mathematics

Ibn Fallus

Ibn Fallus 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 Fallus rather than just read about it. In short: Shams ad-Dīn Abû’t-Tāhir Ismāʽīl ibn-Ibrāhīm ibn-Ġāzī ibn-ʽAlī ibn Muhammad al-Ḥanafī al-Māridīnī (1194–1252), often called Ismāʽīl ibn-Fullūs or Ibn Fallus, was an Arab Egyptian mathematician of the Islamic Golden Age. Whilst on pilgrimage to Mecca, he tells of an epitome he wrote on number theory (extant in manuscript), which building on the work of Nicomachus, added three new perfect numbers (33,550,336; 8,589,86…

Key takeaways

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

Reference excerpt

Shams ad-Dīn Abû’t-Tāhir Ismāʽīl ibn-Ibrāhīm ibn-Ġāzī ibn-ʽAlī ibn Muhammad al-Ḥanafī al-Māridīnī (1194–1252), often called Ismāʽīl ibn-Fullūs or Ibn Fallus, was an Arab Egyptian mathematician of the Islamic Golden Age. Whilst on pilgrimage to Mecca, he tells of an epitome he wrote on number theory (extant in manuscript), which building on the work of Nicomachus, added three new perfect numbers (33,550,336; 8,589,869,056; and 137,438,691,328) to the four already discovered by the Greeks. His table also included seven other supposed perfect numbers which are now known to be incorrect. Roshdi Rashed believes the errors emerged from over-reliance on Nicomachus' method. This work did not reach Europe, and these three perfect numbers were only rediscovered there during the Renaissance, including by Pietro Cataldi.

Further reading Ismāʽīl ibn-Fullūs, Iʽdād al-asrār fī asrār al-iʽdād

See also Regiomontanus Johannes Scheubel Pietro Cataldi

References

Worked examples

Example 1 — a first encounter with Ibn Fallus

Start with the simplest possible case. Write down what Ibn Fallus 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 Fallus 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 Fallus 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 Fallus

In research: Ibn Fallus 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 Fallus 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 Fallus is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1194 births, 1252 deaths, African scientist stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Ibn Fallus 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Ibn Fallus in 20 minutes

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

Frequently asked questions

What is Ibn Fallus in simple terms?

Why does Ibn Fallus 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 Fallus?

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 Fallus.