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Why is this graph both continuous and discrete?

Viorel Negoita

I just installed Mathematica on a Raspberry Pi and I am playing around and I run into this. If I do the graph up to 34, I see discrete steps. Over 35, I start to see a mix of discrete steps and continuous line. This case below, with the graph going from 1 to 50 is a good example. Why is the line changing from steps to continuous, back to steps and back to continuous? changes the 50 to 34 and it looks only steps.

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Gianluca Gorni

Compare:

Plot[Sum[i, {i, 1, n}], {n, 1, 50}]
Plot[Sum[i, {i, 1, Floor[n]}], {n, 1, 50}]
Plot[Evaluate@Sum[i, {i, 1, n}], {n, 1, 50}]

When you evaluate Plot[Sum[i, {i, 1, n}], {n, 1, 50}], floating points values of n are replaced into Sum[i, {i, 1, n}], giving something like, for example,

Sum[i, {i, 1, 20.4}]

The variable i then takes the values 1,2,3,... until 20 and then stops. This accounts for the steps in the plot. The parts in the plot without steps are probably where the refining algorithm does not feel the need to insert further points, because it did not detect a sharp curvature at its first attempt.

With Evaluate@Sum[i, {i, 1, n}] the sum is replaced by 1/2 n (1 + n), which gives a smooth curve.

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Jim Baldwin

There are not enough PlotPoints. Try

Plot[Sum[i, {i, 1, n}], {n, 1, 50}, PlotPoints -> 100]

or

ListStepPlot[Table[Sum[i, {i, 1, n}], {n, 1, 50}]]

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