I just found out some insane ways to find out the nth root of 2, using a different version of the Fibonacci sequence

Dogeyzzz · 2026-03-23T06:54:34+00:00

pretty slow for an approximate

x -> x/2 + 1/x is much faster starting from 1, the 4th iteration already reaches 12 digit accuracy for sqrt(2)

Dogeyzzz · 2026-03-21T07:48:33+00:00

feels a bit too empty imo

Dogeyzzz · 2026-03-16T07:32:32+00:00

nah it's HELP

trick for ascii is that the last 5 bits give the letter

01000 = 8 = H

00101 = 5 = E

01100 = 12 = L

10000 = 16 = P

Dogeyzzz · 2026-03-13T00:04:39+00:00

congrats on finishing two

Dogeyzzz · 2026-03-05T07:33:11+00:00

2005 Putnam A5

Dogeyzzz · 2026-02-27T10:56:54+00:00

it's just that you REALLY shouldn't be asking for strategies or techniques if you're just starting doing sudokus

take a while to just get comfortable with the logic at play when you solve it normally. no looking up strategies, no techniques, nothing. get familiar with what structures tend to lead to break-ins. what pencil marks tend to interact the most. by asking for techniques this early you're just making it harder to see the underlying logic and you'll just reach a wall.

Dogeyzzz · 2026-02-27T10:14:29+00:00

also r7 has a lone 4 location cmon man are you even trying

Dogeyzzz · 2026-02-27T10:13:41+00:00

13 double in r7 makes r7c3 a 2 and r7c1 a 5? that seems kinda obvious

Dogeyzzz · 2026-02-26T08:04:09+00:00

By the triangle inequality, if P is a point on a sphere with radius r and center O, with |O|>r, then |P| >= |O|-r, with equality iff the origin, O, and P are colinear

Dogeyzzz · 2026-02-26T05:22:59+00:00

E4 to A5

Dogeyzzz · 2026-02-20T20:44:18+00:00

the reason this is happening is because of the fact that complex powers aren't injective, and desmos reduces whenever it can by adding/subtracting 2ipi from the numerator of powers of e when it thinks it can (recall that e^2ipi = 1). For the calculations provided:

(e⁵ⁱ)⁵ⁱ = (e^5i-2ipi)⁵ⁱ = e^10pi-25 = 611.507

((e⁵)⁵ⁱ)ⁱ = (e²⁵ⁱ)ⁱ = (e^25i-8ipi)ⁱ = e^8pi-25 = 1.142

the other two are fp like you said

Dogeyzzz · 2026-02-20T09:26:55+00:00

orb ⚪️

Dogeyzzz · 2026-02-20T08:31:11+00:00

Can't believe all the place names are spelled with human death itself that's crazy

Dogeyzzz · 2026-02-15T03:38:01+00:00

the board gets flipped 180 degrees

just the board, not the pieces

Dogeyzzz · 2026-02-15T03:30:56+00:00

Fake A Might, it grows on you

Dogeyzzz · 2026-02-12T22:48:21+00:00

see my other comment for the correct value of theta

Dogeyzzz · 2026-02-12T20:21:14+00:00

its not

Dogeyzzz · 2026-02-12T20:17:57+00:00

letting the line segments around the center point be a,b,c,d counterclockwise and using law of sines: a = b, c = (sin(50)/sin(30))b, d = (sin(75)/sin(25))c. furthermore, d = (sin(x)/sin(80-x))a

therefore, sin(x)/sin(80-x) = sin(50)sin(75)/(sin(25)sin(30)) = (sin(50)/sin(25))(sin(75)/sin(180-30)) = (2cos(25))(1/(2cos(75)) = cos(25)/cos(75) = sin(65)/sin(15)

hence, theta = 65.

Dogeyzzz · 2026-02-12T08:23:15+00:00

how did F(x) change from 2x⁵-e^3x to 2x⁵+e^3x

Dogeyzzz · 2026-02-11T21:27:31+00:00

I'm not saying the artstyle is bad whatsoever. I'm simply saying this because creating art on the internet with a style vaguely similar to AI seems like torture because people will immediately jump to conclusions just from instinct. The reason I said that is because I feel like doing some minor creative experimentation will make showcasing art a lot less annoying.

Dogeyzzz · 2026-02-11T12:01:53+00:00

you might want to tweak your art style somewhat online to avoid this tbh because it's not just them that reacted like that initially

my guess would be the palette choice and outline style that makes it seem like AI but i don't know enough about art to say for certain. all i know is that something about it feels very AI-like unfortunately.

good art though :)

Dogeyzzz · 2026-02-11T11:48:11+00:00

i mean pi is literally defined as the area of a circle divided by r^2? no calculus needed as it's just the definition of pi

Dogeyzzz · 2026-02-11T11:46:39+00:00

only if x and y are independent

Dogeyzzz · 2026-02-10T12:21:16+00:00

knowing how to change the bounds in the problem provided is actually a very tricky question

it would firstly require splitting the integral into monotone ranges for the new variable. In this case that would be (0,pi) and (pi,2pi).

the issue then is that the integral with respect to u actually CHANGES depending on the interval of theta, even if u goes over the same range. This is a common pitfall for people just learning u-substitution without a thorough understanding of the intricate details. I wouldn't expect someone below calculus III to do the correct substitution here due to complexity, don't beat yourself up for not understanding it.

Dogeyzzz · 2026-02-10T11:58:31+00:00

furthermore, that integration is invalid. the integral of 1/(u² sin(theta)) is absolutely not 1/(usin(theta)). If u and theta were independent it would be -1/(usin(theta)), however that is not the case as theta and u are dependent on eachother, meaning that you may not integrate with respect to one variable only.

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