Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail
al-Buzjani, a prominent Muslim mathematics and astronomer.
Abul Wafa was born in Buzjan, Nishapur in 940 A.D., and flourished as a
great mathematician and astronomer at Baghdad and died in 997/998 A.D. He
learnt mathematics in Baghdad. In 959 A.D. he migrated to Iraq and stayed
there till he passed away.
Abul Wafa helped in bringing about a lot of theories in several branches of
mathematics, particularly geometry and trigonometry. In geometry his
contribution lies in solving geometrical problems with opening of the
compass; construction of a square equivalent to other squares; regular
polyhedral; construction of regular hexagon taking for its side half the
side of the equilateral triangle inscribed in the same circle; constructions
of parabola by points and geometrical solution of the equations:
x4 = a and x4 + ax3 = b
Abul Wafa's contribution to the development of trigonometry was extensive.
He was the first to show the generality of the sine theorem relative to
spherical triangles. He developed a new method of constructing sine tables,
the value of sin 30' being correct to the eighth decimal place. He also
developed relations for sine (a+b) and the formula:
2 sin2 (a/2) = 1 - cos a, and sin a = 2 sin (a/2) cos (a/2)
He also made a special study of the tangent and calculated a table of
tangents. He introduced the secant and cosecant for the first time, knew the
relations between the trigonometric lines, which are now used to define
them, and undertook far-reaching studies on conics.
Abul Wafa was not only a mathematician he also contributed to astronomy. In
this field he discussed different movements of the moon, and discovered
'variation'. He was also one of the last Arabic translators and commentators
of Greek works.
He wrote a great number of books on mathematics and other subjects, most of
which have been lost or exist in modified forms. His contribution includes
Kitab 'Ilm al-Hisab, a practical book of arithmetic, al-Kitab al-Kamil (the
Complete Book), Kitab al-Handsa (Applied Geometry). Apart from this, he
wrote rich commentaries on Euclid, Diophantos and al-Khawarizmi, but all of
these have been lost. His books now extant include Kitab 'Ilm al-Hisab,
Kitab al- Handsa and Kitab al-Kamil.
His astronomical knowledge on the movements of the moon has been criticized
in that, in the case of 'variation' the third inequality of the moon as he
discussed was the second part of the 'evection'. But, according to Sedat,
what he discovered was the same that was discovered by Tycho Brache six
Nonetheless, his contribution to trigonometry was extremely significant in
that he developed the knowledge on the tangent and introduced the secant and
cosecant for the first time; in fact a sizeable part of today's trigonometry
can be traced back to him.
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