If the distance between B and C is 0, B and C are the same points. If that is the case, the distances between A and B and A and C must be the same.
However, i ≠ 1.
If you want it to be real (hehe) the triangle should be like this:
C
| \
|i| | \ 0
| \
A---B
|1|
Drawing that on mobile was a pain.
As the other guy said, you cannot have imaginary distances.
Also, you can only use Pythagoras with triangles that have a 90° angle. Nothing in the meme says that there’s a 90° angle. As I see it, there are only 0° and 180° angles.
This is clearly meant to be a right triangle. And the distances between the points are the same (because the squares of the coordinate differences are the same), just the directions are different.
If you move 1 unit forward, turn the correct 90 degrees, and then move i units forward, you will end up back where you started.
You can’t have a distance in a “different direction”. That’s what the |x| is for, which is the modulus. If you rotate a triangle, the length of the sides don’t change.
The vector from one point to another in space has both a distance (magnitude) and a direction. Labeling the side with i only really makes sense if you say we’re looking at a vector of “i units that way”, and not at an assertion that these two points are a directionless i units apart. Then you’d have to break out the complex norms somebody mentioned.
Isnt it fine to assume a 90° angle its just that when u square side AC ur multiplying by i which also represents a rotation by 90° so u now nolonger have a triangle?
This triangle is impossible.
If the distance between B and C is 0, B and C are the same points. If that is the case, the distances between A and B and A and C must be the same.
However, i ≠ 1.
If you want it to be real (hehe) the triangle should be like this:
C | \ |i| | \ 0 | \ A---B |1|Drawing that on mobile was a pain.
As the other guy said, you cannot have imaginary distances.
Also, you can only use Pythagoras with triangles that have a 90° angle. Nothing in the meme says that there’s a 90° angle. As I see it, there are only 0° and 180° angles.
Goodbye, I have to attend other memes to ruin.
This is clearly meant to be a right triangle. And the distances between the points are the same (because the squares of the coordinate differences are the same), just the directions are different.
If you move 1 unit forward, turn the correct 90 degrees, and then move i units forward, you will end up back where you started.
You can’t have a distance in a “different direction”. That’s what the |x| is for, which is the modulus. If you rotate a triangle, the length of the sides don’t change.
The vector from one point to another in space has both a distance (magnitude) and a direction. Labeling the side with i only really makes sense if you say we’re looking at a vector of “i units that way”, and not at an assertion that these two points are a directionless i units apart. Then you’d have to break out the complex norms somebody mentioned.
Incorrect. There are complex valued metric spaces
And even if we assume real valued metrics, then i usually represents the unit vector (0,1) which has distance real 1.
That’s NOT a metric. That’s a measure. Two wholly different things.
It can be a pseudometric
That’s more related to a metric but it still can’t be complex valued and it’s still not a measure.
Context matters. In geometry i is a perfectly cromulent name for a real valued variable.
Oh shit, he used the word cromulent. Every one copy off this guy.
That wouldn’t be cromulent, would it?
Mad mobile drawing!!
Isnt it fine to assume a 90° angle its just that when u square side AC ur multiplying by i which also represents a rotation by 90° so u now nolonger have a triangle?
It’s not fine to assume a 90° angle. The distance between B and C is 0. Therefore the angle formed by AB and AC is 0°.
If the angle is 90°, then BC should be sqrt(2), not 0. Since the length of both sides is 1. sqrt(|i|2+|1|2) = sqrt(2).
So essentially what ur saying is. The imaginary and real arent 90° or pythagoras is only valid for real numbers?