Fibonacci’s Triangle and Other Abominations

2019

I propose an empirical study on theintroduction of an historical perspective onmathematics education at different levels in the French secondary school curriculum (11-18 years old). First of all, I present, in the historical contexts of the twelfth and thirteenth centuries, elements of the biography of Leonardo da Pisa, better known as Fibonacci, and of his mathematical work. I pay close attention to the mathematics of the Islamic countries that had largely fed his thinking. I dedicate an important part of our contribution to excerpts from theLiber Abaci to understandbetterhow his work might contribute to today's classroom. All selected extracts belong to the category of so-called 'recreational' problems. They were chosen for their algorithmic structure that allows us to work with pupils on, among other themes, algebra and algorithmics (including coding). Finally, I give details of mathematical and historical extensions.

The College Mathematics Journal, 1997

MacTutor History of Mathematics, 2014

Herein we investigate the historical origins of the Fibonacci numbers. After emphasising the importance of these numbers, we examine a standard conjecture concerning their origin only to demonstrate that it is not supported by historical chronology. Based on more recent findings, we propose instead an alternative conjecture through a close examination of the historical and historical/mathematical circumstances surrounding Leonardo Fibonacci and relate these circumstances to themes in medieval and ancient history. Cultural implications and historical threads of our conjecture are also examined in this light.

Archive for History of Exact Sciences, 2008

The "unknown heritage" is the name usually given to a problem type in whose archetype a father leaves to his first son 1 monetary unit and 1 / n (n usually being 7 or 10) of what remains, to the second 2 units and 1 / n of what remains, etc. In the end all sons get the same, and nothing remains. The earliest known occurrence is in Fibonacci's Liber abbaci, which also contains a number of much more sophisticated versions, together with a partial algebraic solution for one of these and rules for all which do not follow from his algebraic calculation. The next time the problem turns up is in Planudes's late 13th-c. Calculus according to the Indians, Called the Great. After that the simple problem type turns up regularly in Provençal, Italian and Byzantine sources. It seems never to appear in Arabic or Indian writings, although two Arabic texts (one from c. 1190) contain more regular problems where the number of shares is given; they are clearly derived from the type known from European and Byzantine works, not their source. The sophisticated versions turn up again in Barthélemy de Romans' Compendy de la praticque des nombres (c. 1467) and, apparently inspired from that, in the appendix to Nicolas Chuquet's Triparty (1484). Apart from a single trace in Cardano's Practica arithmetice et mensurandi singularis, the sophisticated versions never surface again, but the simple version spreads for a while to German practical arithmetic and, more persistently, to French polite recreational mathematics. Close analysis of the sources shows that Barthélemy cannot have drawn his familiarity with the sophisticated rules from Fibonacci. It also suggests that the simple version is originally either a classical, strictly Greek or a medieval Byzantine invention, and that the sophisticated versions must have been developed before Fibonacci within an environment (located in Byzantium, Provence, or possibly in Sicily?) of which all direct traces has been lost, but whose mathematical level must have been quite advanced. Contents

International Electronic Journal of Mathematics Education

Various features have been found hidden in the Pascal triangle. In this paper, some very well-known properties of the Pascal triangle will be presented, as well as the properties related to different extensions of the triangle, namely the Pascal pyramid. Given that in the textbooks of the tenth grade, respectively in the school, where we realised the research but also in general in other schools, the importance of the Pascal triangle is not at the right level, then in this paper it has been shown very well that many different exercises in mathematics. The purpose of this paper is to look at the difference and importance of explaining mathematical units against units that students do not have knowledge of, namely the explanation of Pascal’s triangle in the efficiency of solutions to various mathematical exercises. This research is mainly based on descriptive and quantitative method, while research instruments are two tests. From the study of Pascal’s triangle, many solutions of probl...