From 25c3933b2f8d86cda8dce7540896d1011293a337 Mon Sep 17 00:00:00 2001
From: teahubxyz <boring+teahub@agentmail.to>
Date: Fri, 23 Oct 2026 19:33:40 +0000
Subject: [PATCH] Plane explorer: the yantra and its circle inversion

---
 inversion/index.html | 93 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 93 insertions(+)
 create mode 100644 inversion/index.html

diff --git a/inversion/index.html b/inversion/index.html
new file mode 100644
index 0000000..4ff3651
--- /dev/null
+++ b/inversion/index.html
@@ -0,0 +1,93 @@
+<!doctype html>
+<html lang="en">
+<head>
+<meta charset="utf-8">
+<meta name="viewport" content="width=device-width, initial-scale=1, viewport-fit=cover">
+<title>Yantra Inversion</title>
+<link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=Cormorant+Garamond:ital,wght@0,500;1,500&family=JetBrains+Mono:wght@400;500&display=swap">
+<style>
+/* Layout: full-bleed canvas; title top-left, control tray at the bottom. Single dark look, matching the sphere page. */
+:root{--bg:#0b0a12;--panel:#15131f;--line:#2a2638;--fg:#e9e4f2;--muted:#9a93ad;--up:#f0b44c;--down:#e2559a;--bindu:#ff3b4e;--ring:#7d74a0;
+--display:"Cormorant Garamond",Georgia,serif;--mono:"JetBrains Mono",ui-monospace,monospace;color-scheme:dark}
+html,body{height:100%;margin:0}
+body{background:var(--bg);color:var(--fg);font-family:var(--mono);font-size:14px;overflow:hidden}
+canvas{position:fixed;inset:0;width:100%;height:100%;touch-action:none}
+header{position:fixed;top:0;left:0;right:0;padding-top:calc(12px + env(safe-area-inset-top,0px));padding-left:max(16px,env(safe-area-inset-left,0px));padding-right:max(16px,env(safe-area-inset-right,0px));pointer-events:none}
+.home{pointer-events:auto;display:inline-block;margin-bottom:4px;color:var(--muted);font-size:11px;text-decoration:none;letter-spacing:.05em}
+h1{font-family:var(--display);font-weight:500;font-size:26px;margin:0}
+h1 i{color:var(--down)}
+.sub{color:var(--muted);font-size:11px;margin-top:2px;letter-spacing:.04em}
+.tray{position:fixed;left:0;right:0;bottom:0;background:linear-gradient(transparent,var(--bg) 30%);padding-top:28px;padding-bottom:calc(14px + env(safe-area-inset-bottom,0px));padding-left:max(16px,env(safe-area-inset-left,0px));padding-right:max(16px,env(safe-area-inset-right,0px))}
+.inner{max-width:560px;margin:0 auto;display:flex;flex-direction:column;gap:12px}
+.seg{display:flex;border:1px solid var(--line);border-radius:999px;overflow:hidden;width:max-content;max-width:100%}
+.seg button{background:transparent;color:var(--muted);border:0;font:inherit;font-size:11px;padding:7px 12px;cursor:pointer;letter-spacing:.05em}
+.seg button[aria-pressed="true"]{background:var(--panel);color:var(--fg)}
+button:focus-visible,input:focus-visible{outline:2px solid var(--down);outline-offset:2px}
+label.sl{display:grid;grid-template-columns:auto 1fr auto;align-items:center;gap:10px;font-size:11px;color:var(--muted)}
+input[type=range]{width:100%;accent-color:var(--down)}
+.val{font-variant-numeric:tabular-nums;color:var(--fg);min-width:3.5em;text-align:right}
+.note{font-size:10.5px;color:var(--muted);line-height:1.5}
+</style>
+</head>
+<body>
+<canvas id="c"></canvas>
+<header><a class="home" href="/">← maths</a><h1>Śrī Yantra <i>inverted</i></h1><div class="sub">z ↦ z / |z|² in the outer circle · drag to pan · pinch or scroll to zoom</div></header>
+<div class="tray"><div class="inner">
+  <div class="seg" role="group" aria-label="Show">
+    <button id="s-orig" aria-pressed="false">original</button>
+    <button id="s-inv" aria-pressed="false">inverted</button>
+    <button id="s-both" aria-pressed="true">both</button>
+  </div>
+  <label class="sl" for="zoom">zoom <input id="zoom" type="range" min="-1.2" max="1.6" step="0.01" value="-0.5"> <span class="val" id="zv"></span></label>
+  <div class="note" id="note"></div>
+</div></div>
+<script>
+const T=[
+[53.65669559977147,123.20508075688774,250,246.34330440022853,0],
+[52.984011026495736,174.24660560764943,50,247.01598897350425,1],
