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 The Islamic Golden Age was a period of scientific, economic, and cultural flourishing in the history of Islam, traditionally dated from the 8th century to the 13th century. This period is traditionally understood to have begun during the reign o ...

. Whilst on pilgrimage to

Mecca Mecca, officially Makkah al-Mukarramah, is the capital of Mecca Province in the Hejaz region of western Saudi Arabia; it is the Holiest sites in Islam, holiest city in Islam. It is inland from Jeddah on the Red Sea, in a narrow valley above ...

, he tells of an

epitome An epitome (; , from ἐπιτέμνειν ''epitemnein'' meaning "to cut short") is a summary or miniature form, or an instance that represents a larger reality, also used as a synonym for embodiment. Epitomacy represents "to the degree of." A ...

he wrote on

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

(extant in manuscript), which building on the work of

Nicomachus Nicomachus of Gerasa (; ) was an Ancient Greek Neopythagorean philosopher from Gerasa, in the Roman province of Syria (now Jerash, Jordan). Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his ...

, added three new

perfect numbers In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfec ...

(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 the three perfect numbers were only rediscovered there during the

Renaissance The Renaissance ( , ) is a Periodization, period of history and a European cultural movement covering the 15th and 16th centuries. It marked the transition from the Middle Ages to modernity and was characterized by an effort to revive and sur ...

, including by

Pietro Cataldi Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of simple ...

.Scott, Paul
"Just Perfect, part 2"
''The Australian Mathematics Teacher'', vol. 63, no. 2. p. 3.

References

{{Authority control 1194 births Egyptian mathematicians

Further reading

See also

References