/sci/ - Science & Math

>>15031343
music is perfectly in tune when in equal proportions 1:1, 3:2, 5:8, 13:21.
Naturally some triangles just resonante better with me

from paper
>We then exhibit the impressive mathematical power of P322(CR-Decimal8) by showing that P322 holds
its own as a computational device even against Madhava’s sine table from 3000 years later. This is a strong
argument that the essential purpose of P322 was indeed trigonometric: suggesting that an OB scribe unwit-
tingly created an effective trigonometric table 3000 years ahead of its time is an untenable position

>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 set-
tings, including both hyperbolic and elliptic or spherical geometries (Wildberger, 2005, 2013, 2010). The
classical framing of trigonometry and geometry around circles and angular measurement is only one of a
spectrum of possible approaches, so perhaps we should view angular trigonometry as a social construct
originating from the needs of Seleucid astronomy rather than a necessary and intrinsic aspect of geome-
try.

>The paper is laid out as follows. In the first section we introduce P322 itself. Then we review contem-
porary geometric concepts: the roles of reciprocal slope, known as ukullû or indanum, properties of similar
triangles and the Diagonal rule. This is followed by a review of OB numerical procedures: the role of recip-
rocal tables, the square side rule, the square root algorithm and the trailing part algorithm. We then return
to P322 to discuss its method of construction, missing columns and unfilled rows.


this is a natural outcropping of exactness versus precision at iteration versus exactness.

If i were to put forward a competition we would make music triangles of these proportia, and than some other random ones and judge by beauty of hearing