scholarly journals TRIGONOMETRIA ESFÉRICA APLICADA NA ASTRONOMIA DE POSIÇÃO

2018 ◽  
Vol 10 (2) ◽  
pp. 60-67
Author(s):  
Christian Luz Pelissari de Oliveira ◽  
Fernando Pereira de Souza

The present article is the result of a research work of the Degree in Mathematics in the scope of the Tutorial Education Program -PET. The work deals with concepts of Spherical Trigonometry, which has several fields of applications between mathematics and physics, related to cartographic problems, navigation and astronomy. The goal is to explore problems of astronomy applications of celestial bodies by making use of trigonometry concepts in the sphere to study positions and directions of stars in terms of a celestial sphere. In order to reach this objective, the article presents concepts of a smaller distance between two points in the sphere, a triangle of position that is the spherical triangle, the fundamental relation known as law of cosines, the Celestial Sphere, its elements, its coordinates in the equatorial system, horizontal system and time system. Thus, the work seeks to encourage students and teachers to work on Spherical Geometry in the classroom

Author(s):  
Ernesta Molotokienė

The aim of the article is to reveal a fundamental relation between the philosophy of creativity and education in the knowledge society. Knowledge society as a special social space of modern society is formed in the middle of the 20th century with a new system of educational organizations, therefore training a knowledge worker who is able to be productive in a rapidly changing knowledge and technological environment is one of the main challenges of modern education. The contemporary philosophy of creativity has an important impact on education in knowledge society. The creative nature of learning determines the knowledge worker’s ability to achieve social, technical and technological innovations, while research work forms a dynamic competence and socio-economic performance. The article stresses that creativity remains one of the most important educational goals of knowledge society.


2009 ◽  
Vol 5 (S260) ◽  
pp. 135-148 ◽  
Author(s):  
Xenophon Moussas

AbstractIn this review the oldest known advanced astronomical instrument and dedicated analogue computer is presented, in context. The Antikythera Mechanism a mysterious device, assumed to be ahead of its time, probably made around 150 to 100 BCE, has been found in a 1st century BCE shipwreck near the island of Antikythera in a huge ship full of Greek treasures that were on their way to Rome. The Antikythera Mechanism is a clock-like device made of bronze gears, which looks much more advanced than its contemporary technological achievements. It is based on mathematics attributed to the Hipparchus and possibly carries knowledge and tradition that goes back to Archimedes, who according to ancient texts constructed several automata, including astronomical devices, a mechanical planetarium and a celestial sphere. The Antikythera Mechanism probably had a beautiful and expensive box; looking possibly like a very elaborate miniature Greek Temple, perhaps decorated with golden ornaments, of an elegant Hellenistic style, even perhaps with automatic statuettes, ‘daemons’, functioning as pointers that performed some of its operations. Made out of appropriately tailored trains of gears that enable to perform specialised calculations, the mechanism carries concentric scales and pointers, in one side showing the position of the Sun in the ecliptic and the sky, possibly giving the time, hour of the day or night, like a clock. The position of the Moon and its phase is also shown during the month. On the other side of the Mechanism, having probably the size of a box (main part 32×20×6 cm), are two large spiral scales with two pointers showing the time in two different very long calendars, the first one concerning the eclipses, and lasting 18 years 11 days and 8 hours, the Saros period, repeating the solar and lunar eclipses, and enabling their prediction, and the 19 year cycle of Meton, that is the period the Moon reappears in the same place of the sky, with the same phase. An additional four-year dial shows the year of all Greek Festivities, the so-called ‘games’ (Olympic, Pythian, Isthmian etc). Two additional dials give the Exeligmos, the 54 year and 34 day cycle, which provides a more accurate prediction of eclipses. It is possible that the Mechanism was also equipped with a planetary show display, as three of the planets and their motion (stationary points) are mentioned many times in the manual of the instrument, so it was also a planetarium. From the manual we have hints that the mechanism was probably also an observational instrument, as having instructions concerning a viewfinder and possibly how to orient the viewfinder to pass a sunbeam through it, probably measuring the altitude of the Sun. There are fragmented sentences that probably give instructions on how to move the pointers to set the position of the Sun, the Moon and the planets in their initial places in the ecliptic, on a specific day, or how to measure angular distances between two celestial bodies or their coordinates. This mechanism is definitely not the first one of its kind. The fact that it is accompanied with instructions means that the constructor had in its mind to be used by somebody else and one posits that he made at least another similar instrument.


2021 ◽  
Vol 3 (1) ◽  
pp. 1-28
Author(s):  
Hikmatul Adhiyah Syam

Today, tomorrow, yesterday, and later is the time because this life will always talk about the time that can affect the pattern of life in an environment. So that the existence of time becomes important. Based on this, a time system was compiled using the circulation of celestial bodies. Previous people have inherited the traditional calendar in their respective regions. This adapts to the condition of the community and its environment. The research question in this research is how the interpretations of the traditional calendars in the archipelago. The purpose of this research is to explore the essential meaning of the traditional calendars in the archipelago. The method used in this research is library research. This method is used to describe the various existing sources. The results showed that the calendar in each region has its own meaning for the wearer. The Batak calendar is used to determine good and bad days, the Pranatamangsa calendar for season markers, the Saka calendar for marking religious rituals, the Islamic Javanese calendar for historical momentum markers and Islamic teachings, the Bugis calendar for guidelines for daily activities and the Maluku calendar for marking the time of manufacture boat.


