Contents 1 History 1.1 Algebra 1.2 Cubic equations 1.3 Induction 1.4 Irrational numbers 1.5 Spherical trigonometry 2 Other major figures 3 Gallery 4 See also 5 References 6 Sources 7 Further reading 8 External links History[edit] Omar Khayyám's "Cubic equations and intersections of conic sections" the first page of the two-chaptered manuscript kept in Tehran University Algebra[edit]
Further information: History of algebra
The study of algebra, the name of which is derived from the Arabic
word meaning completion or "reunion of broken parts",[3] flourished
during the Islamic golden age. Muhammad ibn Musa al-Khwarizmi, a
scholar in the
"Perhaps one of the most significant advances made by Arabic
mathematics began at this time with the work of al-Khwarizmi, namely
the beginnings of algebra. It is important to understand just how
significant this new idea was. It was a revolutionary move away from
the Greek concept of mathematics which was essentially geometry.
Several other mathematicians during this time period expanded on the algebra of Al-Khwarizmi. Omar Khayyam, along with Sharaf al-Dīn al-Tūsī, found several solutions of the cubic equation. Omar Khayyam found the general geometric solution of a cubic equation. Cubic equations[edit] To solve the third-degree equation x3 + a2x = b Khayyám constructed the parabola x2 = ay, a circle with diameter b/a2, and a vertical line through the intersection point. The solution is given by the length of the horizontal line segment from the origin to the intersection of the vertical line and the x-axis. Further information: Cubic equation
x 3 + a = b x displaystyle x^ 3 +a=bx , with a and b positive, he would note that the maximum point of the curve y = b x − x 3 displaystyle y=bx-x^ 3 occurs at x = b 3 displaystyle x=textstyle sqrt frac b 3 , and that the equation would have no solutions, one solution or two
solutions, depending on whether the height of the curve at that point
was less than, equal to, or greater than a. His surviving works give
no indication of how he discovered his formulae for the maxima of
these curves. Various conjectures have been proposed to account for
his discovery of them.[12]
Induction[edit]
See also: Mathematical induction § History
The earliest implicit traces of mathematical induction can be found in
Euclid's proof that the number of primes is infinite (c. 300 BCE). The
first explicit formulation of the principle of induction was given by
Pascal in his Traité du triangle arithmétique (1665).
In between, implicit proof by induction for arithmetic sequences was
introduced by al-Karaji (c. 1000) and continued by al-Samaw'al, who
used it for special cases of the binomial theorem and properties of
Pascal's triangle.
Irrational numbers[edit]
The Greeks had discovered irrational numbers, but were not happy with
them and only able to cope by drawing a distinction between magnitude
and number. In the Greek view, magnitudes varied continuously and
could be used for entities such as line segments, whereas numbers were
discrete. Hence, irrationals could only be handled geometrically; and
indeed
Other major figures[edit]
Gallery[edit] Engraving of Abū Sahl al-Qūhī's perfect compass to draw conic sections. The theorem of Ibn Haytham. See also[edit] Arabic numerals Indian influence on Islamic mathematics in medieval Islam History of calculus History of geometry Science in the medieval Islamic world Timeline of Islamic science and technology References[edit] ^ Katz (1993): "A complete history of mathematics of medieval Islam
cannot yet be written, since so many of these Arabic manuscripts lie
unstudied... Still, the general outline... is known. In particular,
Islamic mathematicians fully developed the decimal place-value number
system to include decimal fractions, systematised the study of algebra
and began to consider the relationship between algebra and geometry,
studied and made advances on the major Greek geometrical treatises of
Euclid, Archimedes, and Apollonius, and made significant improvements
in plane and spherical geometry." Smith (1958) Vol. 1, Chapter VII.4:
"In a general way it may be said that the Golden Age of Arabian
mathematics was confined largely to the 9th and 10th centuries; that
the world owes a great debt to Arab scholars for preserving and
transmitting to posterity the classics of Greek mathematics; and that
their work was chiefly that of transmission, although they developed
considerable originality in algebra and showed some genius in their
work in trigonometry."
^
Sources[edit] Boyer, Carl B. (1991), "Greek
Further reading[edit] Books on Islamic mathematics Berggren, J. Lennart (1986). Episodes in the
Review: Toomer, Gerald J.; Berggren, J. L. (1988). "Episodes in the
Daffa', Ali Abdullah al- (1977). The Muslim contribution to
mathematics. London: Croom Helm. ISBN 0-85664-464-1.
Katz, Victor J. (1993). A History of Mathematics: An Introduction.
HarperCollins college publishers. ISBN 0-673-38039-4.
