Pocket trigonometry
- Word "Sine" from sinus=fold from Arabic jaib (जेब) = pocket (OED).
- What has trigonometry to do with POCKETS?
- From Sanskrit term for it ardh-jyā
- (half-chord) or जीवा
- rendered in Arabic as jībā (no v sound in Arabic).
Toledo translations ca. 1125
- Was written as consonantal skeleton "jb" (without nukta-s then) like "pls" in SMS.
- Misread by Mozharab/Jew 12th c. Toledo mass translators as common word "jaib" = जेब = pocket.😊
- The word sine itself is proof that trigonometry went from India to Europe
- Where it was not correctly understood.
- but we are convinced that we must ape the "superior" West and its foolish mistakes
- Hence, we still use that translation mistake "sine" .
- Word "trigonometry" involves also a conceptual error: it is about circles not triangles
- as wrongly taught by NCERT
- Hence, students confused by my pre-test question what is \(\sin 92^∘\)?
- (In a right-angled triangle there cannot be any angle of \(92^∘\).)
The other question I ask is
- what is \(\sin 1^∘\)?
- Many students can't answer. They are 1600 years behind the times
- because they do Western math, not ganita.
- Values like \(\sin 1^∘\) required to calculate the radius of the earth.
Because the West did not properly understand trigonometry
- West was unable to calculate the radius of the earth correctly
- Hence, could not determine longitude
- Hence, the European longitude problem persisted till 19th c.
Longitude problem
- (Columbus' estimate of earth radius was off by 40%)
- This led to the famous longitude problem specific to European navigation because
- as Brahmagupta said "ignorance of earth's radius makes longitude calculations futile"
- Recall that the longitude problem was the major scientific challenge facing Europe from 15th to 18th century
- and that as late as 1712 British Parliament passed an act setting up the board of longitude
- to administer a prize of UKP 20,000 for a method of determining longitude at sea.