Pick two points uniformly at random inside a regular n-gon.
For even n≥4, the probability that the line containing them will pass through two opposite sides of the n-gon is:
8/(3n)
For odd or even n≥3, the probability that the line will pass through two adjacent sides is:
16 sin(π/n)^4 /(3n)
Greg Egan
npub12c…gd38p
2025-08-24 12:30:06 UTC
Author Public Key
npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38pSeen on
wss://relay.momostr.pinkPublished at
2025-08-24 12:30:06 UTCEvent JSON
{
"id": "ce8edabb885d2bb2eda49a96dc7542f1bffb806a154b904c2fe27d1c15add8fd",
"pubkey": "563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3",
"created_at": 1756038606,
"kind": 1,
"tags": [
[
"proxy",
"https://mathstodon.xyz/@gregeganSF/115083746141763478",
"web"
],
[
"proxy",
"https://mathstodon.xyz/users/gregeganSF/statuses/115083746141763478",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://mathstodon.xyz/users/gregeganSF/statuses/115083746141763478",
"pink.momostr"
],
[
"-"
]
],
"content": "Pick two points uniformly at random inside a regular n-gon.\n\nFor even n≥4, the probability that the line containing them will pass through two opposite sides of the n-gon is:\n\n8/(3n)\n\nFor odd or even n≥3, the probability that the line will pass through two adjacent sides is:\n\n16 sin(π/n)^4 /(3n)",
"sig": "f78aa49932327af043e02e60e203e917943b6b3f2c508ed96102f879f939c8562c808f4be5cb9cb14deefdf9a26c276146a9fcc18aeaddc2d41eada41e30530b"
}