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sin²x + cos²x =1

The Math Flow

41,531 subscribers

44,346 просмотров • 2 месяцев назад •via X (Twitter)

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cos²x+sin²x =1 (Pythagora in the unit circle) Visualization| Animation | Interactive applet GeoGebra #geogebra #math #science #iteachmath #mtbos #visualization #elearning Bernat ANCOCHEA

Daniel Mentrard

140,622 просмотров • 7 дней назад

a=(x,y,d=5*cos(o=mag(k=x/8-25,e=y/8-25)/3))=>[(q=x/2+k/atan(9*cos(e))*sin(d*4-t))*sin(c=d/3-t/8)+200,(y/3+d+q)/2*cos(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6,19);for(t+=PI/60,y=99;++y<300;)for(x=99;++x<300;stroke(x,y,y+x,36))point(...a(x,y))} #つぶやきProcessing

a=(x,y,d=5cos(o=mag(k=x/8-25,e=y/8-25)/3))=>[(q=x/2+k/atan(9cos(e))sin(d4-t))sin(c=d/3-t/8)+200,(y/3+d+q)/2cos(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6,19);for(t+=PI/60,y=99;++y<300;)for(x=99;++x<300;stroke(x,y,y+x,36))point(...a(x,y))} #つぶやきProcessing

ア

40,398 просмотров • 1 год назад

Hypnosis, 233 chars #つぶやきGLSL for (O *= m; m < 170.;O += .0007 / (abs(length( a + abs(sin(m* mix(.02,.07, sin(f)*.5 + .5) - f)) * vec2(cos(x = m*.05-f), sin(x)))-.5) + .02) * (1.+cos(m++*.1 + length(a)*6. - f + vec4(0,1,2,0))));

Hypnosis, 233 chars #つぶやきGLSL for (O = m; m < 170.;O += .0007 / (abs(length( a + abs(sin(m mix(.02,.07, sin(f).5 + .5) - f)) vec2(cos(x = m.05-f), sin(x)))-.5) + .02) (1.+cos(m++.1 + length(a)6. - f + vec4(0,1,2,0))));

kishimisu

38,594 просмотров • 2 лет назад

a=(x,y,d=cos(mag(k=x/8-25,e=y/8-25)/3)*e/5)=>[(q=x/4+k/cos(y/9)*sin(d*9-t)+25)*sin(c=d-t/8)+200,(q*2+x+y/2+d*90)/4*cos(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6,36).stroke(255,36);for(t+=PI/60,y=99;y<300;y+=2)for(x=99;++x<300;)point(...a(x,y))}#つぶやきProcessing

a=(x,y,d=cos(mag(k=x/8-25,e=y/8-25)/3)e/5)=>[(q=x/4+k/cos(y/9)sin(d9-t)+25)sin(c=d-t/8)+200,(q2+x+y/2+d90)/4*cos(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6,36).stroke(255,36);for(t+=PI/60,y=99;y<300;y+=2)for(x=99;++x<300;)point(...a(x,y))}#つぶやきProcessing

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48,854 просмотров • 1 год назад

a=(x,y,d=5*cos(o=mag(k=x/8-25,e=y/8-25)/3))=>[(q=x/2+k/atan(9*cos(e))*sin(d*4-t))*sin(c=d/3-t/8)+200,(y/4+5*o*o+q)/2*cos(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(255,96);for(t+=PI/60,y=99;++y<300;)for(x=99;++x<300;)point(...a(x,y))} //#つぶやきProcessing

a=(x,y,d=5cos(o=mag(k=x/8-25,e=y/8-25)/3))=>[(q=x/2+k/atan(9cos(e))sin(d4-t))sin(c=d/3-t/8)+200,(y/4+5oo+q)/2cos(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(255,96);for(t+=PI/60,y=99;++y<300;)for(x=99;++x<300;)point(...a(x,y))} //#つぶやきProcessing

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36,330 просмотров • 1 год назад

$t=0,d=5e-4,draw=_=>{t++||createCanvas(w=400,w);background(9).stroke(w,96);for(x=y=z=9,i=3e4;i--;point((q=x*(e=sin(t*PI/20-x*x/99+i%9)+1)+89)*cos(k=z/59-e/29+t*PI/480+i%9*8)+200,200-(q+60*cos(k/2))*sin(k)))[x,y,z]=[x+9*(y-x)*d,y+(x*(28-z)-y)*d,z+(x*y-z-z)*d]}//#つぶやきProcessing$

t=0,d=5e-4,draw=_=>{t++||createCanvas(w=400,w);background(9).stroke(w,96);for(x=y=z=9,i=3e4;i--;point((q=x(e=sin(tPI/20-xx/99+i%9)+1)+89)cos(k=z/59-e/29+tPI/480+i%98)+200,200-(q+60cos(k/2))sin(k)))[x,y,z]=[x+9(y-x)d,y+(x(28-z)-y)d,z+(xy-z-z)d]}//#つぶやきProcessing

