Author Topic: Right angles with equilateral triangles  (Read 75 times)

Offline Philosfr

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Right angles with equilateral triangles
« on: July 09, 2018, 08:27:44 am »
So I'm literally sitting at work right now with a dozen post-it notes (perfect squares) that I've then folded half of them into equilateral triangles. Trying to determine interesting ways to use triangles in walls and still work with triangles to make large areas. I've put together one interesting pattern to make a 90' angle with a mix of squares and triangles. Yes, it required math and yes, I could have just used math or MS Paint, but sometimes it just faster to use physical objects and spot check my math. My last geometry class was over half my life ago...

The pattern is:
Square -> Triangle -> Square -> Triangle -> Triangle -> Square -> Triangle - > Square

The first square and last square are "aligned" in the same direction. This lets you create an interesting corner on a "roundish" wall and keep it aligned to a square castle in the middle. The square before the last triangle ends up making a bit of point and ruins the "round" effect, but call it an architectural embellishment.

Back to doing some more math now. I THINK it's even possible to line this up so both the first and last squares are "lined up", so you could fill the whole thing in and not have a hole

There's a fine line between genius and insanity. I have erased this line.
--Oscar Levant

Offline Philosfr

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Re: Right angles with equilateral triangles
« Reply #1 on: July 09, 2018, 08:44:13 am »
To be specific, the pattern above creates a roundish corner that is big enough to cover an entire square corner. I already knew you could achieve 90' easier and more squarish by going square -> triangle -> reverse triangle -> square, but then you're half a square off from your "grid". The pattern above gets you back "on grid".

But I didn't realize if you built two of the S -> T -> RT -> S patterns together, you achieve an "on-grid" pattern that nestles inside the pattern above...

There's a fine line between genius and insanity. I have erased this line.
--Oscar Levant

Offline Teka

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Re: Right angles with equilateral triangles
« Reply #2 on: July 09, 2018, 08:55:56 am »
How do you reverse an equilateral triangle?

Offline Philosfr

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Re: Right angles with equilateral triangles
« Reply #3 on: July 09, 2018, 09:09:09 am »
How do you reverse an equilateral triangle?

Not a reverse of the triangle, a reverse of the angle you're laying the triangle out in. If you go T > T > T > T >T > T you end up making a circle. If you go T > RT > T > RT you end up making a line. I am trying to mess around with graphics programs and failing. I'm better at math :(

Though I think I just mathematically determined you can't get keep both the X and Y axis on a square "grid" using triangles. I can make one axis line up every other square, but I can't line it up in the other direction.

That said, an interesting pattern for a roundish type building my be squares then a line of T > RT > T > RT, then a line of squares and repeat, alternating squares and T > RT.

There's a fine line between genius and insanity. I have erased this line.
--Oscar Levant

Offline Teka

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Re: Right angles with equilateral triangles
« Reply #4 on: July 09, 2018, 09:12:35 am »
Ah, gotcha. Also, it's a pain in the ass to fold a square into an equilateral triangle.

Offline Philosfr

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Re: Right angles with equilateral triangles
« Reply #5 on: July 09, 2018, 09:23:40 am »
Ah, gotcha. Also, it's a pain in the ass to fold a square into an equilateral triangle.

Not really. I fold the square in half to get a center line. Then I take a another square, and line it up with one corner and see where the length of the other corner intersects the fold line. Bam, instant equilateral triangle of the right size to match up with the original square.

There's a fine line between genius and insanity. I have erased this line.
--Oscar Levant

Offline Teka

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Re: Right angles with equilateral triangles
« Reply #6 on: July 09, 2018, 09:29:35 am »
Ah, gotcha. Also, it's a pain in the ass to fold a square into an equilateral triangle.

Not really. I fold the square in half to get a center line. Then I take a another square, and line it up with one corner and see where the length of the other corner intersects the fold line. Bam, instant equilateral triangle of the right size to match up with the original square.

lol I was just folding to the center line and it was making a slightly "off" equilateral. Makes sense now  :blush:

Offline Teka

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Re: Right angles with equilateral triangles
« Reply #7 on: July 09, 2018, 10:22:24 am »
Just remembered I have the perfect shapes for this. Magnatiles FTW!






Offline Philosfr

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Re: Right angles with equilateral triangles
« Reply #8 on: July 09, 2018, 11:12:03 am »
Very nice! Those are awesome

There's a fine line between genius and insanity. I have erased this line.
--Oscar Levant

Offline Etouffee

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Re: Right angles with equilateral triangles
« Reply #9 on: July 09, 2018, 06:32:28 pm »
How do you reverse an equilateral triangle?

elgnairt laretaliuqe is how I would do it  :philosiraptor:

Offline Bannta

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Re: Right angles with equilateral triangles
« Reply #10 on: July 10, 2018, 05:53:10 am »
How do you reverse an equilateral triangle?

elgnairt laretaliuqe is how I would do it  :philosiraptor:

Finally, something I can read!


"Strike me down with it! Give into your anger! With each passing moment, you make yourself more my servant....wait?! I was just kidd...." ~ Quote Darth Plagueis

Offline Rumblood

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Re: Right angles with equilateral triangles
« Reply #11 on: July 15, 2018, 03:26:45 pm »
How do you reverse an equilateral triangle?

elgnairt laretaliuqe is how I would do it  :philosiraptor:

Finally, something I can read!

Aixelsyd?