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Oh_Tassos OP t1_ja7fntq wrote

Hello! What I've created for you today is, as the title describes, a way to visualise the answer to a problem from the Greek Mathematics Olympiad, named "Archimedes" after the ancient mathematician, which took place on February 18.

Well... sort of. The truth is that we were given some corrections about this problem near the final hour of the 3-hour examination, which vastly limited the actual correct answers (to just 2, from infinite)

Here's my best attempt at a translation of the problem, you can find the original exam (along with the solutions and list of students who passed the exam) over on the Hellenic Mathematical Society's website here.

For the various values of the positive integer n, identify all the positive integers N which are perfect squares and in their decimal representation the digit 2 appears n times and the digit 5 once.

The correction we were given was that these positive integers N only contain the digits 2 and 5, and not any others. The real solutions are 25 and 225, and you can prove by mathematical induction that there is no solution for n ≥ 3.

This visualisation does not take the correction into account. To make it, I used a program I made in C++ (to identify the numbers N), a csv sheet, and a program I made in Python (to actually draw the visualisation).

I will note about the Python program that some parts of the code, those regarding the rescaling of the window when it went off-screen and the colour gradient, were actually written by a fellow r/dataisbeautiful member after an older post of mine about prime numbers. I do not remember their name to credit them correctly, but props to them for the help.

I would also like to share a few graphs I made regarding the difference between two successive numbers N in this "sequence", for I think they look interesting at a sufficient zoom level. Here

That's all, thank you for your time!

Edit: I forgot to mention that this visualisation includes the first 10592 positive integers N, which is how far the C++ program got before it crashed (I assume it was a memory issue)


MathThatChecksOut t1_ja7o2w3 wrote

So what is actually visualized here? You have described a number theory problem and presented a colorful visual but it's not immediately clear how they are related.


Oh_Tassos OP t1_ja7ogku wrote

Ah yes, you're right. I got carried away explaining the context that I forgot to mention what we're actually seeing.

Basically you have this line that's counting non-negative integers, starting from 0, and every time it encounters a number from this problem (let's say 225) it makes a 90*n degree turn (in the case of 225, where n = 2, it'd be a 180 degree turn).

This doesn't hold any inherent meaning, it just creates a pretty visual. You are right that I entirely forgot to explain that part though.

Edit: the start is at the purple zone in the bottom right corner


nankainamizuhana t1_ja7yh0d wrote

So the intent, I assume, was to quickly visualize if there were a finite number of corners or a repeated pattern?

I'm quite curious about the large yellow vertical line. I can't decide whether it's more reasonable that the line is a large swath of integers with no perfect squares containing 2 or 5; or a large swath where all such perfect squares are of the form n=4m+2.


Oh_Tassos OP t1_ja7z72s wrote

It's the former, the difference between 1,530,609,129 and 1,499,470,729 which is equal to 31,138,400. That's way larger than any other numbers until that point. You can see this anomaly more clearly in the graph I linked near the end of my initial comment.


Pakman747 t1_ja7e23q wrote

for a second, I thought this was a Terraria map


Joseluki t1_ja84m09 wrote

Cannot interpretate data if I do not know what I am looking at.


Oh_Tassos OP t1_ja84vts wrote

Luckily for you, it's all explained in the comments, there's no way to fit all of the explanation in the visual itself


pizzet t1_ja7yn8u wrote

Looks like that old Windows screensaver


angerfist9 t1_ja7e0wy wrote

Can you share a link to the image in full size? This would do as a great wallpaper for my phone


Oh_Tassos OP t1_ja7fv2a wrote

I'm sorry but this is the full size, the 1200x1600

Due to the fact I made the visualisation using Python's turtle, I had to sacrifice some detail :(


DanilOcelot t1_ja803c9 wrote

Nice metroidvania map. I’ll use it


imapintobean t1_ja7zfif wrote

It’s a piece of an infinite fractal


bledik t1_ja8dhp7 wrote

Interesting but not understand


Oh_Tassos OP t1_ja8f5ua wrote

Check out the comments :)

I did my best to explain it there


squickley t1_ja8xjtz wrote

This is the good stuff, what the sub should be full of. Infographics are trash. Show the beauty in the data itself.


accord281 t1_ja8yv59 wrote

This looks like my 5 year old's Minecraft mine path.


Oh_Tassos OP t1_ja8z25i wrote

Your 5 year old will learn not to dig straight down, as with that yellow line, the hard way then


SlientlySmiling t1_ja93ift wrote

Looks like a gerrymandered congressional district.


OHitsaKO t1_ja9574y wrote

the map as i search for the plantera bulb in the undergound jungle in terraria:


iamthemosin t1_ja9wsa4 wrote

No. That’s a screensaver.


boonstyle_ t1_ja83jv7 wrote

I swear I’ve played that level


Frui7Lukes t1_ja87ary wrote

Thought it was a map to The Waking Sands for a moment..


Michelrpg t1_ja8jqfv wrote

Okay ngl my nerdy ass thought this was a new map for a metroid game.


StrangeSathe t1_ja8l3xn wrote

I thought this was Umbrella Corp.


Garl_VinIand t1_ja8m4ae wrote

Looks eerily like the map of Dark Souls 1.


tbb2796 t1_ja8nk69 wrote

looks like the subway map of Wyoming I made


CMDR_omnicognate t1_ja8nsi9 wrote

For a while there i thought it was a Terraria map


Adventurous_Tie_2740 t1_jaaa6lb wrote

Looks like a random walk done with Matplotlib


Oh_Tassos OP t1_jaaaw4l wrote

I do see why you'd say that. In this case it isn't random, but there isn't a distinct pattern either (maybe a very loose one, idk)


Zebo1013 t1_jaadiv1 wrote

Umbrella corporation vibes.


logank013 t1_jab95mw wrote

A helicopter is attacking the UK and Ireland (flipped on the vertical axis)