The World of
τριγωνομετρία
τριγωνομετρία
(Greek)
τριγωνομετρία = trigonometria = trigonometry
τριγώνου = Trigó̱nou = trigonon = triangle
μέτρηση = métri̱si̱ = metria = measurement
Hence, trigonometry = triangle measurement
Where did it come from?
Trigonometry was developed from the study of
RIGHT TRIANGLES!
by applying the relationships between measures of its sides and
angles to the study of similar triangles. However, it was not the
creation of just one man or nation….
Egypt
Early Egyptians built their famous pyramids
using a primitive form of trigonometry!
Greece
Hipparchus, a Greek astronomer, was considered
the father of trigonometry. (2nd Century B.C.E.)
Greece
Claudius Ptolemy, another Greek scientist and philosopher, was the
most influential in the development of trigonometry. His theorem
written in the Almagest was similar to the present day Law of Sines.
Proof of Law of Cosines using Ptolemy’s Theorem
India
Influential works from the 4th–5th century, known as the Siddhantas (5
compilations) first defined the sine as the modern relationship
between half an angle and half a chord, while also defining the cosine,
and inverse sine.
ARYABHATA (4th-5th C.E.)
Indian mathematician and astronomer,
Aryabhatta, collected and expanded upon
the developments of the Siddhantas in an
important work called the “Aryabhatiya”.
The Siddhantas and the Aryabhatiya contain
the earliest surviving tables of sine values
and versine (1 − cosine) values, to an
accuracy of 4 decimal places.
Persia and Arabia
The Indian works were later translated and
expanded in the medieval Islamic world by Muslim
mathematicians of mostly Persian and Arab
descent.
Abū al-Wafā' al-Būzjānī (10th C.E.),
Persian Mathematician and
Astronomer’s work had Muslim
Mathematicians using all six
trigonometric functions.
China
Contributions in Spherical Trigonometry
Shen Kuo or Shen Gua (1031–1095 C.E.)
mathematician, astronomer,
meteorologis, geologist, zoologist,
botanist, pharmacologist and more…
Guo Shoujing ( 1231–1316 C.E.)
Chinese astronomer, engineer,
and mathematician.
Europe
In the 17th century, Isaac Newton and James Stirling developed
the general Newton–Stirling interpolation formula for
trigonometric functions.
Sir Isaac Newton (1642 – 1747)
English physicist, mathematician,
astronomer, alchemist and
theologian
James Stirling (1692 - 1770)
Scottish mathematician
The World of Trigonometry
TODAY
The World of Trigonometry
Watch out for the Triangles!
Resources
Adamek T., Penkalski K., Valentine G. (2005). ”The History of Trigonometry”. Retrieved
on March 10th, 2012, from
http://www.math.rutgers.edu/~mjraman/History_Of_Trig.pdf
Anonymous (n.d.), “History of Trigonometry”. Retrieved on March 12th, 2012 from
http://en.wikipedia.org/wiki/History_of_trigonometry
Behera, A (2008). “The World of Trigonometry” Retrieved on from March 8th, 2012
from
http://www.youtube.com/watch?v=Ah9NxAGzlDc&feature=related