Abu L Wafa
Abu l-Wafa and Abu l-Wafa 'Muhammad or Abul-Wafa, (in Persian : ), born in 940 in Bouzjan and died in 998 in Baghdad was an astronomer and mathematician known for his Persian contributions in plane trigonometry and spherical trigonometry.
Summary |
Biography
Born in 939 or 940 to Buzjan in the region Khorosan , a large family of Taif , he studied mathematics with his uncles.
In 959 , he moved to Baghdad where he remained until his death during the height of the dynasty Abbasid. During the reign of Buyids , `Adhud ad-Dawla and his son, Sharaf al-Daula , Baghdad became a major cultural center. Brought to court, Abu l-Wafa al-Quhi and joined al-Sijzi as astronomer.
Along with his astronomical observations, Abu l-Wafa is interested in geometry , the trigonometry , the algebra and corresponds with other scientists of his time
Contributions
Astronomy
Abu l-Wafa is concerned with movements of the moon. He noted in particular in Baghdad, the lunar eclipse of 24 May 997 concomitantly with al-Biruni located Kath, thus to clarify the difference in longitude between the two cities. It corrects the lunar tables of his time emphasizing that Tycho Brahe call the third variation.
Trigonometry
In his book The revision of the Almagest (in allusion to the Almagest of Ptolemy ), he corrects and complete the tables trigonometric its predecessors including the tangent. He is the concept of unit circle, those of secant and cosecant. He also attributed the formula for sinus spherical trigonometry
Geometry
Abu l-Wafa said the works of Euclid , Diophantus and al-Khwarizmi (these comments have disappeared). In his book On the craftsmen needed to actually build it develops constructs approximated by ruler and compass of regular polygons with five, seven or nine sides. He is particularly interested in building a workable compass gauge constant. He proposed construction of the parabola. It offers engineering of trisection of angles and duplication of the cube. It addresses the problem of dividing a square sum of several square.
He is known for a solution by geometrical construction of the following problem. ABCD is a square with center O with a point E on any segment BC and F is the point symmetric to E with respect to the right (AC). The question is: the triangle AEF can be equilateral ?
To resolve this problem, we must first prove that F is on the segment CD. The solution proposed by Abu l-Wafa is:
- Construct the circumscribed circle to ABCD.
- Construct a second circle with center C through O.
- Denote the two points where the circles intersect U and V.
- We can then prove that the lines (AU) and (AV) cut the square into two points are the points E and F sought.
Arithmetic
In his book What is needed in arithmetic for accountants and businessmen, he developed the mathematical theory at the same time (fractions, multiplication, division, measures) and practices (tax calculations, currency units, payment of salaries ). Although knowing the Indian count , it is not used in this book addressed to the general public. However, he developed a theory on negative numbers linking them to the image of a debt: 3 to 5 representing such a debt of 2. He agrees to multiply these numbers by positive and negative to incorporate them in calculations.
Optics
Abu l-Wafa is also interested in the optical and publish a book about mirrors burning, which mirrors all the reflected rays converge at a single point, thus providing at this point sufficient heat to ignite an object.
Writings
Abu l-Wafa wrote many books, some of which have disappeared;
- Kitab fi al-ilayhi my yahtaj wa'l-Kuttab Ummal min 'ilm al-hisab (This is necessary arithmetic for accountants and businessmen) between 961 and 976;
- Kitab al-Handasa (On the indispensable artisans actually building);
- Al-Kitab al-Kamil (The Complete Book), a revision of the Almagest;
- a theory on the Moon (disappeared);
- Wadih El (trigonometric tables, missing);
- a treatise on conics (disappeared);
- Kitab al-Maraya Al muhriqa (Book on burning mirrors).
See also
Sources
- Hebri Bousserouel, Muslim scholars forgotten by history.
- Ahmed Djebbar , A History of Arabic Science, Seuil, 2001 [ detail editions ] .
- Joseph Bertrand, "The theory of the moon Aboul Wefa," in Proceedings of the Meetings of the Academy of Sciences, Paris, No. 73, 1872, p. 581-588
- (In) John J. O'Connor and Edmund F. Robertson, " Abu l-Wafa ", MacTutor History of Mathematics archive , University of St Andrews.
- Biography on the site of Imago Mundi
- Tangram to Abu'l Wafa dynamic geometry, dissection of a triangle into a rectangle of equal area.
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