Al-Tūsī Originates the Concept of Mathematical Function

Circa 1150
Detail map of Midan, Aleppo, Aleppo Governorate, Syria,Hayy An Nabijarjis, Mosul, Nineveh Governorate, Iraq Overview map of Midan, Aleppo, Aleppo Governorate, Syria,Hayy An Nabijarjis, Mosul, Nineveh Governorate, Iraq

A: Midan, Aleppo, Aleppo Governorate, Syria, B: Hayy An Nabijarjis, Mosul, Nineveh Governorate, Iraq

A function that associates any of the four colored shapes to its color.
A function that associates any of the four colored shapes to its color.

About 1150 Persian mathematician and astronomer of the Islamic Golden Age Sharaf al-Dīn al-Muẓaffar ibn Muḥammad ibn al-Muẓaffar al-Ṭūsī, who taught in Aleppo and Mosul, originated the concept of mathematical function

"In his analysis of the equation x3 + d = bx2 for example, he begins by changing the equation's form to x2(b − x) = d. He then states that the question of whether the equation has a solution depends on whether or not the 'function' on the left side reaches the value d. To determine this, he finds a maximum value for the function. Sharaf al-Din then states that if this value is less than d, there are no positive solutions; if it is equal to d, then there is one solution; and if it is greater than d, then there are two solutions" (Wikipedia article on Function (mathematics), accessed 03-26-2009)

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