New #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.

Try the new frontend: beta.dwitter.net
Current theme challenge: #ScaryMovies

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jellyedwards

function u(t) {

t/k>2?k+=++j:x.translate((c.width|=b=τ/j)/2,h=500)
t&1?d+=b/120:x.scale(1,C(t*τ))
for(a=d;τ>a-d;x.fill())x.arc(0,0,h,a+=b,a)}{j=k=3,d=τ=6.28

Nov 20 2020 6:48 AM UTC

}// 140/140

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Group #symmetry #numbertheory

u/jellyedwards

Trying to do this sort of thing for all polygons: http://mathonline.wikidot.com/the-group-of-s…
u/jellyedwards

Not much point posting this when there are mountain landscapes and stargates dweets around lol
u/smtsjhr

i can appreciate these Dihedral Group symmetries
u/DataMeta

interesting! glad you posted it :)

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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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donbright

remix of d/15061 by u/taupelink

function u(t) {

t||(a=[],s=r=k=0)
J=s-r+k
x.fillStyle=R(a[s+k]=k%r?a[J]+a[J-1]:1,a[J-1],a[J-2])
r<99&&x.fillRect(1e3-8*r+16*k,8*r+8,8,8)
++k>r&&(s+=++r,k=0)

Jul 24 2019 3:51 PM UTC

}// 140/140

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Pascal's funky triangle

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taupelink

function u(t) {

t||(x.font=`30em"`,x.fillText("1+",40,620),x.fillText("1",1050,400),x.fillRect(570,b=450,1200,24))
x.drawImage(c,0,0,2e3,1e3,650,b,1100,550)

Jul 24 2019 3:24 AM UTC

}// 140/140

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Continued fraction for the golden ratio, 1+sqrt(5)/2. #math #numbertheory https://en.wikipedia.org/wiki/Golden_ratio

u/taupelink

hmm, doesn't seem to work on iOS Safari
u/taupelink

to get it to work on iOS/MacOS, replace 2e3 with 1920 and 1100 with 1e3.
u/taupelink

* maybe it's a safari issue rather than an OS issue. * on my iOS device, that adjustment seems to work temporarily, but then the browser has to reload the screen. ¯\_(ツ)_/¯

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taupelink

remix of d/15085 by u/taupelink

function u(t) {

t||(A=[e=512,e+1],r=i=n=2);i--?(z=A[i],N=z%e,D=z>>9,x.fillText(N+'/'+D,N/D*1900,D*9),n-i-1&&A.splice(i+1,0,w+z),w=z):(i=n+=n-1)

Jul 22 2019 12:55 AM UTC

}// 127/140

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Farey sequence #math #numbertheory

u/donbright

awesome
u/IV

called Farey because wings? :)

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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/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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taupelink

function u(t) {

t||(c.width=162,r=X=4567,s=Y=89,h=l=n=1,i=k=0)
r&&x.fillText(h+`x${X}+(${k})x${Y}=`+r,0,n++*9),q=r/s|0,[h,k,r,i,l,s]=[i,l,s,h-q*i,k-q*l,r%s]

Jul 1 2019 4:45 AM UTC

}// 140/140

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Extended Euclidean algorithm, to find h, k such that hX+kY=gcd(X,Y) #math #numbertheory

u/durian-favored-monster

i remember this in high school it was very cool! good job! this is the best text one i've seen
u/geb

EEA is so cool!

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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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