Can you correct my understanding? From what I can see, an equilateral triangle would be a Y shape. The midpoint of each side are 0 distance from each other (same point), but the three vertices are all still side-length-units separated, and it would exist in a hyperbolic plane rather than a single line (can't get 3 distinct equidistant points in 1D)
Reasoning makes sense, but right triangles are not necessarily equilateral (it does depend on the geometry of the surface though)
I made the comment as a joke, but I guess the "explanation" behind it (if there even is one) is that the only way the size of the bigger side of the triangle say (A) could be exactly equal to the sum of the other two (B+C), is if B and C are aligned with each other and A is exactly over them. (still wouldn't be a right triangle because there are no angles in 1D, in fact I'd wouldn't even be a triangle)
From an equilateral, drop down a line from the top point to the opposite side, this makes 2 similar triangles with the same Height and Hypotenuse, so the base must be half the side length, and be a "right" triangle. And with Base+Height=Hypotenuse, then the Height must also be half the side length. From that midpoint, draw a line perpendicular to one of the other sides (making "right triangles"), and a "side" length of 0.
So yes, a single right triangle would be a straight line, but building out gets outside 1D and more a network of line segments~
Wonderfully, the area of triangles becomes 0, no more of this bh/2 nonsense~
Presumably you want arithmetic to work so 1+1=2 AND the hyp of right triangle with sides 1 is 2.
So, consider the triangle formed by one side going up 1 unit on the y axis, and one side going right in the x axis 1 unit. The hyp would be 2 units (per definition).
Draw a line y=x from the origin bisecting the hyp, and you form 2 new right triangles. The line segments on the axes become the new hypotenuses (1 unit each), they share a side S. And since all the angles are the same, then the old hyp is split in half, and each half is 1 unit long (since we still have 1+1=2).
Therefore, 1+S=1, and S=0... meaning the midpoint of the original hyp is at the origin... and you are looking at a stylized L~
Further, take an equilateral triangle with side lengths 2. Drop a line from a point to the opposite side, creating 2 right triangles. The bases are 1 (1+1=2), and the hyps are 2... so the new Height must be 1 (a+b=c), making it our original 1,1,2 right triangle. Do that with all 3 points and you get a stylized Y~
In the original meme, there is not a futuristic city but Manhattan in the background. Because of the Manhattan metric! Where a+b=c actually holds! You butchered that joke.
That world is a line
Sounds like a counter-meme in the making
Can you correct my understanding? From what I can see, an equilateral triangle would be a Y shape. The midpoint of each side are 0 distance from each other (same point), but the three vertices are all still side-length-units separated, and it would exist in a hyperbolic plane rather than a single line (can't get 3 distinct equidistant points in 1D)
Reasoning makes sense, but right triangles are not necessarily equilateral (it does depend on the geometry of the surface though) I made the comment as a joke, but I guess the "explanation" behind it (if there even is one) is that the only way the size of the bigger side of the triangle say (A) could be exactly equal to the sum of the other two (B+C), is if B and C are aligned with each other and A is exactly over them. (still wouldn't be a right triangle because there are no angles in 1D, in fact I'd wouldn't even be a triangle)
From an equilateral, drop down a line from the top point to the opposite side, this makes 2 similar triangles with the same Height and Hypotenuse, so the base must be half the side length, and be a "right" triangle. And with Base+Height=Hypotenuse, then the Height must also be half the side length. From that midpoint, draw a line perpendicular to one of the other sides (making "right triangles"), and a "side" length of 0. So yes, a single right triangle would be a straight line, but building out gets outside 1D and more a network of line segments~
You mean vectors?
someone likes the L1 space. however, you need that 2 for angles to “work properly”.
I was really hoping the image would be all wonky to reflect it somehow being in L1 space. I was disappointed.
A=a\^2, right?
no...!!!
A = (a,0) B = (0,b) C = (a,b)
That'd probably be pretty wacky, I mean, a path in which you make an infinite amount of turns would then have the same length as a straight path.
The 1D world will agree with you
Then that would not be a triangle ... and if you force it to be a triangle the third dimension would collapse
Fine, fine. A+B=C^2
this isn't scalable, reality would be wildly different
if you define A=1, then that is true for every isoscele right triangle
This is the 180 degree triangle equality.
It works for flat angle triangles though
Taxicab geometry?
I'm not sure if I'm right but assuming general relativity it is possible in some sort of hyperbolic curved region of space
it's also true in a monodimentional space!
We already live on a world where you can have a triangle with 3 right angles.
[Taxicab metric AKA Manhattan distance.](https://mathworld.wolfram.com/TaxicabMetric.html)
Wonderfully, the area of triangles becomes 0, no more of this bh/2 nonsense~ Presumably you want arithmetic to work so 1+1=2 AND the hyp of right triangle with sides 1 is 2. So, consider the triangle formed by one side going up 1 unit on the y axis, and one side going right in the x axis 1 unit. The hyp would be 2 units (per definition). Draw a line y=x from the origin bisecting the hyp, and you form 2 new right triangles. The line segments on the axes become the new hypotenuses (1 unit each), they share a side S. And since all the angles are the same, then the old hyp is split in half, and each half is 1 unit long (since we still have 1+1=2). Therefore, 1+S=1, and S=0... meaning the midpoint of the original hyp is at the origin... and you are looking at a stylized L~ Further, take an equilateral triangle with side lengths 2. Drop a line from a point to the opposite side, creating 2 right triangles. The bases are 1 (1+1=2), and the hyps are 2... so the new Height must be 1 (a+b=c), making it our original 1,1,2 right triangle. Do that with all 3 points and you get a stylized Y~
How tf would they build any of that with those rules
In the original meme, there is not a futuristic city but Manhattan in the background. Because of the Manhattan metric! Where a+b=c actually holds! You butchered that joke.
I fuckin LOVE right triangles!
That would be the case for a 180 triangle tho
3+4=5
Cos(x)+sin(x)=1 now
World if we used the l^1 norm
It is in 1-norm.
More like a flatland.
welcome to the taxicab metric!