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34,899 просмотров • 29 дней назад

a=(x,y,d=mag(k=x/8-25,e=y/8-25)**2/99)=>[(q=x/3+k*.5/cos(y*5)*sin(d*d-t))*sin(c=d/2-t/8)+e*sin(d+k-t)+200,(q+y/8+d*9)*cos(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(255,96);for(t+=PI/60,y=99;y<300;y+=5)for(x=99;++x<300;)point(...a(x,y))}#つぶやきProcessing

a=(x,y,d=mag(k=x/8-25,e=y/8-25)**2/99)=>[(q=x/3+k.5/cos(y5)sin(dd-t))sin(c=d/2-t/8)+esin(d+k-t)+200,(q+y/8+d9)cos(c)+200] t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(255,96);for(t+=PI/60,y=99;y<300;y+=5)for(x=99;++x<300;)point(...a(x,y))}#つぶやきProcessing

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365,539 просмотров • 1 год назад

x=u=v=f=0,n=200,draw=o=>{for(f||createCanvas(W=400,W),r=2*PI/n,background(0),i=0;i<n;i++)for(j=0;j<55;j+=.1)u=sin(i+v+f)-sin(R=r*i+x-99*f),v=cos(i+v+f)-cos(R),x=u+f,X=n+99*u,Y=n+99*v,stroke(W,2*j+66),line(X,Y,X+1,Y+1);f+=5e-5};//#つぶやきProcessing based on Basic code by ZXDunny

x=u=v=f=0,n=200,draw=o=>{for(f||createCanvas(W=400,W),r=2PI/n,background(0),i=0;i<n;i++)for(j=0;j<55;j+=.1)u=sin(i+v+f)-sin(R=ri+x-99f),v=cos(i+v+f)-cos(R),x=u+f,X=n+99u,Y=n+99v,stroke(W,2j+66),line(X,Y,X+1,Y+1);f+=5e-5};//#つぶやきProcessing based on Basic code by ZXDunny

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a=(x,y,d=abs(e=cos(k=x/8-12.5)+sin(y/24)+cos(k/2)))=>point((q=x/4+90+d*k*(1+cos(d*4-t*2+y/72)))*cos(c=y*e/594-t/8+d/6)+200,(q/2+99*cos(c/2))*sin(c)+e*6+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,36);for(t+=PI/60,i=4e4;i--;)a(i%200,i/200)}#つぶやきProcessing

a=(x,y,d=abs(e=cos(k=x/8-12.5)+sin(y/24)+cos(k/2)))=>point((q=x/4+90+dk(1+cos(d4-t2+y/72)))cos(c=ye/594-t/8+d/6)+200,(q/2+99cos(c/2))sin(c)+e*6+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,36);for(t+=PI/60,i=4e4;i--;)a(i%200,i/200)}#つぶやきProcessing

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a=(x,y,o=mag(k=x/8-12.5,e=y/8-9)/4)=>stroke(255,36).point((q=x+y+e/k+o*k*cos(y/3)*sin(o*2-t)*o/2)/3*atan(3*sin(c=o*e/40-t/8))+200,o*sin(x/9)-y*cos(c)+q/4*cos(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(6);for(t+=PI/120,i=2e4;i--;)a(i%200,i/200<<1)}#つぶやきProcessing

a=(x,y,o=mag(k=x/8-12.5,e=y/8-9)/4)=>stroke(255,36).point((q=x+y+e/k+okcos(y/3)sin(o2-t)o/2)/3atan(3sin(c=oe/40-t/8))+200,osin(x/9)-ycos(c)+q/4*cos(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(6);for(t+=PI/120,i=2e4;i--;)a(i%200,i/200<<1)}#つぶやきProcessing

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a=(x,y,d=5*cos(o=mag(k=x/8-12,e=y/13-14)/2))=> point((q=x/2+10+1/k+k*cos(e)*sin(d*8-t))*sin(c=d/3+t/8)+sin(d*2+t)*k+200,(y/4+5*o*o+q*cos(c*3))/2*cos(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,66);for(t+=PI/60,i=2e4;i--;)a(i%200,i/200)}#つぶやきProcessing

a=(x,y,d=5cos(o=mag(k=x/8-12,e=y/13-14)/2))=> point((q=x/2+10+1/k+kcos(e)sin(d8-t))sin(c=d/3+t/8)+sin(d2+t)k+200,(y/4+5oo+qcos(c3))/2cos(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,66);for(t+=PI/60,i=2e4;i--;)a(i%200,i/200)}#つぶやきProcessing

