Ten Mortal Math Constants

In this video, we show visualizations of ten classic mathematical constants:

1) The square root of 2 as the length of the diagonal of a 1 by 1 square.
2) Pi as the area of the circle with radius 1.
3) Tau as the circumference of the circle with radius 1.
4) The golden ratio as the number satisfying (x+1)/x=x/1.
5) The square root of 3 as the altitude or area of an equilateral triangle with side length 2.
6) Euler's number e as the ending x-coordinate yielding the area under the curve of 1/x starting at x=1.
7) The silver ratio as the horizontal length across the regular octagon with side length 1 or the area of the largest rectangle inside the same regular octagon.
8) The natural logarithm of 2, ln(2), as the sum of the convergent alternating harmonic series.
9) The plastic ratio as the limit of the ratio of side lengths in a spiral of equilateral triangles with side lengths dictated by the Padovan sequence.
10) The Euler-Mascheroni constant as the difference between the harmonic series and the area under the curve y=1/x from 1 to infinity.

#mathvideo​ #math​ #numbertheory #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #constants #goldenratio #silverratio #plasticratio #squareroot #squareroot2 #squareroot3 #euler #eulerconstant #eulermascheroni #ln2 #logarithm #octagon #square #pi #tau

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[ericworm]

Flawless victory in math if you know when to use these constants!

[Satyr]

Wow!!! Great video !!! (Including the music).

[chrisdec]

Well done to Sonic Fox for winning Mortal Kombat at Evo 2024 yesterday.

[GowsBabu-uqbo]

Thank you for your work, we want more formulas 😊

[vennstudios]

The SILVER RATIO?

golden ratio: FINALLY A WORTHY OPPONENT

OUR BATTLE WILL BE LEGENDARY

[TojtekBes]

Gamma; emits a very large gamma ray in all directions

[idknotsterling]

"half the pi doesn't exist, it cant hurt you"
half of the pi:

[UserYouTube]

δ= √2+1
φ= (√5+1)/2
π= arctan1+arctan2+arctan3
τ= 2×(arctan1+arctan2+arctan3)

[sHerlockHolmes-h]

which software you use to make these animations?

[carl]

"Mortal combat" can be heard as "eulers constant"

[error_o]

You mean *immortal* constants, right?

[stapler]

Flawless logicians: If Socrates is mortal, he must do kombat.

[Very.Crazy.Math.Pistols]

Gamma Ray Happy Mortal Constant 😂. Fight.

[IvanovichNavinzkanovReginald]

FYI: square Without √2 Is 1/4 Of A Circle.

[THE_HONOURED_ONE_LOL]

Choose your character. Options: sqrt 2, π, τ, φ, sqrt 3, e, 1+sqrt 2, ln(2), ρ, γ. *chooses sqrt 2* SQRT 2 VS PI. PI WINS, ROUND II…. PI WINS. FINAL ROUND… SQRT 2 WINS. PI IS VICTORUIS. FAIL. Practice mode: PHI VS TAU. *3 minutes later* AND PHI IS VICTORIUS.