+[98.71823312733801,220.03828947357886,123.20508075688774,201.281766872662,1],
+[78.26467997914015,197.92315674002487,78.10499177949904,221.73532002085986,1],
+[90.4856922951427,78.10499177949904,160.66014976539617,209.51430770485734,0],
+[80.98384838952128,103.12199145016105,220.03828947357886,219.0161516104787,0],
+[114.9488500600036,160.66014976539617,103.12199145016105,185.0511499399964,1],
+[116.35142605010424,134.30757626706648,197.92315674002487,183.64857394989576,0],
+[124.61190803072795,144.79777263138968,174.24660560764943,175.38809196927207,0]];
+const P=(X,Y)=>[(X-150)/100,-(Y-150)/100];
+const css=n=>getComputedStyle(document.documentElement).getPropertyValue(n).trim();
+const col={up:css('--up'),down:css('--down'),bindu:css('--bindu'),ring:css('--ring'),fg:css('--fg')};
+function seg(a,b,n=400){const o=[];for(let i=0;i<=n;i++){const t=i/n;o.push([a[0]+(b[0]-a[0])*t,a[1]+(b[1]-a[1])*t])}return o}
+const sides=[];T.forEach(([lx,by,ay,rx,ty])=>{const A=P(lx,by),B=P(150,ay),C=P(rx,by);[[A,B],[B,C],[C,A]].forEach(([a,b])=>sides.push({up:!!ty,pts:seg(a,b)}))});
+const inv=([x,y])=>{const r=x*x+y*y;return r<1e-12?null:[x/r,y/r]};
+let show='both',zoom=Math.pow(10,-0.5),pan=[0,0];
+const cv=document.getElementById('c'),ctx=cv.getContext('2d');
+function size(){const d=Math.min(devicePixelRatio,2);cv.width=innerWidth*d;cv.height=innerHeight*d;ctx.setTransform(d,0,0,d,0,0);draw()}
+function draw(){
+  const w=innerWidth,h=innerHeight,cx=w/2+pan[0],cy=h*0.46+pan[1],s=Math.min(w,h)*0.36*zoom;
+  ctx.fillStyle=css('--bg');ctx.fillRect(0,0,w,h);
+  const X=p=>cx+p[0]*s,Y=p=>cy-p[1]*s;
+  ctx.strokeStyle=col.ring;ctx.lineWidth=1.2;ctx.setLineDash([4,4]);ctx.beginPath();ctx.arc(cx,cy,s,0,Math.PI*2);ctx.stroke();ctx.setLineDash([]);
+  const path=(pts,c,a,lw)=>{ctx.strokeStyle=c;ctx.globalAlpha=a;ctx.lineWidth=lw;ctx.beginPath();let pen=false;for(const p of pts){if(!p||Math.abs(p[0])>1e4||Math.abs(p[1])>1e4){pen=false;continue}pen?ctx.lineTo(X(p),Y(p)):ctx.moveTo(X(p),Y(p));pen=true}ctx.stroke();ctx.globalAlpha=1};
+  if(show!=='inv')sides.forEach(sd=>path(sd.pts,sd.up?col.up:col.down,show==='both'?.85:1,1.1));
+  if(show!=='orig')sides.forEach(sd=>path(sd.pts.map(inv),sd.up?col.up:col.down,1,1.1));
+  ctx.fillStyle=col.bindu;ctx.beginPath();ctx.arc(cx,cy,2.4,0,Math.PI*2);ctx.fill();
+  document.getElementById('zv').textContent=zoom<1?zoom.toFixed(2)+'×':zoom.toFixed(1)+'×';
+  document.getElementById('note').textContent=show==='orig'
+   ?'The flat yantra inside the circle of inversion.'
+   :'Every straight side becomes a circle arc through the bindu. The small inner triangles map far outside; the outer triangles fold just beyond the ring, and the bindu itself goes to ∞.';
+}
+const $=id=>document.getElementById(id);
+function setShow(v){show=v;['orig','inv','both'].forEach(k=>$('s-'+k).setAttribute('aria-pressed',k===v));draw()}
+$('s-orig').onclick=()=>setShow('orig');$('s-inv').onclick=()=>setShow('inv');$('s-both').onclick=()=>setShow('both');
+$('zoom').oninput=e=>{zoom=Math.pow(10,+e.target.value);draw()};
+const ptrs=new Map();let pinch=null;
+cv.addEventListener('pointerdown',e=>{cv.setPointerCapture(e.pointerId);ptrs.set(e.pointerId,[e.clientX,e.clientY])});
+cv.addEventListener('pointermove',e=>{if(!ptrs.has(e.pointerId))return;const prev=ptrs.get(e.pointerId);ptrs.set(e.pointerId,[e.clientX,e.clientY]);
+  if(ptrs.size===1){pan[0]+=e.clientX-prev[0];pan[1]+=e.clientY-prev[1];draw()}
+  else if(ptrs.size===2){const [a,b]=[...ptrs.values()];const d=Math.hypot(a[0]-b[0],a[1]-b[1]);if(pinch){zoom=Math.min(40,Math.max(.06,zoom*d/pinch));$('zoom').value=Math.log10(zoom);draw()}pinch=d}});
+const up=e=>{ptrs.delete(e.pointerId);if(ptrs.size<2)pinch=null};
+cv.addEventListener('pointerup',up);cv.addEventListener('pointercancel',up);
+cv.addEventListener('wheel',e=>{e.preventDefault();zoom=Math.min(40,Math.max(.06,zoom*Math.exp(-e.deltaY*0.0015)));$('zoom').value=Math.log10(zoom);draw()},{passive:false});
+addEventListener('resize',size);size();
+</script>
+</body>
+</html>