4 Color Theorem / Topology Question

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Anonymous
4 Color Theorem / Topology Question 2017-08-01 12:59:02 Post No. 9076823
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4 Color Theorem / Topology Question Anonymous 2017-08-01 12:59:02 Post No. 9076823 [Report]

Okay, so I've been messing around with some math-related drawings, and I was wondering if you all could help.

Basically my goal is to draw an image with four different shapes, so that each shape is in contact with the other three. In other words, this is the most simplified version of the Four Color Theorem, which says that you only need to use four different colors, if you want to color in a map so that the same color is never touching.

Here are a few simple drawings I've come up with. What I'm curious about is:
>Can anyone come up with designs that look cooler, but still solve this problem. And:
>I'm also wondering if it's possible to create a solution to this problem that only uses identical shapes for all four regions.

Anonymous 2017-08-01 01:40:22 Post No.9076869
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Anonymous 2017-08-01 01:40:22 Post No.9076869 [Report]

File: 4 color - 3.png (36KB, 1380x664px) Image search: [Google]

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>I'm also wondering if it's possible to create a solution to this problem that only uses identical shapes for all four regions.

If you are allowed to change the size of the shapes, it's relatively easy, but it's probably impossible to do it with shapes that are the exact same size.

Anonymous 2017-08-01 01:46:49 Post No.9076875
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Anonymous 2017-08-01 01:46:49 Post No.9076875 [Report]

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>>9076823

Anonymous 2017-08-01 01:51:07 Post No.9076878
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Anonymous 2017-08-01 01:51:07 Post No.9076878 [Report]

>>9076875
Damn! That's solid, very good., wish I'd thought of it

Anonymous 2017-08-01 03:21:49 Post No.9077015
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Anonymous 2017-08-01 03:21:49 Post No.9077015 [Report]

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>>9076869
>>I'm also wondering if it's possible to create a solution to this problem that only uses identical shapes for all four regions.
>it's probably impossible to do it with shapes that are the exact same size.

If reflections are allowed, it's possible. Basically make an "L" shape that measures 4x6

Anonymous 2017-08-01 08:08:20 Post No.9077435
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Anonymous 2017-08-01 08:08:20 Post No.9077435 [Report]

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>>9077015
>>9076869
I doubt that anyone cares, but there is, in fact, a solution to this problem that uses only rotations, with no reflections.

I'm aware that Imgur.com will stop allowing adult images since 15th of May. I'm taking actions to backup as much data as possible. Read more on this topic here - https://archived.moe/talk/thread/1694/

I'm aware that Imgur.com will stop allowing adult images since 15th of May. I'm taking actions to backup as much data as possible.
Read more on this topic here - https://archived.moe/talk/thread/1694/