Why does a Calc square root plot have a kink?

[David.Cheshire]

If I make a linear sequence of numbers e.g. from 100 to zero step -10, then take the square root of each number and make a chart of these square roots, it has a kink around 9 and 10. I can’t upload an example sorry, but here is the data:

Sequence Sqrt()
100 10
90 9.48683298050514
80 8.94427190999916
70 8.36660026534076
60 7.74596669241483
50 7.07106781186548
40 6.32455532033676
30 5.47722557505166
20 4.47213595499958
10 3.16227766016838
0 0

The chart of the Sqrt() column has a downward kink at 9 on the x axis, followed by an upward kink before 10. Why is this?

[librebel]

Hello David Cheshire,
i could not reproduce your problem in Calc Version: 5.1.6.2, plz specify which Chart Type produces the kink

[Lupp]

I suppose the chart was “x-y (Scatter)” what is the common way to visualize mathematical functions…
You may have chosen ‘Straight’ for the line type, but expect it ‘Smooth’ nonetheless?

Please note: The diagram of the SQRT function in mathematical mode is a half parabola (divided by the axis of symmetry). The curvature of a parabola has a prominent maximum at its vertex. Even if you choose smooth line type, the chart may look somehow “kinky” if the resolution of the x-axis is not adequate. 10 steps for all the graph is simply too coarse if you put the diagram in a “normal” size, and look at it from a “normal” distance.
See also this demo.

[David.Cheshire]

Hi Lupp, thanks for your answer. It makes no difference whether I choose a normal line or an xy scatter, and I had selected smooth rather than straight, but you are correct, the step size was too big. When I use smaller steps the curve is smoother. Which is something I didn’t expect, I anticipated that the curve smoothing algorithm would produce a smooth curve, but evidently it doesn’t. Something to remember for sparse data sets!

[Lupp]

Quoting @David.Cheshire: “It makes no difference whether I choose a normal line or an xy scatter…”
If you want reasonable lines the ‘Scatter’ type is the only one usable. The ‘Line’ type you call “normal” is for misuse by those not understanding charts - or for deception. Only in the case of equidistant x values it makes sense and does then produce the same result as the ‘Scatter’ type.

[Lupp]

Actually the curve you get with option ‘Smooth’ is smooth. However, the algorith is fortunately not from AI labs. It cannot know therefore that you wanted the line to be a half parabola. For someone having the parabola in mind the result is not satisfactory. But there are many types of curves in the world.

[David.Cheshire]

Hi Lupp, thanks, in this case the x values were equidistant so I could use either a line or scatter chart. Is it possible to change the default chart settings?

[Lupp]

" Is it possible to change the default chart settings?"
I don’t know a way, and most likely there is none.

[David.Cheshire]

OK, thanks.