Do you like triangles, /sci/? I sure do! What are some of your

I like trig. It rhymes with my favorite word. Can you guess it?

>>9109081
cant be pig because thats not kosher

File: 192px-Penrose-dreieck.svg.png (8KB, 192x174px) Image search: [Google]

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>>9109066
Penrose Triangle.

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>>9109081
T H I C C

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>>9109066
>tfw got excited about discussing trianlges for a second but then realized this is just a subtle /pol/ thread

>>9109090
(((They))) use triangles, so triangles cant be trusted

>>9109081
I know you're a prig, anon.

>>9109090
OP her, I'm actually perfectly serious about hearing your favorite triangle facts. I only used the OP image because it was the only triangle-related image I had downloaded, and because I figured it would attract (You)s.

>>9109066
An equilateral triangle in a spherical surface has 270 degrees, that's the on I could fish out of my head

>>9109066
You can inscribe any triangle in a square of the same perimeter, trust me, this is a true triangle fact.

File: Animated_illustration_of_thales_theorem.gif (205KB, 300x300px) Image search: [Google]

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>>9109066
>Thales' theorem

>In geometry, Thales' theorem states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Thales' theorem is a special case of the inscribed angle theorem, and is mentioned and proved as part of the 31st proposition, in the third book of Euclid's Elements.
I don't know why but I always thought that was pretty cool.

>>9109066
Triangles are neat, especially right angled triangles. You can calculate the coordinates of 1 o clock (1/3 through the first quarter) using pythagoras theorem like so.

[math]
r=1\\
y^{2}=3x^{2}\\
x^{2}+y^{2}=r^{2}=1,\ y^{2}=1-x^{2} \\
3x^{2}=1-x^{2}\\
4x^{2}=1,\ x^{2}=\frac{1}{4},\ x=\frac{1}{2}\\
y^{2}=1-\frac{1}{4},\ y=\sqrt{\frac{3}{4}}
[/math]

>>9110178
for very small triangles, the surface is locally euclidian, so this is false

>>9109090
IRRUMINATI JEWISH CONSPIRACY REEEEEEEEEEEEEE

>>9110178
equilateral triangles on spheres can have 270 degrees

homework: show they can also have 810 degrees

>>9110737
Oh, this is easy!
Start by constructing an equilateral triangle with a total of 270 degrees. Each of its angles is a right angle. This triangle covers exactly an eighth of the sphere's surface. However, the remaining seven eigthts of the sphere's surface constitutes a second triangle. This triangle is defined by the same points and sides as the smaller triangle, which means that it is also equilateral, except its angles are on the "outside", which means that they are each equal to 360 - 90 = 270 degrees. Ergo, it is an equilateral triangle with a total of 810 degrees.

>>9110466
I think its cool too. Its one of my favorite theorems in elementary geometry

>>9109081
MIG? They are pretty cool planes

>>9110466
I love that one. Want a right angle? Draw a circle, draw its diameter, put 2 lines towards any point and voila, perfect right angle just like that!

>>9109066
Do you know that there are no words in the english language that rhymes with Triangle.

>>9112538
im not too sure
but thats just my angle

>>9110466
Man, my high school geometry was basically 100s of proofs using this and similar theorems. Once you got the hang of it it was pretty fun but I've heard people say it's not really how proofs work in higher maths.

>>9112538
Bojangle!
Tangle!
Mangle!
Bangle!
Rectangle!

>>9112506
That sounds far more complicated than using the corner of your ruler to make a right angle and the length to make the line segments.

>>9109066
>>>/pol/

>>9110810
I learnt something in this thread, thanks you

2 sides are required for enclosure in 1D space, 3 points are required for enclosure in 2D space, 4 points in 3D space etc...

pretty trivial, but interesting to me nonetheless