Sharaf al-Dīn al-Tūsī
   HOME

TheInfoList



OR:

Sharaf al-Dīn al-Muẓaffar ibn Muḥammad ibn al-Muẓaffar al-Ṭūsī ( fa, شرف‌الدین مظفر بن محمد بن مظفر توسی; 1135 – 1213) was an
Iranian Iranian may refer to: * Iran, a sovereign state * Iranian peoples, the speakers of the Iranian languages. The term Iranic peoples is also used for this term to distinguish the pan ethnic term from Iranian, used for the people of Iran * Iranian lan ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
and
astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...
of the
Islamic Golden Age The Islamic Golden Age was a period of cultural, economic, and scientific flourishing in the history of Islam, traditionally dated from the 8th century to the 14th century. This period is traditionally understood to have begun during the reign ...
(during the
Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...
).


Biography

Tusi was probably born in Tus, Iran. Little is known about his life, except what is found in the biographies of other scientistsO'Connor & Robertson ( 1999) and that most mathematicians today can trace their lineage back to him. Around 1165, he moved to Damascus and taught mathematics there. He then lived in Aleppo for three years, before moving to
Mosul Mosul ( ar, الموصل, al-Mawṣil, ku, مووسڵ, translit=Mûsil, Turkish: ''Musul'', syr, ܡܘܨܠ, Māwṣil) is a major city in northern Iraq, serving as the capital of Nineveh Governorate. The city is considered the second larg ...
, where he met his most famous disciple Kamal al-Din ibn Yunus (1156-1242). This Kamal al-Din would later become the teacher of another famous mathematician from Tus, Nasir al-Din al-Tusi. According to Ibn Abi Usaibi'a, Sharaf al-Din was "outstanding in
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
and the mathematical sciences, having no equal in his time".


Mathematics

Al-Tusi has been credited with proposing the idea of a function, however his approach being not very explicit, Algebra's move to the dynamic function was made 5 centuries after him, by Gottfried Leibniz. Sharaf al-Din used what would later be known as the " Ruffini- Horner method" to numerically approximate the
root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the su ...
of a
cubic equation In algebra, a cubic equation in one variable is an equation of the form :ax^3+bx^2+cx+d=0 in which is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of th ...
. He also developed a novel method for determining the conditions under which certain types of cubic equations would have two, one, or no solutions. The equations in question can be written, using modern notation, in the form  , where    is a cubic polynomial in which the coefficient of the cubic term    is  , and    is positive. The Muslim mathematicians of the time divided the potentially solvable cases of these equations into five different types, determined by the signs of the other coefficients of  . For each of these five types, al-Tusi wrote down an expression    for the point where the function    attained its
maximum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given r ...
, and gave a geometric proof that    for any positive    different from  . He then concluded that the equation would have two solutions if  , one solution if  , or none if  . Al-Tusi gave no indication of how he discovered the expressions    for the maxima of the functions  . Some scholars have concluded that al-Tusi obtained his expressions for these maxima by "systematically" taking the derivative of the function  , and setting it equal to zero. This conclusion has been challenged, however, by others, who point out that al-Tusi nowhere wrote down an expression for the derivative, and suggest other plausible methods by which he could have discovered his expressions for the maxima. The quantities    which can be obtained from al-Tusi's conditions for the numbers of roots of cubic equations by subtracting one side of these conditions from the other is today called the discriminant of the cubic polynomials obtained by subtracting one side of the corresponding cubic equations from the other. Although al-Tusi always writes these conditions in the forms  ,  , or  , rather than the corresponding forms  ,  , or  ,
Roshdi Rashed Roshdi Rashed (Arabic: رشدي راشد), born in Cairo in 1936, is a mathematician, philosopher and historian of science, whose work focuses largely on mathematics and physics of the medieval Arab world. His work explores and illuminates the un ...
nevertheless considers that his discovery of these conditions demonstrated an understanding of the importance of the discriminant for investigating the solutions of cubic equations. Sharaf al-Din analyzed the equation ''x''3 + ''d'' = ''b''⋅''x''2 in the form ''x''2 ⋅ (''b'' - ''x'') = ''d'', stating that the left hand side must at least equal the value of ''d'' for the equation to have a solution. He then determined the maximum value of this expression. A value less than ''d'' means no positive solution; a value equal to ''d'' corresponds to one solution, while a value greater than ''d'' corresponds to two solutions. Sharaf al-Din's analysis of this equation was a notable development in Islamic mathematics, but his work was not pursued any further at that time, neither in the Muslim world nor in Europe. Sharaf al-Din al-Tusi's "Treatise on equations" has been described by Roshdi Rashed as inaugurating the beginning of algebraic geometry. This was criticized by Jeffrey Oaks who claims that Al-Tusi did not study curves by means of equations, but rather equations by means of curves (just as al-Khayyam had done before him) and that the study of curves by means of equations originated with Descartes in the seventeenth century.


Astronomy

Sharaf al-Din invented a linear astrolabe, sometimes called the "staff of Tusi". While it was easier to construct and was known in
al-Andalus Al-Andalus translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label= Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, al-Ándalus () was the M ...
, it did not gain much popularity.


Honours

The main-belt asteroid 7058 Al-Ṭūsī, discovered by
Henry E. Holt Henry E. Holt (27 September 1929 - 5 May 2019) was an American astronomer and prolific discoverer of minor planets and comets, who has worked as a planetary geologist at the United States Geological Survey and Northern Arizona University. Car ...
at Palomar Observatory in 1990, was named in his honor.


Notes


References

* * * Retrieved March 21, 2011 from Encyclopedia.com. * * * * * * *


External links

*
PDF version
{{DEFAULTSORT:Tusi, Sharaf Din 1130s births 1213 deaths 12th-century Iranian mathematicians 13th-century Iranian mathematicians Medieval Iranian astrologers 12th-century Iranian astronomers 13th-century Iranian astronomers 12th-century astrologers 13th-century astrologers People from Tus, Iran 13th-century inventors 12th-century inventors