31 unemployed, elementary school dropout, single, virgin #unschooling #studytwt #langtwt yuukikonno.com

i talk to ai entirely in english. i can't read english so i use google translate

started using deepseek too feels like chatgpt is ahead. don't see the need for anything else

a person like this. she likes to touch cats. she's allergic to them

being wished happy birthday by a schoolgirl—i can't imagine any greater happiness existing in the world of humankind

On Aug 31 last year, i got a dm from a schoolgirl. her name was ‘death’, and she sent me weird nonsense. thought it was from Sadako. said she'd be dead if it weren't for me we lost touch, but she dmed me hbd last month. guess she's got a bf

there are 2 ways 1) draw a point at (x, y) 2) move the point to (x, y) the latter falls into kinematics or “geometry of motion”—a middle ground of physics and math. i've always thought that. en.wikipedia.org/wiki/Kinemat...

what comes next is what an equation is. y = x and x = 2 are lines. x = x seems like the whole plane. some say ancient people considered x² to be area, not a parabola.

couldn't stop bc people in the future would get lost

it took me a whole week and 30 posts just to organize my thoughts from a single day

game of go is left-handed. chess is right-handed. (shogi is rotated right-handed) the difference between go and chess—placing on intersections vs inside squares—could also be formalized mathematically (lattice points?) </end of specializing the cartesian plane> </end of topic 1>

we can also think of a rotated coordinate system. en.wikipedia.org/wiki/Rotatio... a “rotating” coordinate system seems like a different idea—one that keeps spinning. en.wikipedia.org/wiki/Rotatin...

why “right-handed”? maybe because: 1) palm up 🫴 you can line thumb with x-axis, index with y-axis or 2) thumb up 👍 your other four fingers show the angle direction (like a protractor)

Ano Natsu ga Houwa Suru. (That Summer Saturates.) - Mashiro Meme #nowplaying youtu.be/m79OrSy03rs

</end of generalizing the cartesian plane>

seems like planes and surfaces are “manifolds”. two-dimensional manifold or 2-manifold.

thinking of a curved plane leads to a sphere—finite. this intuition may correspond to it.

If all points of a connected surface S are umbilical points, then S is either contained in a sphere or in a plane. do Carmo, M. P. (1976). "Differential Geometry of Curves and Surfaces", §3-2, Proposition 4, p. 147. maybe this. en.wikipedia.org/wiki/Umbilic...

feels like there's a theorem only surfaces that satisfy a certain condition are planes and spheres. like “the two principal curvatures are equal and constant”.

“curvature” is way too difficult for me to understand at this point.

a cylinder 🥫 is if the radius is infinite, it's a plane. if the radius is finite, and the height is infinite, it's an infinite surface. its “curvature” is constant—but zero, it seems.

1) a paraboloid of revolution 🥣 comes to mind first. food sits at the bottom, but the rim is infinitely far. but 🥣 doesn't have a constant “curviness”. (if it were, it'd be a sphere 🌐—finite)

been using five AIs, ChatGPT, Gemini, Grok, Perplexity, and Claude, in five windows on my macbook. still figuring them out.

2) Yes, a sphere with an infinite radius is a plane. a circle with an infinite radius is a line—called a generalized circle, cline, or circline. en.wikipedia.org/wiki/General...

a plane is infinite, but a sphere is finite. (the area of a sphere is 4πr²) 1) are there any infinite curved surfaces? 2) can a sphere have an infinite radius? (would it become a plane...??)

took a stimulant

woke up (2am)

rocking my body to keep my brain fast enough to understand what i'm working on

slept 12 hrs 😊

i might be studying math. might've learned something new for the first time since my teens

before coordinates, what even is space? one way is to research it. another way: consider 2d euclidean space with various coordinate systems.

rectilinear (affine) coordinates may require each scale be an arithmetic sequence. general curvilinear coordinates do not.

Cartesian coordinates are both orthogonal and rectilinear. (polar coordinates are orthogonal but non-linear)

curvilinear ┣━ rectilinear ⟺ affine ┗━ non-linear curvilinear ┣━ orthogonal (rectangular) ┗━ skew (oblique)

gridlines or scales⸻there's more than one way to draw them. the standard is orthogonal (rectangular) and rectilinear, but oblique and/or curvilinear are also possible.

when drawing figures, there are 2 ways • drawing on blank paper • drawing on graph paper i.e., drawing in a blank space, or in a space with a grid. the former is called synthetic geometry; the latter, analytic geometry.

still thinking about the continuation of this, need a few more sleeps to sort it out

just remembered i might've discovered in middle school that if (not (A and B)) { ... } is equivalent to if (not A or not B) { ... } (de morgan's laws). i'd totally forgotten

Example: Area of triangle △ABC Synthetic: √(s(s - a)(s - b)(s - c)) Analytic: 1/2 |Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)|

the former is called Heron's formula, and the latter the shoelace formula (or the surveyor's formula or Gauss's area formula).

just woke up (it's 8pm)

historically, Descartes' book "La Géométrie" (1637) is said to have contributed it. that book was difficult. it was expanded by mathematicians including van Schooten, de Beaune, Hudde, de Witt, van Heuraet, and Huygens, it seems. en.wikipedia.org/wiki/La_G%C3...

first of all, what exactly are coordinates? i've been researching it but it's tough. i think there are 3 topics • synthetic vs analytic geometry • how to represent the position of a point • how to view a space: as a collection of what?

could there be a new theory: poop then eat my recent breakfast www.instagram.com/p/DKH4YsgzXq0/

isn't it healthy to drink monster energy every morning? after a good night's sleep. what do you think?

took a morning bath

just founded “drawPoint geometry”. the study of drawing lines using only the function drawPoint(x, y) that draws a point (x, y) on the plane. i've successfully drawn a horizontal line in a 1d space. github.com/yuuki15/draw...

i didn't know the pythagorean theorem √((x₂ - x₁)² + (y₂ - y₁)²) and was using the sum of the side lengths |x₂ - x₁| + |y₂ - y₁| to find the distance. it's called the manhattan distance. my only discovery in math.

around 2008, at 14, i was studying analytic (or coordinate) geometry. i was making a VRChat bot and needed to move a character to a specific position (x, y). so i was thinking about linear motion etc.

yuuki's morning routine wake up try to nap again, like after exercising drink coffee don't eat until hungry work i sleep with an eye mask—important ℹ️

slept at 8 woke up at 18

i understood the reason at 31. □□□□□□□□□□ □□□ □□□□□□□□ when you picture this, you can clearly see that 2+3 is the answer. the equation 13-(10-2) tells you nothing. i finally understood calculus (latin: pebble)

i discovered in elementary school to calculate 13 - 8, think: 8 needs 2 to make 10. adding that 2 to 3 gives the answer fsr. i discovered this.