Ronan, Colin A. (1983). The Cambridge Illustrated History of the
World's Science. Cambridge University Press.
ISBN 0-521-25844-8.
Smith, David E. (1958). History of Mathematics. Dover Publications.
ISBN 0-486-20429-4.
Rashed, Roshdi (2001). The Development of Arabic Mathematics: Between
Arithmetic and Algebra. Translated by A. F. W. Armstrong. Springer.
ISBN 0-7923-2565-6.
Rosen, Fredrick (1831). The
Book chapters on Islamic mathematics Berggren, J. Lennart (2007). "
Books on Islamic science Daffa, Ali Abdullah al-; Stroyls, J.J. (1984). Studies in the exact sciences in medieval Islam. New York: Wiley. ISBN 0-471-90320-5. Kennedy, E. S. (1984). Studies in the Islamic Exact Sciences. Syracuse Univ Press. ISBN 0-8156-6067-7. Books on the history of mathematics Joseph, George Gheverghese (2000). The Crest of the Peacock:
Non-European Roots of
Journal articles on Islamic mathematics Høyrup, Jens. “The Formation of «Islamic Mathematics»: Sources and Conditions”. Filosofi og Videnskabsteori på Roskilde Universitetscenter. 3. Række: Preprints og Reprints 1987 Nr. 1. Bibliographies and biographies Brockelmann, Carl. Geschichte der Arabischen Litteratur. 1.–2. Band, 1.–3. Supplementband. Berlin: Emil Fischer, 1898, 1902; Leiden: Brill, 1937, 1938, 1942. Sánchez Pérez, José A. (1921). Biografías de Matemáticos Árabes que florecieron en España. Madrid: Estanislao Maestre. Sezgin, Fuat (1997). Geschichte Des Arabischen Schrifttums (in German). Brill Academic Publishers. ISBN 90-04-02007-1. Suter, Heinrich (1900). Die Mathematiker und Astronomen der Araber und ihre Werke. Abhandlungen zur Geschichte der Mathematischen Wissenschaften Mit Einschluss Ihrer Anwendungen, X Heft. Leipzig. Television documentaries
External links[edit] Hogendijk, Jan P. (January 1999). "Bibliography of
v t e
Mathematicians 9th century 'Abd al-Hamīd ibn Turk Sind ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Al-Mahani al-Dinawari Banū Mūsā Hunayn ibn Ishaq al-Khwārizmī Yusuf Al-Khuri ibn Qurra Na'im ibn Musa Sahl ibn Bishr al-Marwazi Abu Said Gorgani 10th century al-Sufi Abu al-Wafa al-Khāzin Abū Kāmil Al-Qabisi al-Khojandi Ahmad ibn Yusuf Aṣ-Ṣaidanānī al-Uqlidisi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus Ibrahim ibn Sinan Al-Battani Sinan ibn Thabit Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud al-Majriti al-Jabali 11th century al-Zarqālī Abu Nasr Mansur Said al-Andalusi Ibn al-Samh Al-Biruni Alhazen ibn Fatik Al-Sijzi al-Nasawī Al-Karaji Avicenna Muhammad al-Baghdadi ibn Hud al-Jayyānī Kushyar Gilani Al-Muradi Al-Isfizari Abu Mansur al-Baghdadi 12th century Al-Samawal al-Maghribi Avempace Al-Khazini Omar Khayyam Jabir ibn Aflah al-Hassar Al-Kharaqī Sharaf al-Dīn al-Ṭūsī Ibn al-Yasamin 13th century al-Hanafi al-Abdari Muhyi al-Dīn al-Maghribī Ibn 'Adlan Nasir al-Din al-Tusi Shams al-Dīn al-Samarqandī Ibn al‐Ha'im al‐Ishbili Ibn Abi al-Shukr al-Hasan al-Marrakushi 14th century al-Umawī Ibn al-Banna' Ibn Shuayb Ibn al-Shatir Kamāl al-Dīn al-Fārisī Al-Khalili Qutb al-Din al-Shirazi Ahmad al-Qalqashandi Ibn al-Durayhim 15th century al-Qalaṣādī Ali Qushji al-Wafa'i al-Kāshī al-Rūmī Ulugh Beg Ibn al-Majdi Sibt al-Maridini al-Kubunani 16th century Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi Ibn Ghazi al-Miknasi Ahmad Ibn al-Qadi Mathematical works The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Almanac Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij Concepts Alhazen's problem Islamic geometric patterns Centers Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi al-Din Madrasa Maktab Maragheh observatory University of Al Quaraouiyine Influences Babylonian mathematics Greek mathematics Indian mathematics Influenced Byzantine mathematics European mathematics |