Euler's identity

[audience]

I was just click baited in by the outrageous claim that it doesn't exist.

[theidioticbgilson]

actually it's not eulers constant, euler's constant is γ, e is called euler's number

[marco_martin]

Your "Cool little equation" is literally what makes our reality exist

[dariusconstantinpascu]

What a better way of understanding Euler's number than asking Euler himself

[SamanthaPyper-slye]

Euler's Identity - Transcendental Relationships

Contradictory:
Euler's identity, e^(iπ) + 1 = 0, is often considered one of the most beautiful and mysterious equations in mathematics. It relates five fundamental mathematical constants (e, i, π, 1, and 0) in a single compact expression. However, the nature of this relationship remains largely unexplained, and the appearance of the imaginary unit i in the exponent leads to apparent contradictions when interpreted in physical terms.

Non-Contradictory:
Using the monadological framework, Euler's identity could be understood as a consequence of the deep symmetries and dualities between monadic perspectives. The imaginary unit i could be interpreted as a generator of rotations or transformations between these perspectives, rather than a literal physical quantity:

e^(iπ) + 1 = 0 → ⟨e^(i_mπ_m)⟩ ⊕_m 1_m ≅_m 0_m

Here, ⟨...⟩ represents an average over monadic perspectives, ⊕_m is a monadic sum, ≅_m is a monadic equivalence relation, and i_m, π_m, 1_m, 0_m are monadic constants.

[acaryadasa]

Don't say, "i doesn't exist".

[lukewilson]

Euler's constant is γ which is the diffence between the harmonic series for n terms - ln(n) ≈ 0.577

[thedying_insidelady]

It is the most beautiful equation in the world.

[JohnBerry-qh]

Actually, exp[i pi] is actually what you might call a WALK AROUND table. Draw a Unit Circle. Now, on the Unit Circle, starting at the coordinate (1, 0), “walk” CCW around the circle for an “angle sweep” of ‘pi’ radians. On the Unit Circle, the new coordinate will be (-1, i0). This “walk around” table result is identically just the output value -1. Substituting back into the original equation yields…
-1 + 1 = 0 . Done!

[BenizU]

Yeah I just learned about that from my 10 grade math teacher he says that this equation is considered to be one of the most beautiful equations in math

[sumitvishwakarma]

this equation shows the beauty of Math ❤🥰

[TheGildedMackerel]

e^(ix) draws a circle because its derivative is itself multiplied by i, which represents a 90° rotation, there it is the function with a rate of change perpendicular to its position. the tangents to a circle is perpendicular to the radius/ velocity of a ball travelling in a circle is perpendicular to its position

[wayneosaur]

This is really a special case. The full equation is e^it = cos(t) + isin(t) ... just let t = pi to get the equation in the video. I think it is much cooler to let t = pi/4 and then you get e^{i pi/4} - sqrt(2)/2 * (1 + i) = 0. This allows the constant sqrt(2) be part of the fun. Side note, imaginary numbers are no less "real" that real numbers -- I have never stubbed my toe on the number 2.

[Farooqueakhan]

Its people you with half knowledge who confuse serious seekers of knowledge, who are sincerely trying to understand something .

[TheFinav]

May as well deny the existence of all numbers, as their existence is no more real than i's.

[mariano.deheza]

This equation is for me the most brilliant of all mathematics. i is the number that doesen't exists, but it is related to 3 numbers that exist (e, pi, one). Really incredible and VERY MISTERIOUS!!!

[mugesang]

I realized it from a Korean movie called In Our Prime, my favorite movie and the main actor too

[foxypiratecove]

The square root of -1 is actually... i, j, k, l, li, lj, lk, m, mi, mj, mk, lm, lmi, lmj and lmk.

[anonymous_FoX]

When you realized that those are the 5 are special numbers in mathematics, 0, 1, i, e, π

[gco]

Yah sure but did Euler make it from Taylor series ?