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submitted 3 weeks ago by muntedcrocodile@lemm.ee to c/science_memes@mander.xyz

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[-] calcopiritus@lemmy.world 85 points 3 weeks ago

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.

[-] thomasloven@lemmy.world 22 points 3 weeks ago

Context matters. In geometry i is a perfectly cromulent name for a real valued variable.

[-] Clinicallydepressedpoochie@lemmy.world 4 points 3 weeks ago

Oh shit, he used the word cromulent. Every one copy off this guy.

[-] stevedice@sh.itjust.works 2 points 3 weeks ago

That wouldn't be cromulent, would it?

[-] Dayroom7485@lemmy.world 12 points 3 weeks ago

Mad mobile drawing!!

[-] technocrit@lemmy.dbzer0.com 5 points 3 weeks ago* (last edited 3 weeks ago)

As the other guy said, you cannot have imaginary distances.

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.

[-] stevedice@sh.itjust.works 1 points 3 weeks ago

That's NOT a metric. That's a measure. Two wholly different things.

[-] diaphanous@feddit.org 3 points 3 weeks ago

It can be a pseudometric

[-] stevedice@sh.itjust.works 1 points 3 weeks ago

That's more related to a metric but it still can't be complex valued and it's still not a measure.

[-] planish@sh.itjust.works 2 points 3 weeks ago

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.

[-] calcopiritus@lemmy.world 1 points 3 weeks ago

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.

[-] planish@sh.itjust.works 2 points 3 weeks ago

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.

[-] muntedcrocodile@lemm.ee -1 points 3 weeks ago

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?