Coda

These interesting situations in which generics play a key role in interactional pragmatics sparked my memory of solid geometry and spherical trigonometry class at Stuyvesant High School in the early 1960s. Each morning our instructor, the somewhat irascible Mr. Burns, would start off by asking a question on the day's material, calling for a response by ‘[student surname]’. Stuyvesant, in those days an all-male institution, functioned, like prep schools, on a surname basis for both reference and address; the teachers’ names were prefaced by Mr. or Mrs. or Miss, while student names had no prefixed title.

Specifics of teaching the academic discipline “Sea astronomy” to future boatmaster

The article presents the scientific problem solution of improving the professional training of future boatmasters of higher educational maritime institutions. The purpose of the article is to analyse and summarize the specific teaching of the academic discipline “Sea Astronomy” by future navigators. For this purpose, a number of scientific works on the research topic authored by domestic and foreign scientists are analysed. The specifics of professional training of these specialists are revealed. The content of the academic discipline “Sea Astronomy” is analysed. The specific features of teaching the discipline are also presented, which are the formation of skills in future navigators to use devices to ensure the safety of navigation; learning the basics of instruments and tools preparation in training for the flight and during the voyage; solving problems to determine the errors of the chronometer, determining the location of the ship by astronomical methods; teaching to operate small but fairly simple devices, the methods of which require high accuracy of measurements and calculations; a significant proportion of classroom hours falls on practical classes; combination in seafaring astronomy of autonomous sections of celestial mechanics, spherical trigonometry, optics, etc., which require their separation into independent topics in the discipline; combination at the end of the discipline study into a complete holistic system of all the above individual sections of science; taking into account certain recommendations by future boatmasters: implementation of preliminary training in the performance of laboratory and practical work; carrying out continuous control of measurements and calculations at each stage. The conclusions of the research and prospects for further research are formulated. Key words: future boatmasters; seafaring astronomy; specifics of the discipline; navigation; professional training.

Antoni Wyrwicz – professor of higher mathematics at the Vilnius university (1817–1831)

Antoni Wyrwicz (1791–1865) was a professor of higher mathematics at the Vilnius university in the period from 1817 until 1831. Wyrwicz taught algebra by tractate of Sniadecki and Burdon, spherical trigonometry by Sniadecki, Cagnoli, Delambre Neper, astronomy by Delambre and Biot. Wyrwicz in 1819 published translation of Biot Analytical geometry. From 1824 until 1831 Wyrwicz taught differential and integral calculus by Lacroix and Lagrange. He translated 6 school books for algebra from Lacroix and 6 school books for geometry from Legendre.

An Axiom of True Courses Calculation in Great Circle Navigation

Based on traditional expressions and spherical trigonometry, at present, great circle navigation is undertaken using various navigational software packages. Recent research has mainly focused on vector algebra. These problems are calculated numerically and are thus suited to computer-aided great circle navigation. However, essential knowledge requires the navigator to be able to calculate navigation parameters without the use of aids. This requirement is met using spherical trigonometry functions and the Napier wheel. In addition, to facilitate calculation, certain axioms have been developed to determine a vessel’s true course. These axioms can lead to misleading results due to the limitations of the trigonometric functions, mathematical errors, and the type of great circle navigation. The aim of this paper is to determine a reliable trigonometric function for calculating a vessel’s course in regular and composite great circle navigation, which can be used with the proposed axioms. This was achieved using analysis of the trigonometric functions, and assessment of their impact on the vessel’s calculated course and established axioms.

Metode Perhitungan Awal Bulan Kamariah Uzal Syahruna dalam Kitab Tasḥīl al-Mithāl wa al-Aqwāl Li ‘Amal al-Hilāl

This study aims to determine the method of ḥisāb early in the lunar month in the book Tasḥīl al-Mithāl by Uzal Syahruna and assess its advantages and disadvantages compared to the same process in other books. It is undeniable that the dichotomization between the existence of classical ḥisāb books and contemporary ḥisāb books with the beginning to fade in people's belief in the results occurred in Falak Science. Through literature study and interviews, this paper finds that the method of determining the beginning of the lunar month in the book falls into the ḥisāb ḥaqīqī bi taḥqīq category. The theory and calculation system are based on modern astronomical formulas (spherical trigonometry), using calculators and computational programs. The advantage of this book is that it establishes its procedures on current astronomical formulas, the output of ḥisāb is not much different from other ḥaqīqī bi taḥqīq books. Simultaneously, the weakness is that it still uses unlimited astronomical data as a basis. Some have not been corrected, especially for determining irtifā 'al-hilāl and hilāl mar'i corrections.

Rumus Arah Kiblat Saadoeddin Djambek Perspektif Spherical Trigonometry

Saadoeddin Djambek adalah tokoh yang sangat berperan dalam memperkenalkan rumus-rumus ilmu falak yang didaptasi dari rumus astronomi. Hal yang menarik bagi peneliti adalah tentang komparasi rumus arah kiblat Saadoeddin Djambek ditinjau dari teori spherical trigonometry dalam hubungannya tentang eksistensi suatu teori lama dan teori baru dalam satu bidang kajian ilmu Penelitian ini mengukur tingkat akurasi rumus. Hal ini karena rumus dipaparkan secara sederhana dengan rumus turunan berasal dari sumber yang sama maka hasil perhitungannya juga akan sama. Dengan demikian akan tersedia opsi/pilihan rumus yang dapat digunakan dalam pengukuran arah kiblat sehingga pengukuran arah kiblat akan lebih mudah dan sederhana.

Pemikiran Syeikh Thahir Jalaluddin tentang Awal Waktu Shalat dalam Kitab Pati Kiraan

Thahir Jalaluddin seringkali disebut sebagai tokoh falak Indonesia pertama. Pemikirannya berbeda dengan kitab lain yang juga memakai logaritma dalam perhitungannya. Artikel ini membahas bagaimana Thahir Jalaluddin memformulasikan perhitungan waktu shalat dalam kitab Pati Kiraan. Artikel disusun menggunakan metode library research dengan deskriptif-analitik untuk menganalis dan mendeskripsikan pemikirannya. Kesimpulan yang diperoleh bahwa pemikiran Thahir Jalaluddin banyak dipengaruhi oleh guru-gurunya, terlihat pada penggunaan tabel logaritma sebagai media menghitung. Konsep astronomi modern juga dipakai dalam menghisab waktu shalat, seperti konsep koreksi dalam menentukan ketinggian Matahari. Konsep matematika yang dipakai sudah menggunakan teori spherical trigonometry walaupun dalam merumuskannya masih sangat rumit apabila dibandingkan dengan tokoh falak yang sezaman dengannya dimana sama-sama memakai logaritma dalam menghitung.

An approach to truth: aspects of his thought

This thematic discussion of Biruni’s thought examines his general approach as well as elements which distinguish him as a person and scholar. When treating such a polymath, it is often necessary for us to go beyond our common presuppositions to grasp the range of knowledge traversed by this great thinker, who felt as much at ease with spherical trigonometry and geology as with history, literature, and cultural study. Attention to languages was a recurring feature in Biruni’s writing, whether on Khwarazmian, Arabic, Persian, or Sanskrit. His engagement with the human sciences showed at an early period and persisted even when he explored mathematics and pharmacology. The stars and our planet, its formation and substances, remained a major focus for him, alongside his secondary concern for astrology and wonders.