Criteria for Polygonal Shape To Be Tileable On Contiguous 2D Grid?

I am experimenting with a game engine and want to come up with a generic solution for creating tileable 2D grids. That got me thinking… not all regular polygons are able to be tiled contiguously & not all tileable polygons (at least for triangles & quadrilaterals) have to be regular.

What exactly are the criteria a polygonal shape must meet to be tileable?

submitted by /u/form_d_k
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What car brand or model attracts the worst drivers?

I was driving from Seattle to Portland yesterday and I don’t know what it was but there was a disproportionate amount of Nissan Altimas and Honda Pilots driving like a maniacs. One Altima in particular was tailgating me for half an hour. The second it looked like there was an opportunity to pass, he would blow by me, get stopped 3-5 car lengths ahead because of traffic, then get right back behind me.

submitted by /u/Bigfrie192
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Is there a geometric solution to the integral of sin x?

I was wondering why the Intergral from 0 to π of sin x equals exactly 2. I know how to integrate and this makes sense, but having this special graph makes me think that there might be more behind. I mean, the area of this half sine wave is the same as the area of a 2×1 rectangle.

So more specificly my question is: can you get a 2×1 rectangle by geometric transformation of a half-sine-wave-area? Allowed is cutting, rotating and mirroring.

submitted by /u/FelicxzZ
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Are matrices objects in their own right, or are they forever intimately tied to linear transformations?

In other words, can we study matrices without ever mentioning a linear transformation (much like one can study linear algebra without mentioning matrices)?

I mean, matrices form a very nice algebraic structure, all operations are quite well defined, etc.

submitted by /u/extremeaxe5
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I’d like to know which statistic software I should start learning

Hey, I’m sorry if this is a stupid question or not the right location to post this.

I’ve recently graduated in an MSc in Social Anthropology, and have secured a job as a policy researcher. However, I’m looking to improve my CV for future interviews and promotions down the road. I have a lot of experience in Qualitative research (fieldwork, ethnography etc) but not much at all in Quantitative research. Too cut this post short, where the hell do I start? I’ve heard that R Studio is a great place to begin with, and I luckily still have online access to a introduction module on the software at my university, but I have also heard of SPSS, Python, SQL, SAS.

If any of you could give me a run down of where a good starting place would be to learn statistics software/the differences between softwares that would be extremely helpful. I am a policy researcher at a political organisation, and most of my future research work will revolve around social science/social policy, health etc.


submitted by /u/Memo_moto
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Teachers and professors of math, how do you keep up with advanced math and avoid plateauing when your career doesn’t require you to keep learning?

Im really looking into switching to a math major to teach but i’m worried about teaching a single set of subjects whilst my higher level classes collect dust in my mind.

submitted by /u/colors1234
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