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"Trigonometry History."
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Ensino de trigonometria numa abordagem histórica: um produto educacional
Este trabalho objetiva relatar a construção de um caderno de atividades para o ensino de trigonometria, enfocando a fusão possível entre a abordagem histórica no ensino de matemática e o mestrado profissional. Para isso, são expostos aspectos teóricos considerados na construção desse produto educacional, uma descrição detalhada da estrutura desse produto, algumas considerações sobre sua aplicação e os principais resultados observados. Ainda, apresentamos parte do produto educacional com o intuito de promover, entre professores de matemática, possíveis articulações pedagógicas envolvendo a trigonometria e sua história.
Journal Article
Heavenly mathematics
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught.Heavenly Mathematicstraces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.
Heavenly Mathematicsis illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.
eBook
The Plane Scale and stereographic projection in early navigation
The Plane or Plain Scale is a navigational device that dates back to the early 1600s but has long since ceased to be used in practice. It could perform the function of a protractor and be used to solve problems in plane trigonometry. In addition, coupled with a suite of remarkable geometric constructions based on stereographic projection, the Plane Scale could efficiently solve problems in spherical trigonometry and hence navigation on a sphere. The methods used seem today to be largely unknown. This paper describes the Plane Scale and how it was used.
Journal Article
A History of Mathematics Technology Changes
The biggest concern was that I would no longer need to remember “math facts” (multiplication facts), making math too easy for students. [...]it is a time-saving tool that provides quick responses for educational activities, work reports and research investigations. [...]of one’s approach to AI, it is transforming teaching and providing powerful tools for preparing lessons, assignments, activities and assessment.
Journal Article
Professor Radha Charan Gupta (1935 - 2024)
An obituary for Professor Radha Charan Gupta, who died on Sep 5, 2024, is presented. Gupta was a towering personality in the field of the history of Indian Mathematical Sciences. Since the late 1960's, Gupta's research work focused on the history of mathematics in India, particularly the development of trigonometry, including interpolation rules and infinite series for trigonometric functions. Among his groundbreaking works in this field are his analysis of Paramesvara's third-order series approximation for the sine function in the fifteenth century.
Journal Article
Nutrigonometry II: Experimental strategies to maximize nutritional information in multidimensional performance landscapes
Animals regulate their nutrient consumption to maximize the expression of fitness traits with competing nutritional needs (“nutritional trade‐offs”). Nutritional trade‐offs have been studied using a response surface modeling approach known as the Geometric Framework for nutrition (GF). Current experimental design in GF studies does not explore the entire area of the nutritional space resulting in performance landscapes that may be incomplete. This hampers our ability to understand the properties of the performance landscape (e.g., peak shape) from which meaningful biological insights can be obtained. Here, I tested alternative experimental designs to explore the full range of the performance landscape in GF studies. I compared the performance of the standard GF design strategy with three alternatives: hexagonal, square, and random points grid strategies with respect to their accuracy in reconstructing baseline performance landscapes from a landmark GF dataset. I showed that standard GF design did not reconstruct the properties of baseline performance landscape appropriately particularly for traits that respond strongly to the interaction between nutrients. Moreover, the peak estimates in the reconstructed performance landscape using standard GF design were accurate in terms of the nutrient ratio but incomplete in terms of peak shape. All other grid designs provided more accurate reconstructions of the baseline performance landscape while also providing accurate estimates of nutrient ratio and peak shape. Thus, alternative experimental designs can maximize information from performance landscapes in GF studies, enabling reliable biological insights into nutritional trade‐offs and physiological limits within and across species. In behavioral ecology, we have a powerful method, known as the Geometric Framework for Nutrition (GF), to study nutritional ecology. However, we have not yet, in the three decades since it was proposed, fully investigated whether its fundamental experimental design is likewise powerful. This study investigate the original and alternative sampling designs to reconstruct GF performance landscapes.
Journal Article
Plimpton 322: A Study of Rectangles
Plimpton 322 is one of the most sophisticated and interesting mathematical objects from antiquity. It is often regarded as teacher’s list of school problems, however new analysis suggests that it relates to a particular geometric problem in contemporary surveying.
Journal Article
THE DISTRIBUTION OF THE ZEROS OF RANDOM TRIGONOMETRIC POLYNOMIALS
We study the asymptotic distribution of the number Z N of zeros of random trigonometric polynomials of degree N as N → ∞. It is known that as N grows to infinity, the expected number of the zeros is asymptotic to $\\frac{2}{\\sqrt{3}}\\cdot N$ . The asymptotic form of the variance was predicted by Bogomolny, Bohigas and Leboeuf to be cN for some c > 0. We prove that $\\frac{Z_{N}-{\\Bbb E}Z_{N}}{\\sqrt{cN}}$ converges to the standard Gaussian. In addition, we find that the analogous result is applicable for the number of zeros in short intervals.
Journal Article
