Designed by mathematics
Every spacing value and font size on this site is derived from the golden ratio. Not because we had to. Because a sock-themed terminal deserves irrational beauty.
What is the golden ratio?
The golden ratio (phi, φ) is an irrational number approximately equal to 1.618. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two: a/b = (a+b)/a = φ. It appears in nature (sunflower spirals, nautilus shells, galaxy arms), classical architecture (the Parthenon), and Renaissance art (da Vinci's Vitruvian Man).
In design, φ creates proportions that feel balanced without being symmetrical. The human eye finds φ-derived relationships naturally pleasing, probably because we evolved surrounded by them.
How we use it
We built a complete design token system where every value is a power or root of φ. The base unit is 1rem. Multiply by φ to go up a step, divide by φ to go down. This gives us two scales: one for typography, one for spacing.
Type scale
Nine stops from 0.65rem to 4.236rem. Each step is related to its neighbors by φ or √φ, creating a smooth visual hierarchy.
| Token | Value | Derivation |
|---|---|---|
| --text-2xs | 0.65rem | 1 / φ² × √φ |
| --text-xs | 0.786rem | 1 / √φ² |
| --text-sm | 0.875rem | ≈ 1 / √φ |
| --text-base | 1rem | base |
| --text-md | 1.272rem | √φ |
| --text-lg | 1.618rem | φ |
| --text-xl | 2.058rem | φ × √φ |
| --text-2xl | 2.618rem | φ² |
| --text-3xl | 4.236rem | φ³ |
Spacing scale
Thirteen stops from 0.25rem to 6.854rem. The same φ-power logic governs padding, margins, and gaps across the entire site.
| Token | Value | Derivation |
|---|---|---|
| --space-3xs | 0.25rem | 1 / φ³ |
| --space-2xs | 0.382rem | 1 / φ² |
| --space-xs | 0.5rem | ≈ 1 / (φ × √φ) |
| --space-sm | 0.618rem | 1 / φ |
| --space-md | 1rem | base |
| --space-lg | 1.272rem | √φ |
| --space-xl | 1.618rem | φ |
| --space-2xl | 2rem | φ × √φ |
| --space-3xl | 2.618rem | φ² |
| --space-4xl | 3.236rem | φ² × √φ |
| --space-5xl | 4.236rem | φ³ |
| --space-6xl | 5.236rem | φ³ × √φ |
| --space-7xl | 6.854rem | φ&sup4; |
Other φ-derived values
The body line-height is exactly φ (1.618). Our asymmetric two-column grids use a 1:φ ratio (1fr 1.618fr). Even the relationship between section padding and element spacing follows the golden proportion.
“The golden ratio is not magic. It is geometry that agrees with biology. Our eyes parse φ-derived layouts faster because the proportions match patterns we already know.”
Why bother?
Most sites pick sizes by feel. That works until a new section breaks the rhythm. A φ-based system is self-consistent: every value relates to every other by the same constant. Add a new element, snap it to the nearest φ stop, and it fits. No eyeballing required.
It also means we can tighten or loosen the entire site by shifting every token one step on the scale. The proportions stay golden. Only the density changes.
We did all of this for a terminal named after a sock. It’s fine. We’re fine. Mostly.