Difference between revisions of "User:5849206328x"

Latest revision as of 17:35, 1 June 2023

$[asy] size(216); draw((0,10)--(0,0)--(10,0)); draw((5,10)--(0,0)--(10,5)); label("$ct$",(0,10),N); label("$x$",(10,0),E); label("$ct'$",(5,10),N); label("$x'$",(10,5),E); dot((0,3),blue); dot((3,6),blue); draw((0,3)--(3,6),blue); label("$ct_1$",(0,3),W,blue); label("$ct_2'$",(3,6),NW,blue); [/asy]$

$[asy] size(216); pair[] nodes; for (int i = 0; i < 10; ++i) { nodes.push(dir(36 * i)); dot(dir(36 * i)); label(string(i), 1.1 * dir(36 * i)); } draw(circle(nodes[0] - 0.1, 0.1), Arrow); draw(nodes[1] -- nodes[7], Arrow); draw(nodes[2] -- nodes[4], Arrow); draw(nodes[3] -- nodes[1], Arrow); draw(nodes[4] -- nodes[8], Arrow); draw(arc(nodes[5] + 0.1, 0.1, 180, 540), Arrow); draw(nodes[6] -- nodes[2], Arrow); draw(nodes[7] -- nodes[9], Arrow); draw(nodes[8] -- nodes[6], Arrow); draw(nodes[9] -- nodes[3], Arrow); [/asy]$

$[asy] unitsize (1 cm); pair A, B, C; A = (3,2); B = intersectionpoint(arc(A,4,200,340),C--(10,0)); C = (0,0); draw(B--A--C--(8,0), Arrow(6)); draw(arc(A,4,200,340), dashed); label("$A$", A, N); label("$B$", B, SE); label("$C$", C, NNW); label("$b$", (A + C)/2, NW); label("$c$", (A + B)/2, NE); label("$\theta$", (1,0.3)); [/asy]$

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Difference between revisions of "User:5849206328x"

Latest revision as of 17:35, 1 June 2023

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 <asy>
-import slopefield;
+size(216);
-Label f;
+draw((0,10)--(0,0)--(10,0)); draw((5,10)--(0,0)--(10,5));
-f.p=fontsize(6);
+label("$ct$",(0,10),N); label("$x$",(10,0),E);
-xaxis(0,4);
+label("$ct'$",(5,10),N); label("$x'$",(10,5),E);
-yaxis(-2,3);
-real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353;
+dot((0,3),blue); dot((3,6),blue); draw((0,3)--(3,6),blue);
-real y(real t, real a) { return (a - e^(-t^2))/(a + e^(-t^2)); }
+label("$ct_1$",(0,3),W,blue); label("$ct_2'$",(3,6),NW,blue);
-real f(real x) { return y(x,1); }
+</asy>
-real g(real x) { return y(x,-3); }
-real h(real x) { return y(x,1/5); }
-real j(real x) { return y(x,-1/5); }
-real z(real t, real y) { return t * (1 - y^2); }
+<asy>
-add(slopefield(z,(0,-2),(4,3),20,Arrow));
+size(216);
-pair one(real y) { return (1/(1 - y^2),y); }
+pair[] nodes;
-pair two(real y) { return (-1/(1 - y^2),y); }
+for (int i = 0; i < 10; ++i) {
+  nodes.push(dir(36 * i));
+  dot(dir(36 * i));
+  label(string(i), 1.1 * dir(36 * i));
+}
+draw(circle(nodes[0] - 0.1, 0.1), Arrow);
+draw(nodes[1] -- nodes[7], Arrow);
+draw(nodes[2] -- nodes[4], Arrow);
+draw(nodes[3] -- nodes[1], Arrow);
+draw(nodes[4] -- nodes[8], Arrow);
+draw(arc(nodes[5] + 0.1, 0.1, 180, 540), Arrow);
+draw(nodes[6] -- nodes[2], Arrow);
+draw(nodes[7] -- nodes[9], Arrow);
+draw(nodes[8] -- nodes[6], Arrow);
+draw(nodes[9] -- nodes[3], Arrow);
+</asy>
-draw(graph(f,0,4),red);
+<asy>
-draw(graph(g,0,4),darkgreen);
+unitsize (1 cm);
-draw(graph(h,0,4),blue);
-draw(graph(j,0,0.71),purple); draw(graph(j,1.52,4),purple);
-draw((0,1)--(4,1));
-draw((0,-1)--(4,-1));
-draw(graph(one,-0.867,0.867),dashed);
+pair A, B, C;
-draw(graph(two,-2,-1.118),dashed);
-draw(graph(two,1.118,3),dashed);
-label("$-3/2$",(0,-3/2),W);
+A = (3,2);
-label("$-1$",(0,-1),W);
+B = intersectionpoint(arc(A,4,200,340),C--(10,0));
-label("$-2/3$",(0,-2/3),W);
+C = (0,0);
-label("$0$",(0,0),W);
-label("$1$",(0,1),W);
+draw(B--A--C--(8,0), Arrow(6));
-label("$2$",(0,2),W);
+draw(arc(A,4,200,340), dashed);
+label("$A$", A, N);
+label("$B$", B, SE);
+label("$C$", C, NNW);
+label("$b$", (A + C)/2, NW);
+label("$c$", (A + B)/2, NE);
+label("$\theta$", (1,0.3));
 </asy>