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a=(x,y,o=mag(k=x/4-12.5,e=y/9+5)/9)=>point((q=x+99+tan(1/k)+o*k*(cos(e*9)/4+cos(y/2))*sin(o*4-t))*.7*sin(c=o*e/30-t/8)+9*cos(y/19+t)+200,200+q/2*cos(c)) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,46);for(t+=PI/90,i=2e4;i--;)a(i%100,i/100)} //#つぶやきProcessing

a=(x,y,o=mag(k=x/4-12.5,e=y/9+5)/9)=>point((q=x+99+tan(1/k)+ok(cos(e9)/4+cos(y/2))sin(o4-t)).7sin(c=oe/30-t/8)+9cos(y/19+t)+200,200+q/2cos(c)) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,46);for(t+=PI/90,i=2e4;i--;)a(i%100,i/100)} //#つぶやきProcessing

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a=(x,y,o=mag(k=x/4-12.5,e=y/9)/9)=>point((q=x/3+99+3/k*sin(y)+k*(1+cos(y)/3+sin(e+o*4-t*2)))*cos(c=o/5+e/4-t/8)+200,(q+49)*sin(c)*cos(c)-q/3+30*o+220) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,46);for(t+=PI/90,i=2e4;i--;)a(i%100,i/350)}// #つぶやきProcessing

a=(x,y,o=mag(k=x/4-12.5,e=y/9)/9)=>point((q=x/3+99+3/ksin(y)+k(1+cos(y)/3+sin(e+o4-t2)))cos(c=o/5+e/4-t/8)+200,(q+49)sin(c)cos(c)-q/3+30o+220) t=0,draw=$=>{t||createCanvas(w=400,w);background(6).stroke(w,46);for(t+=PI/90,i=2e4;i--;)a(i%100,i/350)}// #つぶやきProcessing

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Finding the roots of a polynomial is one of the oldest and most central problems in Algebra. Once the coefficients are allowed to move through the complex plane, the roots start revealing a much richer geometry. Here is the Mathematics, try it yourself and play around with the coefficients and polynomial structure: P(x) = x¹² + a x⁸ + b x⁶ + c x⁴ + d x + 1 a = (sin(t₁) + i cos(sin(t₂) + 0.5 sin(2t₂))) M b = 0.3 (t₁ + t₂) Mᶜ c = (exp(i t₁) - cos(t₂)) M d = (cos(t₁) - 0.5 i sin(sin(t₂) + 0.5 sin(2t₂))) Mᶜ M = 1 + ∑ₖ₌₁ᵐ Aₖ exp(i 2π sₖ n / N) Mᶜ = 1 + ∑ₖ₌₁ᵐ Aₖ exp(-i 2π sₖ n / N) Here t₁ and t₂ lie on the unit circle, n is the frame index, N is the total number of frames, and Aₖ, sₖ are the modulation amplitudes and speeds.

Finding the roots of a polynomial is one of the oldest and most central problems in Algebra. Once the coefficients are allowed to move through the complex plane, the roots start revealing a much richer geometry. Here is the Mathematics, try it yourself and play around with the coefficients and polynomial structure: P(x) = x¹² + a x⁸ + b x⁶ + c x⁴ + d x + 1 a = (sin(t₁) + i cos(sin(t₂) + 0.5 sin(2t₂))) M b = 0.3 (t₁ + t₂) Mᶜ c = (exp(i t₁) - cos(t₂)) M d = (cos(t₁) - 0.5 i sin(sin(t₂) + 0.5 sin(2t₂))) Mᶜ M = 1 + ∑ₖ₌₁ᵐ Aₖ exp(i 2π sₖ n / N) Mᶜ = 1 + ∑ₖ₌₁ᵐ Aₖ exp(-i 2π sₖ n / N) Here t₁ and t₂ lie on the unit circle, n is the frame index, N is the total number of frames, and Aₖ, sₖ are the modulation amplitudes and speeds.

