διάμετρος

Diámetros in Greek means measuring through, from dia (through, across) and metron (measure). The word was used by Euclid in his Elements (~300 BCE) for the line segment passing through the center of a circle and touching both sides. The diameter is the longest possible straight line within a circle. It is also twice the radius — a relationship so simple it seems not worth stating, but Euclid stated it precisely because precision was the point.

The diameter was the primary measurement of circles in antiquity. The circumference-to-diameter ratio (π) was the central problem. Archimedes, Zu Chongzhi in China (who achieved a 7-digit approximation by 480 CE), and Madhava of Sangamagrama in India (who developed infinite series for π around 1400 CE) all worked with diameter as the base measurement. The modern convention of using radius (half the diameter) as the base came later.

The word expanded beyond circles. The diameter of a sphere, of a lens, of a pipe, of a bullet, of a tree trunk — the word measures across anything approximately circular in cross-section. Telescope and microscope specifications use diameter for the aperture (opening). A 200-inch telescope has a primary mirror 200 inches across. The Greek 'measure through' works for every round object.

In graph theory and network science, the diameter of a network is the longest shortest path between any two nodes — how many steps it takes to get from the most distant node to any other via the most efficient route. The word has been abstracted from physical circles to relational structures. The measurement is no longer across a shape. It is across a system of connections.