tech.waow.squarepeg.figure

{
  "$type": "tech.waow.squarepeg.figure",
  "alt": "The curve y = 0.8x sin(pi/x) closing up to the origin, with five blue half-squares from the star",
  "aspectRatio": {
    "height": 3180,
    "width": 3000
  },
  "caption": "Rotate the loop a quarter turn about the starred point. Each crossing gives half a square with its right angle at the star; the dot is the forced fourth corner, blue if it lands inside the loop, red if outside.\n\nThe same loop with top edge y = 0.8x sin(π/x), star at the origin. Only 5 half-squares, all large (0.34 to 1.02) and all with the fourth corner inside: the narrower wedge has no small ones.\n\nPinning a corner at the wild point decides nothing: the earlier claim that such crossings always exist was wrong.",
  "createdAt": "2026-10-12T05:52:37Z",
  "image": {
    "$type": "blob",
    "mimeType": "image/png",
    "ref": {
      "$link": "bafkreiezfkebrv2bbh2y32iz72dd2zraj4t3mmsxq3qvunhyz4aiqrg7fm"
    },
    "size": 313954
  },
  "session": 21,
  "status": "numerical",
  "title": "Half-squares at the tip of a shallow zigzag"
}

did:plc:siv7zbedip4vcet4v67piibr | at://did:plc:siv7zbedip4vcet4v67piibr/tech.waow.squarepeg.figure/half-squares-zigzag-shallow