mathematics

Ibn Mu'adh al-Jayyani

Ibn Mu'adh al-Jayyani 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 Mu'adh al-Jayyani rather than just read about it. In short: Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī (Arabic: أبو عبد الله محمد بن معاذ الجياني; 989, Cordova, Al-Andalus – 1079, Jaén, Al-Andalus) was an Arab mathematician, Islamic scholar, and Qadi from Al-Andalus (in present-day Spain). Al-Jayyānī wrote important commentaries on Euclid's Elements and he wrote the first known treatise on spherical trigonometry.

Key takeaways

Ibn Mu'adh al-Jayyani 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 Mu'adh al-Jayyani to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Ibn Mu'adh al-Jayyani from memory before moving on to harder problems.

Reference excerpt

Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī (Arabic: أبو عبد الله محمد بن معاذ الجياني; 989, Cordova, Al-Andalus – 1079, Jaén, Al-Andalus) was an Arab mathematician, Islamic scholar, and Qadi from Al-Andalus (in present-day Spain). Al-Jayyānī wrote important commentaries on Euclid's Elements and he wrote the first known treatise on spherical trigonometry.

Life Little is known about his life. Confusion exists over the identity of al-Jayyānī of the same name mentioned by ibn Bashkuwal (died 1183), Qur'anic scholar, Arabic Philologist, and expert in inheritance laws (farāʾiḍī). It is unknown whether they are the same person. There is some evidence that he lived in Cairo from 1012/13 to 1016/17.

Works Al-Jayyānī wrote The book of unknown arcs of a sphere, which is considered "the first treatise on spherical trigonometry", although spherical trigonometry in its ancient Hellenistic form was dealt with by earlier mathematicians such as Menelaus of Alexandria, whose treatise the Spherics included Menelaus' theorem, still a basic tool for solving spherical geometry problems in Al-Jayyānī's time. However, E. S. Kennedy points out that while it was possible in pre-Islamic mathematics to compute the magnitudes of a spherical figure, in principle, by use of the table of chords and Menelaus' theorem, the application of the theorem to spherical problems was very difficult in practice. Al-Jayyānī's work on spherical trigonometry "contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle." This treatise later had a "strong influence on European mathematics", and his "definition of ratios as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced Regiomontanus. There is strong consensus in attributing to him the authorship of a manuscript about the duration of twilight, and using that to measure the thickness of the atmosphere. The short treatise On twilight was incorrectly attributed to Ibn al-Haytham for several centuries, due to a reference made by Gerard of Cremona, who translated it into Latin. The first printed edition of Cremona's translation (Allacen arabis uetustissimi liber de crepusculis, Gerardo Cremonensi interprete) was made in 1542, by the Portuguese mathematician and cosmographer Pedro Nunes.

See also List of Arab scientists and scholars Islamic mathematics

Notes

References Calvo, Emilia (2007). "Ibn Muʿādh: Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 562–3. ISBN 978-0-387-31022-0. (PDF version) O'Connor, John J.; Robertson, Edmund F., "Abu Abd Allah Muhammad ibn Muadh Al-Jayyani", MacTutor History of Mathematics Archive, University of St Andrews Dold-Samplonius, Yvonne; Hermelink, Heinrich (1970). "Al-Jayyānī, Abū'Abd Allāh Muḥammad Ibn Mu'ādh". Complete Dictionary of Scientific Biography. Encyclopedia.com.

Worked examples

Example 1 — a first encounter with Ibn Mu'adh al-Jayyani

Start with the simplest possible case. Write down what Ibn Mu'adh al-Jayyani 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 Mu'adh al-Jayyani 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 Mu'adh al-Jayyani 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 Mu'adh al-Jayyani

In research: Ibn Mu'adh al-Jayyani 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 Mu'adh al-Jayyani 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 Mu'adh al-Jayyani is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1079 deaths, 11th-century mathematicians, 11th-century people from al-Andalus, so understanding it makes those chapters shorter.
In everyday life: Look for Ibn Mu'adh al-Jayyani 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 Mu'adh al-Jayyani in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ibn Mu'adh al-Jayyani 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 Mu'adh al-Jayyani out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ibn Mu'adh al-Jayyani in simple terms?

Why does Ibn Mu'adh al-Jayyani 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 Mu'adh al-Jayyani?

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 Mu'adh al-Jayyani.