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ABUL WAFA MUHAMMAD AL-BUZJANI
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Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn
Ismail al-Buzjani was born in Buzjan, Nishapur in 940 C.E. He flourished as a
great mathematician and astronomer at Baghdad and died in 997/998 C.E. He learnt
mathematics in Baghdad. In 959 C.E. he migrated to Iraq and lived there till his
death.
Abul Wafa's main contribution lies in several branches of mathematics,
especially geometry and trigonometry. In geometry his contribution comprises
solution of geometrical problems with opening of the compass; construction of a
square equivalent to other squares; regular polyhedra; construction of regular
hectagon 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)
In addition, he 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 extensive studies on conics.
Apart from being a mathematician, Abul Wafa also contributed to astronomy. In
this field he discussed different movernents of the moon, and discovered
'variation'. He was also one of the last Arabic translators and commentators of
Greek works.
He wrote a large 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 centuries
later. 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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