# ^^Trigonometria Old Babylonian.

Appunti articolo Plimpton 322 is Babylonian exact sexagesimal trigonometry

## The OB (Old Babylonian) scribes used a richer sexagesimal (base 60) system

which is more suitable for exact computation than our decimal system

• while they were not shy of approximation
• they had a preference for exact calculation.

The novel approach to trigonometry and geometrical problems encapsulated by P322 resonates with modern investigations centered around rational trigonometry both in the Euclidean and non-Euclidean settings, including both hyperbolic and elliptic or spherical geometries.

Finally we follow Knuth (1972) in showing that the OB tablet AO 6770 demonstrates an understanding of linear interpolation, which increases the potential range and power of P322 considerable

it is becoming increasingly clear that the OB tradition of step-by-step procedures based on their concrete and powerful arithmetical system is much richer than we formerly imagined.

Geometry in ancient Babylon arose from the practical needs of administrators, surveyors, and builders. From their measurements of fields, walls, poles, buildings, gardens, canals, and ziggurats, a metrical understanding of the fundamental types of practical shapes was forged; typically squares, rectangles, trapezoids and right triangles, with general triangles very much of secondary interest.

## Inclinazione

The seked of a right pyramid is the inclination of any one of the four triangular faces to the horizontal plane of its base, and is measured as so many horizontal units per one vertical unit rise. It is thus a measure equivalent to our modern cotangent of the angle of slope. In general, the seked of a pyramid is a kind of fraction, given as so many palms horizontally for each cubit vertically, where 7 palms equals one cubit.

## Terminologia

1. Babylonian Exact Sexagesimal Trigonometry”, so we call the OB ratio-based framework for the study of triangles, to distinguish it from the more familiar modern angle based framework.
2. Angular Trigonometry” The usual framing of trigonometry (and geometry) around circles and angular measurement.
We should view angular trigonometry as a social construct originating from the needs of Seleucid astronomy rather than a necessary and intrinsic aspect of geometry.