Sunday, 6 December 2015

Post about Al Khwarizmi by No3 Son

No3 Son was writing about "The father of Algebra" -Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi for his maths homework today. NSB learnt a lot, so sharing what No3 wrote (Image caption banter is all from NSB though)....

Al Khwarizmi was born in 800 CE Baghdad in modern day Iraq. Al Khwarizmi studied mathematics and Astronomy also he wrote a book Hisab Al-jabr W’al-Muqabala which was on quadratic and linear equations.

Linear..... Quadratic
(subtle Father Ted joke there...)

Al Khwarizmi was part of the House of Wisdom which was made up of a group of scholars who tried to solve problems of lawsuit, trade and inheritance using maths. The House of Wisdom used translated texts from the Greeks and others but did their own work too.

He is also famous for bringing The Indian number system, which was base 10, to Arabic science.

Some of his work used quadratic equations. These equations have two solutions. Al-Khwarizmi used words instead of letters. For example to solve x2+10x=39 he wrote:

“... a square and 10 roots are equal to 39 units. The question therefore in this type of equation is about as follows: what is the square which combined with ten of its roots will give a sum total of 39? The manner of solving this type of equation is to take one-half of the roots just mentioned. Now the roots in the problem before us are 10. Therefore take 5, which multiplied by itself, gives 25, and an amount which you add to 39 giving 64. Having taken then the square root of this, which is 8, subtract from it half the roots, 5, leaving 3. The number three therefore represents one root of this square, which itself, of course, is 9. Nine therefore gives the square.”
To make it understandable, here is a diagram of how he would solve the equation:

Bit easier to understand like this...maybe...

And here is a diagram of how we would solve the equation today:

Solving Quadratics the Modern Way.

Further Reading
Gulf News Article
Al Jazeera Article
Intmaths Article


  1. Were negative numbers understood at the time Ash? Could he have realised that there were two solutions? Jon

  2. Negative numbers had been known about for a long time, but were only just becoming recognised in Arabia :