Math Memes

"um actually" I guess to properly apply the pythagoras theorem here, you'd need to consider the magnitude of the lengths of each of these vectors in complex space, both of which are 1 (for the magnitude of a complex number you ironically can use pythag, with the real and imaginary coefficients of each complex number.

So for 1 you get mag(1+0i)=root(1^2 + 0^2) and for i you get mag(0+1i)=root(0^2 + 1^2)

Then using pythag on the magnitudes, you get hypotenuse = root(1^2 + 1^2) = root 2, as expected

Shit I meant uhh imaginary number go brr it zero

I feel I must offer the superior version of that meme template. Lemmy’s not a fan of crowder for reasons likely mirroring those of his ex wife.

I get that this is just a meme, but for those who are curious about an actual mathematical argument, it is because Pythagoras's theorem only works in Euclidean geometries (see proof below). In Euclidean geometry, distances must be real numbers of at least 0.

There exists at least one ∆ABC in a 2-D non-Euclidean plane G where (AB)² + (AC)² ≠ (BC)² and m∠A = π/2

Proof: Let G be a plane of constant positive curvature, i.e. analogous to the exterior surface of a sphere. Let A be any point in G and A' the point of the furthest possible distance from A. A' exists because the area of G is finite. Construct any line (i.e. form a circle on the surface of the "sphere") connecting A and A'. Let this line be AA'. Then, construct another line connecting A and A' perpendicular to the first line at point A. Let this line be (AA')' Mark the midpoints between A and A' on this (AA')' as B and B'. Finally, construct a line connecting B and B' that bisects both AA' and (AA')'. Let this line be BB'. Mark the intersection points between BB' and AA' as C and C'. Now consider the triangle formed at ∆ABC. The measure of ∠A in this triangle is a right angle. The length of all legs of this triangle are, by construction, half the distance between A and A', i.e. half the maximum distance between two points on G. Thus, AB = AC = BC. Let us define the measure of AB to be 1. Thus, 1² + 1² = 2 ≠ 1². Q.E.D.

I like it.

Read the "1" unit side as "move left 1 unit" and the "i" side as "move up i units", and the hypotrnuse is the net distance travelled.

The imaginary line is perpendicular to the real line, so "up i unit" is equivalent to "right 1 unit". The two movements cancel out giving a net distance of zero.