Greg Egan on Nostr: If you pick 3 points at random in the unit disk, the probability that they lie on a ...
If you pick 3 points at random in the unit disk, the probability that they lie on a perfectly straight line is zero.
However, the probability that the curvature of the circle they lie on is less than ε is, in the limit of small ε, equal to:
1024 ε / (525 π²)
≈ 0.2 ε
Published at
2026-10-04 13:36:29 UTCEvent JSON
{
"id": "e3d6ad2fb56d949e027d33da1a4d1177f2c3286d645e3811876dc313e11d24be",
"pubkey": "563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3",
"created_at": 1791120989,
"kind": 1,
"tags": [
[
"imeta",
"url https://media.mathstodon.xyz/media_attachments/files/117/382/901/003/155/492/original/443c8a282112a18a.png",
"m image/png"
],
[
"proxy",
"https://mathstodon.xyz/@gregeganSF/117382905198347066",
"web"
],
[
"proxy",
"https://mathstodon.xyz/users/gregeganSF/statuses/117382905198347066",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://mathstodon.xyz/users/gregeganSF/statuses/117382905198347066",
"pink.momostr"
],
[
"-"
]
],
"content": "If you pick 3 points at random in the unit disk, the probability that they lie on a perfectly straight line is zero.\n\nHowever, the probability that the curvature of the circle they lie on is less than ε is, in the limit of small ε, equal to:\n\n1024 ε / (525 π²)\n≈ 0.2 ε\nhttps://media.mathstodon.xyz/media_attachments/files/117/382/901/003/155/492/original/443c8a282112a18a.png\n",
"sig": "05a557547ff1ac37edff349fee95f8469d42d488d2de55ab244c6238f9585265ab7a2bbe4839059b95e61312ab726dbb34ad8219fa1d8e0f96c2330be097225e"
}