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a=(x,y,k=x/8-12.5,d=abs(e=cos(k)+sin(y/3)+cos(k/2)))=>point((q=x/4+90+d*k*(.5+cos(d*4-t*2+y/12)))*.7*(cos(c=y*e/198-t/8+d/5))+200,(q+70)*.7*sin(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0,96).stroke(w,26);for(t+=PI/90,i=4e4;i--;)a(i%200,i/500)}//#つぶやきProcessing

a=(x,y,k=x/8-12.5,d=abs(e=cos(k)+sin(y/3)+cos(k/2)))=>point((q=x/4+90+dk(.5+cos(d4-t2+y/12))).7(cos(c=ye/198-t/8+d/5))+200,(q+70).7*sin(c)+200) t=0,draw=$=>{t||createCanvas(w=400,w);background(0,96).stroke(w,26);for(t+=PI/90,i=4e4;i--;)a(i%200,i/500)}//#つぶやきProcessing

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$=[],t=0,draw=_=>t++?background(0,14)+($=[...$.slice(-5e3),...[...'#つぶやきProcessing'].map(p5.Vector.random3D)]).map(_=>stroke(255,96).point((_.x+=sin(r=((_.x*2*(k=_.x*4+2^_.y*4|2+_.z*4)^_.y*k+t/299)&1)*2-1)/99*_.z)*109+270,(_.y+=cos(r)/99*_.z)*109+270)):createCanvas(540,540)

$=[],t=0,draw=_=>t++?background(0,14)+($=[...$.slice(-5e3),...[...'#つぶやきProcessing'].map(p5.Vector.random3D)]).map(_=>stroke(255,96).point((_.x+=sin(r=((_.x2(k=_.x4+2^_.y4|2+_.z4)^_.yk+t/299)&1)2-1)/99_.z)109+270,(_.y+=cos(r)/99_.z)*109+270)):createCanvas(540,540)

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56,941 просмотров • 2 лет назад

a=(x,y,d=.5+5*cos(o=mag(k=x/8-12.5,e=y/8-12.5)**2/169))=>stroke((d*sin(k)*sin(t*4+e))**2*w,36).point(x+d*k*sin(d*2+o+t)+e*cos(e+t)+100,o*135-y/4-d*6*cos(d*3+o*9+t)+125) t=0,draw=$=>{t||createCanvas(w=400,w);background(6);for(t+=PI/120,i=4e4;i--;)a(i%200,i/200)}#つぶやきProcessing

a=(x,y,d=.5+5*cos(o=mag(k=x/8-12.5,e=y/8-12.5)**2/169))=>stroke((dsin(k)sin(t*4+e))**2w,36).point(x+dksin(d2+o+t)+ecos(e+t)+100,o135-y/4-d6cos(d3+o9+t)+125) t=0,draw=$=>{t||createCanvas(w=400,w);background(6);for(t+=PI/120,i=4e4;i--;)a(i%200,i/200)}#つぶやきProcessing

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47,773 просмотров • 1 год назад

a=(x,y,d=9*cos(o=mag(k=x/8-12.5,e=y/8-12.5)**2/139))=>stroke(99+99/sin(k)*sin(t+e)**2,66).point((x+sin(d)*d*k)/2+150+o*k*sin(t+d*o),y/9-d*15-cos(d*2)*d+220+d*sin(d-t)) t=0,draw=$=>{t||createCanvas(w=400,w);background(6);for(t+=PI/90,i=4e4;i--;)a(i%200,i/200)} #つぶやきProcessing

a=(x,y,d=9*cos(o=mag(k=x/8-12.5,e=y/8-12.5)**2/139))=>stroke(99+99/sin(k)*sin(t+e)**2,66).point((x+sin(d)dk)/2+150+oksin(t+do),y/9-d15-cos(d2)d+220+d*sin(d-t)) t=0,draw=$=>{t||createCanvas(w=400,w);background(6);for(t+=PI/90,i=4e4;i--;)a(i%200,i/200)} #つぶやきProcessing

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21,817 просмотров • 1 год назад

for(f=0,a=[],W=400,y=0;y<W;y+=10)for(x=0;x<W;x+=10)a.push([x,y]);draw=o=>{for(f||createCanvas(W,W),background(0,9),stroke(W),C=a=>constrain(a,100,300),i=W;i--;)d=PI/noise(i+sin(f)/13),point(a[i][0]=C(sin(d+f)+a[i][0]),a[i][1]=C(cos(d+f)+a[i][1]));f+=.01};//#つぶやきProcessing

for(f=0,a=[],W=400,y=0;y<W;y+=10)for(x=0;x<W;x+=10)a.push([x,y]);draw=o=>{for(f||createCanvas(W,W),background(0,9),stroke(W),C=a=>constrain(a,100,300),i=W;i--;)d=PI/noise(i+sin(f)/13),point(a[i][0]=C(sin(d+f)+a[i][0]),a[i][1]=C(cos(d+f)+a[i][1]));f+=.01};//#つぶやきProcessing

Koma Tebe

17,902 просмотров • 1 год назад