Radical sign
Also called square root, surd, radix
Christoff Rudolff, 1525; the bar is later
Modern symbolsRadical sign meaning
The radical sign means a root: what number, times itself, gives this. Christoff Rudolff printed a check-mark for it in 1525. Descartes added the bar on top so the sign knows where it stops.
The check that asks what number, times itself, makes this one.
The name. Latin radix, a root. Surd comes through Latin surdus, deaf — a translation of the Arabic word for an irrational, which had meant mute or unhearable.
Where it comes from
Christoff Rudolff’s Coss (1525) prints a check-like mark for the square root, without a bar over the number. Descartes, in the Geometry (1637), draws the vinculum across the top so the sign knows where it stops. A small index in the crook turns it into a cube root or worse. “Radical” in politics is the same Latin — go to the root — and it is not descended from this mark. The words collided. The signs did not.
Geometry
The diagonal that will not be a fraction
The diagonal of a unit square is √2. Euclid proves it is not a ratio of whole numbers. The story that the Pythagoreans drowned the man who said so is late and thin. The proof is in the Elements and does not need a murder. The golden ratio has √5 inside it for the same reason a pentagon will not behave.
Modern
The bar is punctuation
Without Descartes’s line, a root sign does not say how far it reaches. √2 + 3 can be read two ways. The vinculum is grammar. A great many symbols in this cabinet are pictures of a thing. This one is a piece of sentence structure that learned to look like a picture.
Near this
- Golden ratioA cut where the whole stands to the larger part as that part stands to the smaller.
- EqualsTwo parallels of one length, because nothing is more equal than that.
- Vesica piscisTwo equal circles, each through the other’s center. A third shape appears.
- PentagramFive lines in one stroke. The doctrines came later, and they disagree.
Sources
- Christoff Rudolff, Coss (1525)
- Descartes, La Géométrie (1637), the vinculum
Named when the entry depends on a text, a date, or a standard. Catalog numbers are not invented.
Your margin
Private. It stays in this browser and never joins the canon.
symbol.wiki, edited as Sigilla. Last reviewed 2 October 2026. A reading of public tradition, not a ruling.