The Math Thread

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Jatsko
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Re: The Math Thread

Post by Jatsko »

WHO'S READY FOR A S O C I A L E X P E R I M E N T

It's fairly straightforward and you don't have to understand the math concepts I've been talking about to participate. In the Skype chat I talked about these graphs that were implemented by this Marc Renault guy and how I had started to "connect the dots", not using any specific rule but in a way that just "feels right". So what I would like you guys to do is take a look at the picture in the link below, which is all the graphs for m = 2 through 15, and draw (via Paint, Illustrator, Photoshop, whatever) lines that connect them in a way that "feels right". Don't post them below; send them to me via PM and I'll collect all of them to compare. There are no right or wrong answers.

https://i.imgur.com/qBtvdbo.jpg

A few guidelines/things to point out:

1) Draw the first connections that come into your head; don't think about them any longer than that.
2) The graphs naturally repeat farther than the immediate grid; you'll notice that I repeated the 0 axes to give you a sense of how the patterns start to repeat in both a horizontal and vertical direction, so connect those dots (white circles) as well just to make the image more complete.

I'll demo with my version of #2:
2.JPG
2.JPG (16.13 KiB) Viewed 5262 times
I will probably be making more videos on the Fibonacci series in the future and wouldn't be surprised if this project made it in there as well as part of a more in-depth discussion about the connection between math and psychology, so if you participate you'll probably have your work shown in a future video :D

Remember, don't post your results here!
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Vortex
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Re: The Math Thread

Post by Vortex »

I sent you the PM.
Apocrypha wrote:
Vortex wrote: wouldn't that happen with all of them, not just 10? or am I misunderstanding what you say?
No; if you look at the last link you'll see that some examples given especially later on in the document might have rotational symmetry but if you were to copy them along the axes in any direction there's no tesselation pattern that continues between them. I'm looking at ones like m=39 and the rotational ones like m = 82, 221, 257.
Oh, I see. I was thinking that trivially all of them will form tessellations of the plane, but I see what you mean, not all tessellations will visually appear to match up at the edges of the square (the ones with a period lower than the modulus have a greater chance to do so).
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Empoeria
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Re: The Math Thread

Post by Empoeria »

oh my god. I just spent way too long trying to do this on my phone, hit save, and ....... it didn't save. AAAARGH
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Jatsko
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Re: The Math Thread

Post by Jatsko »

Why would you feel to do anything on a phone ever


naw but seriously take your time, there's no rush :D
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Empoeria
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Re: The Math Thread

Post by Empoeria »

Apocrypha wrote:Why would you feel to do anything on a phone ever
because I don't have my graphics tablet here and my phone has an app with a ruler option.
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Jatsko
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Re: The Math Thread

Post by Jatsko »

Anyone else?

No rush still, but I'd like to keep this semi fresh in everyone's mind (including my own lol)
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Jatsko
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Re: The Math Thread

Post by Jatsko »

Reminder that I'm still accepting submissions for this!
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Jatsko
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Re: The Math Thread

Post by Jatsko »

PISANO THING UPDATE (THIS IS MY LIFE NOW)

/s

Towerofnix has been a really big help in renovating the Khan Academy program so (hopefully) no circle graph (not "symbol"! bad!) will be blank due to Java's computing limitations.

https://www.khanacademy.org/computer-pr ... 5193645056

So use this one from now on. It's got a few new interactive features as well, including a step-by-step path tracer so you can follow each period every step of the way. Pretty genius if you ask me.

They'll be massively credited in the upcoming video on these explorations.
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Jatsko
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Re: The Math Thread

Post by Jatsko »

Alright, I finally put out a new and improved, shiny version of that video I once did regarding Fibonacci and Pisano periods. Have a look here: https://www.youtube.com/watch?v=o1eLKODSCqw
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Vortex
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Re: The Math Thread

Post by Vortex »

Whoa, it looks so professional :D

Do you plan to make more math videos? or is this just a one-off thing?
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