This is the third of three articles on the History of Trigonometry. Part 2 Sections 5 - 7 can be found here.
Trigonometry is not the work of any one person or nation. Its history spans thousands of years and has touched every major civilization.
Our modern word "sine", is derived from the Latin word sinus, which means "bay" or "fold", from a mistranslation via Arabic of the Sanskrit word jiva, alternatively called jya. The words "minute" and "second" are derived from the Latin phrases partes minutae primae and partes minutae secundae.
Early developments Sumerian astronomers studied angle measure, using a division of circles into degrees.
The ancient Nubians used a similar method. But pre-Hellenic societies lacked the concept of an angle measure and consequently, the sides of triangles were studied instead, a field that would be better called "trilaterometry".
Iraqi mathematics The Babylonian astronomers kept detailed records on the rising and setting of starsthe motion of the planetsand the solar and lunar eclipsesall of which required familiarity with angular distances measured on the celestial sphere.
Ancient Egyptian mathematics See also: Egyptian mathematics The Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC.
In other words, the quantity he found for the seked is the cotangent of the angle to the base of the pyramid and its face. Hellenistic mathematics The chord of an angle subtends the arc of the angle.
Ancient Hellenistic mathematicians made use of the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc.
A chord's perpendicular bisector passes through the center of the circle and bisects the angle. Due to this relationship, a number of trigonometric identities and theorems that are known today were also known to Hellenistic mathematicians, but in their equivalent chord form.
Theorems on the lengths of chords are applications of the law of sines. And Archimedes' theorem on broken chords is equivalent to formulas for sines of sums and differences of angles.
Hipparchus may have taken the idea of this division from Hypsicles who had earlier divided the day into parts, a division of the day that may have been suggested by Babylonian astronomy. A seasonal cycle of roughly days could have corresponded to the signs and decans of the zodiac by dividing each sign into thirty parts and each decan into ten parts.
In Book I, he established a basis for spherical triangles analogous to the Euclidean basis for plane triangles. The thirteen books of the Almagest are the most influential and significant trigonometric work of all antiquity.
A special case of Ptolemy's theorem appeared as proposition 93 in Euclid's Data. Ptolemy's theorem leads to the equivalent of the four sum-and-difference formulas for sine and cosine that are today known as Ptolemy's formulas, although Ptolemy himself used chords instead of sine and cosine.
Indian mathematics Statue of Aryabhata. As there is no known information regarding his appearance, any image of Aryabhata originates from an artist's conception.
The next significant developments of trigonometry were in India.The Beginnings of Trigonometry. Joseph Hunt History of Mathematics Rutgers, Spring The ancient Greeks transformed trigonometry into an ordered science. Astronomy was the driving force behind advancements in trigonometry.
Most of the early advancements in trigonometry were in spherical trigonometry mostly because of its application to astronomy. The History of Trigonometry is one type of mathematics that deals with the sides and the angles. In the First paragraph I would like to explain the main history of trigonometry and also go into detail about the certain aspects of the mathematic branch.
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler ().
Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. There are six functions of an angle commonly used in trigonometry.
The history of trigonometry Trigonometry and Pi We can not talk about Mathematics without mentioning Pi, the constant that has turned the .