The most beautiful triangle!

bprp #shorts #270 #geometry #satisfying #beautiful #math #asmr

[brutecarnelgo]

Next, you will make a triangle with the sum of angles less than 180 degrees!

[felineboy]

Student: But how do I know which side is the hypotenuse?
Prof: Easy, it's the one opposite the right angle.
This triangle:

[MathAdam]

The sum of the angles of a right triangle is 270 degrees.

[lukandrate]

This is called "spherical geometry". It may be wrong because I don't really remember the name. It is just a geometry subject where's everything is on a sphere

[peterbayonet]

Aha! Are you going to start making videos about non-Euclidean geometry?

[thecataphractal]

you think that's nice? what about five sided square!

[lava_melon]

I very like pythagorean theorem in spherical geometry, "cos(a) cos(b) = cos(c)".

(a, b and c are angles from one corner of arc to center of sphere and to another corner)

In that case:
cos(π/2)cos(π/2) = cos(π/2)
0 * 0 = 0
0 = 0, so it's true

also i like formula to area of triangle: "A + B + C - π"
where A, B and C are sides of that shape (here it will be π/2 in each side)

in this triangle:

π/2 + π/2 + π/2 - π =
3(π/2) - π =
1/2 π

formula for the area of sphere is 4πr^2

so when r = 1, then Area = 4π

Our triange is one eighth of sphere so
4π / 8 = 1/2 π


and that's right
1/2 π = 1/2 π

(i'm from poland, sorry for mistakes in translate
)

[sakshameditzz]

Le me-who is noticing that small red dot under dotted line😅😅

[johnchessant]

Fun fact: The amount by which the sum of the three angles of a spherical triangle exceeds 180 degrees is proportional to the area of the triangle!! This results from the fact that a sphere has uniform curvature.
(For a unit sphere, they're actually equal: e.g., the triangle in the video has angle excess (3pi/2 - pi) = pi/2 radians, and the area of the triangle is (1/8)(4pi) = pi/2)

[brian]

Don't use white board markers for paper

[catsmeow]

Tbh I’m more impressed by that flawless circle

[Saransh_Tiwari]

Teacher:The sum of all the angle in a triangle is fixed and that is 180⁰.
Me: Showings him this triangle.
Teacher: Resigns

[sumitrahi]

Modern problem require modern solutions

[Bhavesh_g]

It is beautiful
I have been looking at it for 5 hours now

[nikolaalfredi]

Traingle is defined only on Euclidean Geometry, Here the shape may resemble a triangle but is not a triangle rather it is just geodesic array over sphere.

[joupoes]

It’s because it’s curved out, that’s how we measure the curvature of space

[Mothuzad]

Me: This triangle looks...

all right 😎

[ridwanraja]

What's the name of that triangle?

[soyanshumohapatra]

This triangle is *right-right-right* angled. 😂😂

[ahuang]

This has to do with Gaussian curvatures. Positive and negative curvatures result in this “3 sided square” or a “5 sided square”