# ^^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

- “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.
- “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.

## Links

- Geometria quadratica. Trigonometria
quadratica.
- Dividere in parti
intere 360.