Top #numbertheory dweets

function u(t) {

c.width=1920 // clear the canvas
for(i=0;i<9;i++)
x.fillRect(400+i*100+S(t)*300,400,50,200) // draw 50x200 rects

} // 122/140

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    u(t) is called 60 times per second.
    t: Elapsed time in seconds.
    S: Shorthand for Math.sin.
    C: Shorthand for Math.cos.
    T: Shorthand for Math.tan.
    R: Function that generates rgba-strings, usage ex.: R(255, 255, 255, 0.5)
    c: A 1920x1080 canvas.
    x: A 2D context for that canvas.

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taupelink

function u(t) {

c.width=500;p=37;a=2+t|0;for(n=0,m=a;++n<=p;)x.fillStyle=R((n-1)%(p-1)?0:255),x.fillText(n,270+(k=40+n)*C(z=m*6.28/p),140-k*S(z)),m*=a,m%=p

Jul 1 2019 1:21 AM UTC

}// 139/140

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Demonstration of Fermat's little theorem. Powers of 2, 3, 4..., modulo 37, arranged around a circle broken up into 37 equal arcs. #math #numbertheory https://en.wikipedia.org/wiki/Fermat%27s_lit…

u/donbright

p is 37?
u/taupelink

Yep, I picked an arbitrary prime number for demonstration purposes
u/donbright

awesp,e

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taupelink

remix of d/14855 by u/taupelink

function u(t) {

c.width=500;p=37;a=(t|0)%(p-1)+1;for(n=0,m=a;++n<=p;m*=a,m%=p)x.fillStyle=R((n-1)%(p-1)?0:255,0,(n-p+1)?0:255),x.fillText(n,12+m*12,7+n*7)

Jul 6 2019 6:29 PM UTC

}// 138/140

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Powers of a=1, 2, 3, ..., 36 modulo 37, arranged in rows. The 36th power is always 1; the 37th is a.

u/taupelink

#math #numbertheory Fermat's little theorem https://en.wikipedia.org/wiki/Fermat's_l…
u/DataMeta

Cool!

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andrea270872

function u(t) {

a=~~t
b=~~(t%1*10)
x.setTransform(A=a*9,B=b*9,-B,A,800,600)
for(i=-7;i++<7;)for(j=14;j--;x.fillRect(i,j-7,.05,.05));

Jun 27 2019 8:25 AM UTC

}// 116/140

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Sieve of Eratosthene for Gauss Integers - all white pixels left will be Gauss Primes

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KilledByAPixel

function u(t) {

for(s="",a=[i=1];i++<300;s+=a[i-2]+"/"+a[i-1]+"&emsp;")i%2?(n=(i-1)/2,m=n+1,a.push(a[n-1]+a[m-1])):(n=i/2,a.push(a[n-1]))
t?0:c.outerHTML=s

Jun 5 2019 8:36 PM UTC

}// 139/140

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Generating every fraction in order using the Stern–Brocot sequence.

u/KilledByAPixel

Minified version of this https://jan.jarfalk.se/infinite-fractions/
u/taupelink

#math
u/taupelink

#numbertheory
u/KilledByAPixel

https://en.wikipedia.org/wiki/Stern%E2%80%93…

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geb

remix of d/19254 by u/geb

function u(t) {

for(l=0,o=[0];l++-19;)o.push(l*(l+1)/2)
throw o+'\n https://oeis.org/A000217'

Jun 26 2020 5:53 PM UTC

}// 77/140

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In this sequence only 3 is prime

u/geb

I noticed this when i studied pascal's triangle
u/geb

#numbertheory #oeis

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taupelink

remix of d/14936 by u/taupelink

function u(t) {

c.width=500;p=37;m=1;for(n=p,o=1;--n;x.fillText(m,30+12*m,7*o++))m*=n,m%=p,o-1&&x.fillText('x'+n+'≡',0,7*o)

Aug 10 2019 4:39 AM UTC

}// 107/140

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Illustration of Wilson's theorem: 37 is prime, and 36! is congruent to 36 mod 37. #numbertheory https://en.wikipedia.org/wiki/Wilson%27s_the…

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taupelink

function u(t) {

t||(A=[e=1<<9,e+1],r=i=n=2,q=s="");i--?(z=A[i],s=`${z%e}/${z>>9} `+s,n-i-1&&A.splice(i+1,0,w+z),w=z):r++<12&&(q=s,i=n+=n-1,s="")
throw q

Jul 22 2019 12:30 AM UTC

}// 136/140

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Farey sequence of rational numbers. #math #numbertheory https://en.wikipedia.org/wiki/Farey_sequence

u/taupelink

a/b+c/d is NOT equal to (a+b)/(c+d), but the latter quantity is known as the "mediant" and is of interest. https://en.wikipedia.org/wiki/Mediant_(mathe…
u/taupelink

See also https://www.dwitter.net/d/14451 by u/KilledByAPixel
u/KilledByAPixel

👍
u/donbright

I did a Ford's Circles dweet a while back, https://www.dwitter.net/d/1951 ... love this stuff

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taupelink

remix of d/14770 by u/donbright

function u(t) {

f=frame;g=(a,b)=>b?g(b,a%b):a
e=X=>{n=0;for(i=X;--i;)n+=(g(i,X)==1);return n}
y=e(f);x.fillRect(f,1080-y/2,1,y/2)

Jun 27 2019 12:41 AM UTC

}// 113/140

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Graph of Euler's totient function, a remix that reuses donbright's compact definition of gcd. https://en.wikipedia.org/wiki/Euler%27s_toti…

u/taupelink

#math
u/taupelink

better version? t||(A=[]);f=frame;g=(a,b)=>b?g(b,a%b):a;for(X=0;X++<1920;) {n=0;for(i=X;--i;)n+=(g(i,X)==1);A[X]=n;x.fillRect(X,1080-n/2,1,2e3)}
u/taupelink

better version without gcd: t||(A=[0,1]);for(X=2;X++<1920;) {n=X;for(i=X;--i;)if(X%i==0)n-=A[i];A[X]=n;x.fillRect(X,1080-n/2,1,2e3)}
u/donbright

lol why do i think this looks like a city skyline?
u/donbright

#euler #totient #numbertheory

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