mathematics

Ibn Turk

Ibn Turk is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Ibn Turk rather than just read about it. In short: ʿAbd al-Hamīd ibn Turk (fl. 830), known also as ʿAbd al-Hamīd ibn Wase ibn Turk al-Jili (Arabic: ابومحمد عبدالحمید بن واسع بن ترک الجیلی) was a ninth-century Islamic mathematician. Not much is known about his life.

Key takeaways

Ibn Turk belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Ibn Turk to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Ibn Turk from memory before moving on to harder problems.

Reference excerpt

ʿAbd al-Hamīd ibn Turk (fl. 830), known also as ʿAbd al-Hamīd ibn Wase ibn Turk al-Jili (Arabic: ابومحمد عبدالحمید بن واسع بن ترک الجیلی) was a ninth-century Islamic mathematician. Not much is known about his life. The two records of him, one by Ibn al-Nadim and the other by Al-Qifti, are not identical. Al-Qifi mentions his name as ʿAbd al-Hamīd ibn Wase ibn Turk al-Jili. Jili means from Gilan. On the other hand, Ibn Nadim mentions his nisbah as khuttali (ختلی), which is a region located north of the Oxus and west of Badakhshan. In one of the two remaining manuscripts of his al-jabr wa al-muqabila, the recording of his nisbah is closer to al-Jili. David Pingree / Encyclopaedia Iranica states that he originally hailed from Khuttal or Gilan. He wrote a work on algebra entitled Logical Necessities in Mixed Equations, which is very similar to Al-Khwarzimi's Al-Jabr and was published at around the same time as, or even possibly earlier than, Al-Jabr. Only a chapter called "Logical Necessities in Mixed Equations", on the solution of quadratic equations, has survived. The manuscript gives exactly the same geometric demonstration as is found in Al-Jabr, and in one case the same example as found in Al-Jabr, and even goes beyond Al-Jabr by giving a geometric proof that if the discriminant is negative, then the quadratic equation has no solution. The similarity between these two works has led some historians to conclude that algebra may have been well developed by the time of Al-Khwarizmi and 'Abd al-Hamid.

References

Worked examples

Example 1 — a first encounter with Ibn Turk

Start with the simplest possible case. Write down what Ibn Turk claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Ibn Turk before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Ibn Turk ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Ibn Turk

In research: Ibn Turk appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Ibn Turk in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Ibn Turk is common in secondary-school and first-year university syllabi. It links to neighbouring topics 9th-century mathematicians, 9th-century people from the Abbasid Caliphate, Asian mathematician stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Ibn Turk outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Ibn Turk in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ibn Turk means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Ibn Turk out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ibn Turk in simple terms?

Why does Ibn Turk matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Ibn Turk?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Ibn Turk.