Related papers: Origin of the numerals, Al biruni testimony
In this paper, we connect two well established theories, the Fibonacci numbers and the Jordan algebras. We give a series of matrices, from literature, used to obtain recurrence relations of second-order and polynomial sequences. We also…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
In this era of rapid technological advancements, communication continues to evolve as new linguistic phenomena emerge. Among these is Arabizi, a hybrid form of Arabic that incorporates Latin characters and numbers to represent the spoken…
All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…
Our number system is a magnificent tool. But it is far from perfect. Can it be improved? In this paper some possibilities are discussed, including the use of a different base or directed (negative as well as positive) numerals. We also put…
This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…
By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…
Recently, Araci-Acikgoz-Sen derived some interesting identities on weighted q-Euler polynomials and higher-order q-Euler polynomials from the applications of umbral calculus (See [1]). In this paper, we develop the new method of q-umbral…
We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…
The ambition of a character recognition system is to transform a text document typed on paper into a digital format that can be manipulated by word processor software Unlike other languages, Arabic has unique features, while other language…
In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture…
We study a bijective map from integer partitions to the prime factorizations of integers that we call the "supernorm" of a partition, in which the multiplicities of the parts of partitions are mapped to the multiplicities of prime factors…
We prove a curious identity for the Bernoulli numbers.
We survey the classical results on the prime number theorem
Bibliographic data is a rich source of information that goes beyond the use cases of location and citation -- it also encodes both cultural and technological context. For most of its existence, the scholarly record has changed slowly and…
We present a new proof of the Rogers-Ramanujan identities. Surprisingly, all its ingredients are available already in Rogers seminal paper from 1894, where he gave a considerably more complicated proof.
This paper expounds very innovative results achieved between the mid-14th century and the beginning of the 16th century by Indian astronomers belonging to the so-called "M\=adhava school". These results were in keeping with researches in…
We have summarized here the astronomical knowledge of the ancient Hindu astronomers. This knowledge was accumulated from before 1500 B.C. up to around 1200 A.D. In Section \ref{equiv} we have correlated terms used by the Hindu astronomers…
We initiate the complexity theoretic study of the problem of computing the bits of (real) algebraic numbers. This extends the work of Yap on computing the bits of transcendental numbers like \pi, in Logspace. Our main result is that…
Prime numbers have attracted the attention of mathematiciansand enthusiasts for millenniums due to their simple definition and remarkable properties. In this paper, we study primorial numbers (the product of the first prime numbers) to…