Thought Provoking Graphs

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Re: Thought Provoking Graphs

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?

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Re: Thought Provoking Graphs

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Re: Thought Provoking Graphs

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The flash of light you saw in the sky was not a UFO. Swamp gas from a weather balloon was trapped in a thermal pocket and reflected the light from Venus.

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Re: Thought Provoking Graphs

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Image

"smok" = Smaug? :wink:

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Re: Thought Provoking Graphs

Post by Abdul Alhazred »

No particular reason, I just decided I like the word "aerouant". :)
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Re: Thought Provoking Graphs

Post by Pyrrho »

@fermatslibrary

Proof that √2 is irrational
If √2 is rational, √2=a/b (a,b>0 lowest terms)
Then a²=2b²=b²+b² - place 2 carpets bxb in an axa room

Since the sum of the overlap and uncovered areas is equal
(2b-a)²=2(a-b)²=>√2=(2a-b)/(a-b) a contradiction since a,b were the lowest terms!
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Witness
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Re: Thought Provoking Graphs

Post by Witness »

↑ That proof is unnecessarily contrived (in my opinion).

Supposing a/b in simplest terms:
√2=a/b ⤇ 2=a2/b2 ⤇ 2b2=a2 ⤇ a2 is even ⤇ a is even ⤇ a=2a'.
Now 2b2=a2 ⤇ 2b2=(2a')2=4a'2 ⤇ b2=2*something and b is also even.
So a/b can't be reduced/in simplest terms as both a and b are even: contradiction.

No geometry, nos sums or differences, just arithmetic. (And al jabr. :MuhammadBoom: )

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Re: Thought Provoking Graphs

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Image

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Re: Thought Provoking Graphs

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Image
The flash of light you saw in the sky was not a UFO. Swamp gas from a weather balloon was trapped in a thermal pocket and reflected the light from Venus.

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Re: Thought Provoking Graphs

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Witness
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Re: Thought Provoking Graphs

Post by Witness »

↑ Yeah, but what's the algorithm?



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Re: Thought Provoking Graphs

Post by Anaxagoras »

Witness wrote:
Tue Feb 18, 2020 1:10 am
↑ Yeah, but what's the algorithm?
For the roundest country?

I figure, take the area of a country (from atlas or whatever).

Make a circle of that area (scaled down of course). Superimpose circle on map of country.
Add up areas of all parts of the country that fall outside the circle and all areas inside the circle but outside the borders of the country. Take that number and divide by the total, then take that number and subtract from one. Largest result is closest to circular.
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robinson
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Re: Thought Provoking Graphs

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This shit is important
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Rob Lister
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Re: Thought Provoking Graphs

Post by Rob Lister »

Anaxagoras wrote:
Tue Feb 18, 2020 4:32 am
Witness wrote:
Tue Feb 18, 2020 1:10 am
↑ Yeah, but what's the algorithm?
For the roundest country?

I figure, take the area of a country (from atlas or whatever).

Make a circle of that area (scaled down of course). Superimpose circle on map of country.
Add up areas of all parts of the country that fall outside the circle and all areas inside the circle but outside the borders of the country. Take that number and divide by the total, then take that number and subtract from one. Largest result is closest to circular.
That's an interesting solution but I don't think it relies on observation.

As you said, take the documented area (A) of the country.

Then, take the sum of the documented length of land and water border (B).

Perhaps the roundness of a country can be deduced:

Σ (Bl + Bw)-A

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Witness
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Re: Thought Provoking Graphs

Post by Witness »

Anaxagoras wrote:
Tue Feb 18, 2020 4:32 am
Superimpose circle on map of country.
How?

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Witness
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Re: Thought Provoking Graphs

Post by Witness »

Rob Lister wrote:
Tue Feb 18, 2020 6:16 pm
As you said, take the documented area (A) of the country.

Then, take the sum of the documented length of land and water border (B).

Perhaps the roundness of a country can be deduced:

Σ (Bl + Bw)-A
Mixing lengths and areas (i. e different dimensionalities as the physicists say) is generally frowned upon as your result will change wildly with different units. (Furlongs & acres, to please ed? :lmao: )
The best is to get a dimensionless measure of "roundness". (E. g. π needs no unit, being the quotient of two lengths, or equivalent definition.)

[Gallicism expurgated.]
Last edited by Witness on Wed Feb 19, 2020 2:47 am, edited 1 time in total.

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Witness
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Re: Thought Provoking Graphs

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Source & details: https://old.reddit.com/r/dataisbeautifu ... tracks_oc/

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Anaxagoras
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Re: Thought Provoking Graphs

Post by Anaxagoras »

Witness wrote:
Wed Feb 19, 2020 12:45 am
Anaxagoras wrote:
Tue Feb 18, 2020 4:32 am
Superimpose circle on map of country.
How?
Well, all shapes supposedly have a centroid or barycenter. I suppose you could line up the center of the circle with the centroid of the map.
Don't ask me how to find the centroid of an irregular shape, because I don't know.
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Rob Lister
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Re: Thought Provoking Graphs

Post by Rob Lister »

Witness wrote:
Wed Feb 19, 2020 1:00 am
Rob Lister wrote:
Tue Feb 18, 2020 6:16 pm
As you said, take the documented area (A) of the country.

Then, take the sum of the documented length of land and water border (B).

Perhaps the roundness of a country can be deduced:

Σ (Bl + Bw)-A
The best is to get a dimensionless measure of "roundness". (E. g. π needs no unit, being the quotient of two lengths, or equivalent definition.)
Intuitively, I know that is true but I'm pretty stoned right now and can't work it out in my wee brain. I usually like puzzles like this. Give me the solution. Pretty please, cherry on top, yada.
Fuzzy Witness wrote:Mixing lengths and areas (i. e different dimensionalities as the physicists say) is generally frowned upon as your result will change wildly with different units
It strikes me that the accuracy would be a curve with the peak representing a perfect match between your selected units and the units used originally documenting the linear measurement.

Take a shoreline as an example: It's fuzzy, so how long it is depends on the granularity of your measurement; infinite resolution of your ruler gives you infinite length. So the unit used originally must have been reasonable: call it a meter.

So we take that linear meter and treat it as a square meter. Convert the documented area into meters, plug them in, and rejoice.

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ceptimus
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Re: Thought Provoking Graphs

Post by ceptimus »

You can find the barycentre by printing the map on cardboard (or some other stiff flat uniform density plate), cutting it out, and balancing it on a pin.

You can do it with a computer by successive approximation - take the coordinates of each pixel inside the boundary relative to the guessed centre and sum all the x values - adjust guessed position until sum is zero. Same for y coordinates.