to one side of it?
I want to plot the curve $f[x]=\frac{1}{x}$, and draw a solid red dot at every lattice point in the following set: $$\{(m,n)\in \mathbb N^2\colon mn\geq 1\}$$
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1 Answer
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In V10.1 or later, you can use CoordinateBoundingBoxArray to generate the lattice.
With[{m = 5},
Plot[1/x, {x, 0, m},
Epilog -> {
Red, PointSize[Medium],
Point[Flatten[CoordinateBoundingBoxArray[{{1, 1}, {m, m}}], 1]]},
AspectRatio -> Automatic,
PlotRange -> {0, m},
PlotRangePadding -> .15,
Frame -> True]]
answered Jul 23, 2015 at 10:46
Tuples, filter it withSelect, plot withListPlot, combine it with the curve usingShow. $\endgroup$Epilog -> {Red, Point[Flatten[Array[List, {5, 5}], 1]]}to your plot. $\endgroup$