Mark math

Two spirals: Six other named curves were built and cut. They lost for the same reason twice: a named curve gives rigour, not beauty. Lune, cardioid and limaçon are impeccable and ordinary — a crescent is a crescent. Cassini’s oval failed more interestingly: with b < c it genuinely is two lobes about a centre, but they are detached ovals flanking the middle rather than arms cradling it.

These two win because a spiral is the only one here whose character matches the mark’s job — it turns. Both have a handedness, so the mirrors below are a real choice, not a cosmetic one.

current

For comparison. Today’s lobe is a trace of a drawing, so it matches no equation — which is exactly the thing being fixed here.

Euler · shortthe turn arrives late — a compact hook
Euler · longruns further round the centre
Euler · slimbite pushed out — a thinner arm, more air
Euler · mirroredthe same curve, turning the other way
Golden · classicφ per quarter turn, as it comes
Golden · longa longer wrap — the tail reaches past its partner
Golden · small centrea smaller eye, so the arms carry the mark
Golden · mirroredthe other handedness

halo 55 units