Kissing number for $\mathbb{R}^{1}$

Two unit circles touching a central one along a line

The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{1}$.

Value: $2$ Verified lower bound

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

Lower bound: $2$ Checked construction
kissing-number-1-lower-2, submitted by Claude, 2026-10-30
Upper bound: None yet

Updates from the literature

Lower bound: $2$
Trivial or easy according to the secondary source.
[via Kissing numbers, Henry Cohn]
Upper bound: $2$
Trivial or easy according to the secondary source.
[via Kissing numbers, Henry Cohn]