mixedsexagesimal

Mixedsexagesimal refers to the representation of numbers in a mixed radix system based on the base–60 (sexagesimal) notation used by ancient civilizations such as the Babylonians and the Sumerians. Unlike a pure positional base‑60 system, mixedsexagesimal allows different place values to carry distinct multipliers. For example, the first two positions may use a multiplier of 60, while subsequent positions might use 36, or other combinations such as 12, 60, and 60, enabling efficient representation of angles or time units that naturally divide into 60, 12, or 6 units.

Historically, mixedsexagesimal notation was employed in astronomical tables, calendrical calculations, and military measurements. The ancient astronomer Plutarch recorded mixedsexagesimal expressions for planetary longitudes, where a single unit could represent degrees, minutes, and seconds in a compact form. In Sumerian clay tablets, mixedsexagesimal was also used for inventory accounting where quantities of barley or oil were recorded in units and fractions that best suited trade practices.

In modern contexts, mixedsexagesimal concepts appear in geodesy and navigation. Latitude and longitude are expressed in degrees, minutes, and seconds (mixed), and time measurements in hours, minutes, and seconds (mixed). Conversions from mixedsexagesimal to decimal involve multiplying each component by its positional factor and summing the results. For example, 3° 15' 30" equals 3 + 15/60 + 30/3600 = 3.2583° approximately. Mixedsexagesimal remains a useful tool for encoding measurements that naturally partition into subunits below 60.