# Periodic spiral graph interpretation

Gold Member
Summary:
Is this graph spiral or merely polar?
Could someone explain the geometry of this graph?
• Why does the radial distance vary non-uniformly? To-wit: Distance from origin to Nov 2020 is much larger than Nov 2020 to Nov 2021
• Why are there two areas - one above and one below - the centre line?
https://www.nytimes.com/2022/01/06/opinion/omicron-covid-us.html

Mark44
Mentor
Summary:: Is this graph spiral or merely polar?

Could someone explain the geometry of this graph?
• Why does the radial distance vary non-uniformly? To-wit: Distance from origin to Nov 2020 is much larger than Nov 2020 to Nov 2021
It's spiral, and the only reason for doing it this way is to convey the information in less space than a linear graph would take. The radial distance varies, I believe, to leave room for the bulging sections.
Why are there two areas - one above and one below - the centre line?
To display the data for 1) Apr to Oct of 2020, and 2) for Apr to Oct of 2021.

Don't overthink this...

DaveE
Gold Member
To display the data for 1) Apr to Oct of 2020, and 2) for Apr to Oct of 2021.

Don't overthink this...
No, I mean why is it symmetrical about the centerline? This is common in graphs that differentiate gender - having male on one side and female on the other, but I doubt that the case here.

Gold Member
The radial distance varies, I believe, to leave room for the bulging sections.
Except it doesnt do that.

FactChecker
Gold Member
No, I mean why is it symmetrical about the centerline?
I think that is just a decision that the graph-maker made. It may have no significance at all, except that someone thought the graph looked better that way (and I tend to agree).

Mark44
Mentor
No, I mean why is it symmetrical about the centerline?
Because that's how the person who made the graph wanted it.
Except it doesnt do that.
Sure it does -- look how fat the sections for January are.

Again, don't overthink this.

Gold Member
Sure it does -- look how fat the sections for January are.
Yet the biggest gap between 2020 and 2021 is in October.

Anyway, I grant your point. So much visualization opportunity lost. I will just have to out this rendering down as an affront to the god of graphs.

mfb
Mentor
It's weird. The width of the path is the daily cases, the angle is the time in the year, the distance to the origin seems to have no significance.

berkeman
Mentor
IMO, it looks like some intern at the NYT had way too much time on their hands, and basically hand-drew a graph to try to visualize the data. There are clear non-symmetries that suggest the hand-drawn aspect. Whatever.

Gold Member
There are clear non-symmetries that suggest the hand-drawn aspect.
Are you sure that's an asymmetry? The curve on the bottom will have will appear to have an amplified amplitude, because its ... er ... x-axis is compressed.

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mfb and berkeman
berkeman
Mentor
Are you sure that's an asymmetry? The curve on the bottom will have will appear to have an amplified amplitude, because its ... er ... x-axis is compressed.
Whelp, if I were an intern trying out different graphing schemes and saw that apparent misinformation in my graph, I'd change to a single-sided representation... Interns, kids, what'cha gonna do...

Gold Member

berkeman
Mentor
Wait, so YOU are the intern?

mfb
Gold Member
Wait, so YOU are the intern?
What? No.
I just Photoshopped the diagram.

When you see the lines that are perpendicular to the curve, the asymmetry disappears.

These circles are centred on the central black line. Their radii touch both red curves. So upper and lower red curves are symmetrical about the black central line.

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berkeman
OmCheeto
Gold Member
It's weird. The width of the path is the daily cases, the angle is the time in the year, the distance to the origin seems to have no significance.
Comparing their graph to an Archimedean spiral(r = aθ + b), I found that if I shift their graph to the right by ≈58 pixels, it comes out pretty close.

DaveC426913
Gold Member
Comparing their graph to an Archimedean spiral(r = aθ + b), I found that if I shift their graph to the right by ≈58 pixels, it comes out pretty close.
Huh. I guess the asymmetry of the spiral is also an optical delusion.

OmCheeto
Gold Member
Huh. I guess the asymmetry of the spiral is also an optical delusion.
Possibly. I notice that if I fiddle with the constants for the Archimedean spiral, I get an even closer fit, and an apparent stretching in the quadrant 1 and 3 directions displays itself.

I'm not sure I've ever smooshed something diagonally, mathematically.
I might be able to get a perfect fit, if I can figure that out.
Off the top of my head, it looks like a pain in the butt.
I could rotate everything 45° counter clockwise and then smoosh it in the y direction.
Perhaps I'll try googling this for a better method. My brain is just too old.

Gold Member
Sunuvagun. I would not have believed it if I hadn't seen it.

I think two things threw me.