2018 ◽  
Vol 72 (2) ◽  
pp. 503-512
Author(s):  
Tsung-Hsuan Hsieh ◽  
Shengzheng Wang ◽  
Wei Liu ◽  
Jiansen Zhao

Spherical trigonometry formulae are widely adopted to solve various navigation problems. However, these formulae only express the relationships between the sides and angles of a single spherical triangle. In fact, many problems may involve different types of spherical shapes. If we can develop the different formulae for specific spherical shapes, it will help us solve these problems directly. Thus, we propose two types of formulae for combined spherical triangles. The first set are the formulae of the divided spherical triangle, and the second set are the formulae of the spherical quadrilateral. By applying the formulae of the divided spherical triangle, waypoints on a great circle track can be obtained directly without finding the initial great circle course angle in advance. By applying the formulae of the spherical quadrilateral, the astronomical vessel position can be yielded directly from two celestial bodies, and the calculation process concept is easier to comprehend. The formulae we propose can not only be directly used to solve corresponding problems, but also expand the spherical trigonometry research field.


2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Han Peng ◽  
Xiaoli Zhang ◽  
Guozhen Cao ◽  
Zhouzhou Liu ◽  
Yuejuan Jing ◽  
...  

Event-B is a formal modeling language that is very suitable for software engineering, but it lacks the ability of modeling time. Researchers have proposed some methods for modeling time constraints in Event-B. The limitations with existing methods are that, first of all, the existing research work lacks a systematic time refinement framework based on Event-B; secondly, the existing methods only model time in the Event-B framework and cannot be smoothly converted to automata-based models such as timed automata that facilitate the verification of time properties. These limitations make it more difficult to model and verify real-time systems with Event-B because it is very time-consuming to prove time properties in the Event-B framework. In this paper, we firstly proposed a systematic time refinement framework to express and refine time constraints in Event-B. Secondly, we also proposed various vertical refinement patterns and horizontal extension patterns to guide modelers to refine the Event-B real-time model step by step. Finally, we use a real-time system case to demonstrate the practicality of our method. The experimental results show that the proposed method can make the real-time system modeling in Event-B more convenient and the models are easier to convert to the timed automata model, thereby facilitating the verification of various time properties.


2018 ◽  
Vol 71 (6) ◽  
pp. 1344-1362 ◽  
Author(s):  
Frankiskos Pierros

Finding one's geographical position (fix) without the use of a Global Navigation Satellite System (GNSS), which was common place before the establishment of the latter, could be tedious and/or inaccurate. Apart from sound knowledge of spherical trigonometry and navigational methods, it also requires the knowledge of the navigator's approximate or assumed position, the use of the current year's celestial bodies' ephemeris (Nautical Almanac), and graphical methods (Lines of Position – LOP) which sometimes can prove wanting in accuracy and/or challenging for the unaccustomed user. The method proposed here is based on sight reduction from two celestial bodies, and directly calculates the geographical position, both for stationary and moving observers (“running fix”) using easily available modern programmable calculating devices, without the need of the assumed position, graphical methods (LOP) or the current year's ephemeris, hence the term “stand-alone”. This self-contained method is implemented by the author in a software application, which can be easily used in a portable computer (for example, a smartphone). The results are considered satisfactorily accurate.


Author(s):  
Ajitesh Kumar

Background: Nowadays, there is an immense increase in the demand for high power computation of real-time workloads and the trend towards multi-core and multiprocessor CPUs. The real-time system needs to be implemented upon multiprocessor platforms. Introduction: The nature of processors in an embedded real-time system is changing day by day. The two most significant challenges in a multiprocessor environment are scheduling and synchronization. The popularity of real-time multi-core systems has exploded in recent years, driving the rapid development of a variety of methods for multiprocessor scheduling of essential tasks, on the other hand, these systems have constraints when it comes to maintaining synchronization in order to access shared resources. Method: This research work presents a systematic review of different existing scheduling algorithms and synchronization protocols for shared resources in a real-time multiprocessor environment. The manuscript also presents a study based on various metrics of resource scheduling and comparison among different resource scheduling techniques. Result and Conclusion: The survey classifies open issues, key challenges, and likely useful research directions. Finally, we accept that there is still a lot of capacity in getting better resource management and further maintaining the overall quality. The paper considers such a future path of research in this field.


2021 ◽  
Vol 45 (01) ◽  
pp. 21-37
Author(s):  
S. OSTADHADI-DEHKORDI

The aim of this research work is to define a new class of hyperstructure as a generalization of semigroups, semihypergroups and Γ-semihypergroups that we call (Δ,G)-sets. Also, we define fundamental relation on (Δ,G)-sets and prove some results in this respect. Then, we introduce the notions of quotient (Δ,G)-sets by using a congruence relations. Finally, we introduce the concept of complete parts and Noetherian(Artinian) (Δ,G)-sets.


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