Karaji's L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula
نویسندگان
چکیده
In this paper, we first review two folkloric summation techniques 
 due to Islamic medieval scholars Karaji and Ibn al-Haytham by emphasizing on their higher-dimensional extensions. We also include several interesting examples of algebraic identities obtained
 form the generalized formulas Karaji's L-summing method. Finally, will show interplay between these different methods summation.
منابع مشابه
Ibn Al-Haytham: father of modern optics.
After the fall of the Roman Empire in AD 476, scientific progress in Europe had come to a standstill. This era between fall of Rome and the Renaissance is commonly known as the dark ages. However, from the 8th till 13th century, scientific and cultural knowledge had flourished in the Islamic world. This period, which began soon after the establishment of the Abbasid Khalifate in Baghdad in the ...
متن کاملIbn al-Haytham and the Origins of Computerized Image Analysis
† This paper originated from research supported by ARO grant W911NF0610359 and DARPA grant NBCH1050008. AbstractIbn al-Haytham (Latinized as Alhazen or Alhacen) was born in Basra in 965 A.D. [354 A.H.], but produced nearly all of his work in Cairo's al-Azhar Mosque, where he wrote nearly one hundred works on topics as diverse as poetry and politics. Al-Haytham is primarily known for his writing...
متن کاملIdentities by Generalized L−summing Method
In this paper, we introduce 3-dimensional L−summing method, which is a rearrangement of the summation P Aabc with 1 ≤ a, b, c ≤ n. Applying this method on some special arrays, we obtain some identities on the Riemann zeta function and digamma function. Also, we give a Maple program for this method to obtain identities with input various arrays and out put identities concerning some elementary f...
متن کاملthe theologian and the mathematician: fakhr al-dīn al-rāzī and the geometrical works of ibn al-haytham
fakhr al-dīn al-rāzī, theologian and philosopher of the 12th centuriy (1148-1209), has a huge literary production in many scholary disciplines of his time. nothwithstanding some original ideas which are mostly found in his theological and philosophical writings, most of his other works are compilations based on other sources. some of these sources still exist, while most of the others seem to h...
متن کاملibn al-haytham, kamāl al-dīn al-fārsī and wave motion of light
apart expressing the cause of the reflection of light from the surface of polished objects, ibn al-haytham in his al-manāẓir claims that the acceptance or rejection of light by these objects is only due to their polished surfaces and have nothing to do with their solidity, because the reflection of light from the surface of soft polished objects such as water is also possible. kamāl al-dīn al-f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Turkish journal of mathematics & computer science
سال: 2021
ISSN: ['2148-1830']
DOI: https://doi.org/10.47000/tjmcs.717074