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@yuuki26

yuuki@yuuki26

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705日(2021/11/25より)
ツイート数
793(1.1件/日)

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2023年10月29日(日)5 tweetssource

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2023年10月24日(火)2 tweetssource

2023年10月23日(月)8 tweetssource

10月23日

@yuuki26

yuuki@yuuki26

probably the key is “Euclidean theorem”:
gcd(a, b) = gcd(b, a mod b).

i.e., the gcd of two numbers equals the gcd of some smaller numbers.
smtg like gcd(32, 24) equals gcd(24, 8).

the algorithm may be based on this theorem.
so the question is why this holds.

posted at 11:40:02

   

10月23日

@yuuki26

yuuki@yuuki26

i’m currently researching the Euclidean algorithm

function gcd(a, b) {
if (b === 0) {
return Math.abs(a);
}

return gcd(b, a % b);
}

but haven’t figured it out yet.
seems this can also be applied to polynomials n is related to Bézout’s identity etc., tho.

posted at 11:06:05

   

2023年10月22日(日)4 tweetssource

2023年10月21日(土)14 tweetssource

10月21日

@yuuki26

yuuki@yuuki26

Anime i recently watched
2022
- kiki’s delivery service
- the tale of the princess kaguya
- re:zero s1
2020
- detective conan all eps
2019
- tokyo ghoul s1-3
- demon slayer s1
2017
- age 12 s1-2

posted at 18:30:31

   

10月21日

@yuuki26

yuuki@yuuki26

this is called a generating function n was discovered by de Moivre in the 18c, according to wiki.

seems using aₙ = aₙ₋₁ + aₙ₋₂, it follows
𝑓(x) = x/(1 - x - x²).

n some reasoning leads to
aₙ = (ϕⁿ - (-ϕ)⁻ⁿ)/√5.

posted at 10:28:19

   

10月21日

@yuuki26

yuuki@yuuki26

• Recurrence relation
seems one way to find an exact formula for a sequence like
aₙ = 1, 1, 2, 3, 5, 8, …
is the “inverse of the Taylor expansion.”

its known that
eˣ = 1/0! x⁰ + 1/1! x¹ + 1/2! x² + …,
but the idea is to find 𝑓 such that
𝑓(x) = 1x¹ + 1x² + 2x³ + 3x⁴ + ….

posted at 10:04:41

   

10月21日

@yuuki26

yuuki@yuuki26

• Limit
lim[x→∞] f(x) = L
basically means that the point where the value gets closer (as x gets larger) is L.
nothing more, nothing less.
not smtg like “equals L after infinite steps.”
(idk if such an interpretation is possible in higher math.)

posted at 08:59:26

   

10月21日

@yuuki26

yuuki@yuuki26

• Consider drawing a figure using only a function that draws a point (x,y) on a plane, say, drawPoint(x,y).

considering drawing a line leads to the equation of a line.

considering drawing a circle leads to trig functions.

posted at 07:53:52

   

10月21日

@yuuki26

yuuki@yuuki26

however, it was discovered that this can be interpreted as the point (x,y) being moved to (e,f) by the matrix ((a,b),(c,d)). (by Cayley in the 19th century, according to wikipedia.)

so matrix multiplication represents the composition of maps f∘g, and so on.

posted at 07:33:44

   

10月21日

@yuuki26

yuuki@yuuki26

My current understanding of mathematics.

• Matrices are linear maps.
matrices were historically just a notation for simultaneous equations with coefficients and variables separated.

e.g. writing

ax + by = e
cx + dy = f

as

(a b)(x) = (e)
(c d)(y) = (f).

posted at 07:33:11

   

2023年10月20日(金)7 tweetssource

2023年10月04日(水)14 tweetssource

10月4日

@yuuki26

yuuki@yuuki26

conclusion: speleology is hard. i still havent figured out what a limestone cave is. it could be commercial caves arent interesting.

posted at 15:28:38

   

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