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Tortured by algebra? Who can you blame?

Summary

19 April 2010

Have you ever woken up sweating from the nightmare that you were back at school, with the teacher throwing questions at you like the one below?

You are working in a shop that mixes milk to order for customers. You stock whole milk containing 4% fat, and buttermilk containing 50% fat. The customer wants 50 litres of milk which is 25% fat. How much whole milk and how much buttermilk do you need to mix together for the customer?

Some readers will find this question “a piece of cake.” For others, it may be impossible, although you might vaguely remember that it is something to do with algebra. Unless you can do it, you are unlikely to remember that, in mathematical jargon, it requires solving two simultaneous linear equations. However, even those who never understood it should agree that without algebra, the modern world of science and engineering would be impossible.

So who is to blame for inventing it? The answer is Muslims.

The genius who started it all was an Iranian, Abu Abdullah Muhammad bin Musa al-Khwarizmi, also variously called Muhammad ibn-Musa al-Khwarizmi, Muhammad ibn-Musa al-Khowarizmi, and Mohammad Bin Musa Al-Khawarizmi, and most commonly referred to simply as Al-Khawarizmi who lived around 800 AD – 850 AD. The Latinised version of his name is the origin of the word “algorithm” used in mathematics and computing for a step by step set of rules for solving a computational problem. His most famous book is “Al-Jabr wa-al-Muqabilah” and from al-jabr we get the word algebra.

Why does this matter?

Many people think that our civilisation started with the Greeks and Romans, went into stagnation for thousand years with the dark ages, and then burst into renewed vigour with the enlightenment. I often hear our civilisation being referred to as Christian, Judeo-Christian, or sometimes Judeo-Christian with Greek roots. This categorisation is completely wrong, and the dark ages were only dark in certain parts of Europe, such as Britain! There was nothing dark about Spain or North Africa for example, where Muslim scholars were busy advancing our shared civilisation. However, both non-Muslims and indeed many Muslims seem to have collective amnesia about the contribution that Muslims have made to modern civilisation.

Non-Muslims need to know the contribution that Muslims have made to modern human civilisation, which is not the private property of one religious, racial or geographical grouping. Equally, many Muslims need to understand that this “Western civilisation” that they are so busy rejecting was created by the collective efforts of Muslims as well as non-Muslims.

Need help with the problem?

Let:

W = the amount of whole milk that you need for the mixture
B = the amount of buttermilk that you need for the mixture

The total mixture will be 50 litres. So you know that:

W + B = 50.                (Equation 1)

The mixture needs to be 25% fat. So writing the percentages as decimals you know that:

W x 0.04 + B x 0.5 = 50 x 0.25   (Equation 2)

Multiply all of Equation 2 by the number 2, and write Equation 1 beneath it:

W x 0.08 + B x 1 = 50 x 0.5 = 25
W + B = 50

Subtract the first of the two equations above from the second one:

W x (1-0.08) = 25
W x 0.92 = 25
W = 25 / 0.92 = 27.1739 stopping at four places of decimals

W + B = 50 so B = 50 – 27.1739 = 22.8260 stopping at four places of decimals

To check that the answer is correct, the fat content of the mixture is:

W x .04 + B x 0.5 = 27.1739 x 0.04 + 22.8268 x 0.5 = 12.49999

25% of 50 is 12.5, the slight difference is of course due to rounding the calculations to four decimal places.

Mohammed Amin

 

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