Trigonometry

The word of Trigonometry has been taken from the Greek, Trigonon,

which means triangle and the other word, metron, has the meaning of measure.

The trigonometry is the connecting link between mathematics and astronomy,

between the way calendars are calculated, the Gnomon, and the sundial. In the

Islamic world, the calculation of the spherical triangles was necessary to

carry out the ritual custom. The direction to Mecca (qibla) was

indicated that the next to the hour lines on all public sundials.

Muslim mathematicians have been contributed in this trigonometry

fields. For a long time, the chord was used along with the sine. The magnitude

theory has been found in the al-Battani work around 858-929 CA. In his

astronomical work Islah al-Majisti (The Perfection of the Almagest), he

systematically employed the trigonometric function sine and versed sine with

arguments between 0? and 180?. Since the cosine is defined as the sine of the

complement of the angle and since no negative numbers are used, the versed sine

is defined in the second quadrant as a sum of two quantities.

The elements of trigonometry are set forth in an even more

systematic way in the Kitab al-Kamil (Perfect Book) of Abu I-Wafa

(940-997/998). He defined several trigonometric functions in the circle with

radius 1. The trigonometric tangent function is defined as a line on a tangent

to the circle.

The proof of the general spherical sine theorem was given by Abu

I-Wafa in his al-Majisti (Almagest), by his pupil Abu Nasr ibn Iraq (d.

1036) in Risala fi ma’rifa al-qisi al-falakiyya (Treatise on the

Determination of Celestial Arcs), and by al-Khujandi, in the Kitab Maqalid

‘ilm al-hay’a (Book on the Keys of Astronomy).

The use of trigonometry was expended through al-Biruni (973-1048).

He is the author of the Mas ‘udic Canon, which is a summary of the

results from the works of many predecessors and of personal observations and

calculations. It comprises 11 books. Book 3 is dedicated to trigonometry.

Another important scholar in the area of trigonometry was Nasir

al-Din al-Tusi (1201-1274). He wrote Kitab al-shakl al-qatta’ which

means The Book of the secant figure, also known as Treatise on the Complete

Quadrilateral. It was written in Persian and translated by the author into

Arabic in 1260 possibly for the needs of the observatory of Maragha. While in those

five books have contains a full system of trigonometric formulas for the plane

and spherical triangles. This work played an important role in the development

of mathematics in Europe.

Algebra:

The word “Algebra”

is derived from the Arabic language ?????

(Al-Jabr) which means the completion or “reunion of broken

parts” and throve during the Islamic golden age (especially in the year

830). Algebra comes from the treatise by the medieval Persian mathematician,

Muhammad Ibn Musa Al-khwarizmi, who wrote a book with Arabic title, Kit?b

al-mu?ta?ar f? ?is?b al-?abr wa-l-muq?bala, which can be translated as “The

Compendious Book on Calculation by Completion and Balancing”. The treatise

provided for the systematic solution of linear and quadratic equations. The

word al-jabr, presumably has meant restoration or completion and refer to the

transposition of subtracted terms to the other side of an equation. The word muqabalah

is said to refer to reduction or balancing that is the cancellation of like

terms on opposite sides of the equation. The term is used by al-Khwarizmi to

describe the operations that he introduced, “reduction” and

“balancing”, referring to the transposition of subtracted terms to

the other side of an equation, that is, the cancellation of like terms on

opposite sides of the equation.

The origin of Algebra can be traced back to ancient Babylon which

developed a fairly complicated mathematical system, in which case they were

able to calculate in a similar way to algebra today. Using this system, they

are able to apply formulas and compute solutions for unknown values ??for

problem classes that are usually solved by using Linear equations, Quadratic

equations and Indefinite Linear Equations. In contrast, the Egyptians and most

of the Indian, Greek, and Chinese peoples in the first millennium, they are usually

still using geometrical methods to solve such equations, such as those

mentioned in “the Rhind Mathematical Papyrus”, “Sulba

Sutras”, “Eucilid’s Elements “And” The Nine Chapters on the

Mathematical Art “. The result of the Greeks in Geometry has been written

in the book of elements, provides a framework for generalising the formula of

mathematics beyond the specific solution of a particular problem into the more

general system of expressing and solving equations, i.e. the framework of the

deduction logic of thought.

Besides Al-Khwarizmi, many other figures also have been developed

in Algebra theorem. Among others are:

Al-Qalasadi: introduce algebraic symbols. The symbols were

developed in the 14th century by Ibnu al-Banna. Then, in the 15th

century, Al-Qalasadi has been developed this. Al-Qalasadi has introduced the

mathematics symbols which use the characters of Arabic alphabet.

Sharaf al-D?n al-Muzaffar ibn Muhammad ibn al-Muzaffar al-??s?

(1135-1213) is a Mathematician and Islamic Astronomer from Persian. Sharif

al-Din has been taught the various topics such mathematics, astronomy and

related fields like numbers, astronomical tables, and astrology. Al- ??s? has

been written several papers on Algebra. He gave the Ruffini-Horner methods to approach the

roots of cubic equations. Although this method had previously been used

by Arab mathematicians to find almost the nth root of an integer, al- ??s? was the first to apply this method to solve

this general equation. In Al-Mu’adalat (About Equations), al-??s? finds

algebraic and numerical solutions of cubic equations and which first finds a

cubic polynomial derivative, an important result in differential calculus.

Omar Khayyam, a Persian scientist who has been developed the

algebra of geometry and found the general shape of the geometry of the cubic equation.