On the special spherical triangles for physical and cosmological applications

It is well known that a spherical triangle of 270 degree triangle is constructible on the surface of a sphere; a globe is a good example. Take a point (A) on the equator, draw a line 1/4 the way around (90 degrees of longitude) on the equator to a new point (B).

Development of Fuel Calculation Applications Android Based for Ship Operations

This study aims to develop an android-based application to calculate the amount of fuel adjusted to the distance and speed of the ship based on the trajectory (way point). The calculation of distance in this application uses the concept of a spherical triangle which is used in voyage navigation. This development adopts the Waterfall model with the stages of Requirement Engineering, Design and implementation, Testing, Release and Maintenance. At the product review stage, it involves software experts (to provide criticism and suggestions for improvement), then testing is carried out by comparing the results of calculations using applications with manual calculations and ECDIS (electronic Chart Display Information System). The test results show that there is no significant difference between the results of calculations using the application with manual calculations and ECDIS. Thus, this application can be used to calculate the amount of fuel needed according to the distance traveled and the speed of the ship based on the selected trajectory.

Reaktualisasi Pengukuran Arah Kiblat Dengan Metode Segitiga Bola Pada Masjid Dan Musholla

An understanding of the Qibla direction is very important for Muslims, because facing the Qibla is one of the legal requirements for performing prayers. Although now the technology to determine the Qibla direction is sophisticated, it is necessary to know how to determine the actual Qibla direction. The determination of the direction of the Qibla with the spherical triangle method is based on a triangle on the surface of the globe which is formed by three large circles of the globe, namely two circles of the earth's longitude and one circle of Qibla. The intersection of the three large circles forms three points, namely point A (Makkah), point B (the location where the Qibla direction will be calculated), and point C (the North Pole). The steps in determining the Qibla direction include: (1) Prepare the data needed in calculating the Qibla direction of a place, namely latitude and longitude data for the Kaaba (Makkah city), as well as latitude and longitude data for the location/city to be calculated. the qibla direction; (2) Calculation of the Qibla direction using the formula , with: B = Angle of the direction of the Qibla of a place, C = The difference between the longitude of the Kaaba and the longitude of the place where the Qibla direction is being sought, a = 90o – tp (latitude), and b = 90o – ka (Kaaba latitude); (3) Calculation of true Qibla azimuth from true north in a clockwise direction, where true Qibla azimuth = 360o – Qibla direction angle (B); (4) Determination of the actual Qibla direction by measuring using an arc ruler as large as true Qibla azimuth from true north.

Analysis of errors according to Newman in solving the spherical triangle

Penelitian deskriptif dengan pendekatan kualitatif ini bertujuan untuk mengidentifikasi tipe kesalahan dan penyebabnya, serta mengatasinya. Tipe-tipe kesalahan menurut Newman mencakup kesalahan pembacaan, pemahaman terhadap soal, melakukan transformasi, ketrampilan pengerjaan, dan penulisan simbol. Subyek penelitian ini adalah mahasiswa semester pertama Program Studi Nautika yang berjumlah 25 mahasiswa, dengan memakai metode tes, wawancara, dan pengumpulan data. Hasil wawancara dibandingkan dengan jawaban tes mahasiswa, metode dokumentasi digunakan untuk mengetahui nama mahasiswa sebagai subyek penelitian. Berdasarkan luaran penelitian, didapatkan 23,6% mahasiswa mengalami kesalahan pada tahap membaca, 21,8% mahasiswa menghadapi kesalahan dalam tahap pemahaman, 17,3% mahasiswa melakukan kesalahan dalam tahap transformasi, 26,4% mahasiswa mengalami kesalahan pada tahap ketrampilan proses, 10,9 % mahasiswa mengalami kesalahan pada tahap notasi. Kesalahan-kesalahan tersebut disebabkan kurangnya memahami soal, mahasiswa tidak mampu mengubah soal cerita menjadi bahasa matematika, kurang teliti, kurang latihan dalam mengerjakan soal cerita, dan lupa tentang rumus yang digunakan. Dosen diharapkan sering mengenalkan persoalan segitiga bola yang kontekstual kepada mahasiswa untuk meningkatkan pemahaman mahasiswa, mahasiswa harus sering dilatih untuk menyelesaikan soal cerita yang berkaitan dengan segitiga bola dengan berbagai variasi untuk melatih ketelitian dan keterampilannya.

PEMANFAATAN ANALISA MATEMATIS DALAM PENYELESAIAN PERMASALAHAN FIKIH

This article intends to clarify the role of mathematics in the study of fiqh. Apart from inheritance, the study of astronomy is in direct contact with the improvement of fiqh worship, especially the prayers and fasting of Ramadan. However, its role is a supporter that must be strengthened by the main fiqh sources. This is evident in the process of determining the initial time of the five daily prayers. Through literature explanations relating to the coordinate system of celestial bodies, a celestial spherical triangle can be formulated in sin, cos and tangent which can be converted into measurements of praying time on earth. So it is not wrong if falak also knows the science of Hisab

Synthesis of the base curves for <i>n</i>-lobed noncircular bevel gears

As a type of spatial transmission mechanism, noncircular bevel gears can transfer power and motion between two intersecting axes with variable transmission. In this paper, the relation of arc length is expressed by Angle in spatial polar coordinate system, utilizing the spherical triangle theorem, the parametric equations of base curves are established by applying arc length relation. Further, an example is given to verify whether pitch curves is concave on osculating circle of noncircular bevel gear section cone. Similarly, this example illustrates the cause of the mutation for the base curves.

Conception of spherical triangle in terms of learning styles

Penelitian ini bertujuan untuk mendeskripsikan konsepsi mahasiswa pada materi segitiga bola ditinjau dari gaya belajar. Konsepsi mahasiswa dideskripsikan berdasarkan identifikasi mahasiswa terhadap segitiga bola serta penerapan segitiga bola untuk menentukan jarak pelayaran dan haluan kapal dalam pelayaran. Representasi mahasiswa terhadap segitiga bola difokuskan pada menghitung besarnya bagian-bagian segitiga bola, penggunaan aturan-aturan segitiga bola untuk menghitung jarak dan haluan kapal dalam pelayaran. Penelitian ini merupakan penelitian eksploratif dengan pendekatan kualitatif. Subyek penelitian ini adalah mahasiswa semester I Program Studi Nautika yang bergaya belajar visual, auditori, dan kinestetik. Hasil penelitian menunjukkan bahwa terdapat perbedaan konsepsi antara mahasiswa yang bergaya belajar visual, auditori, dan kinestetik. Dosen diharapkan memiliki strategi yang tepat dalam menyampaikan materi perkuliahan, sehingga materi dapat dengan mudah dipahami oleh mahasiswa yang memiliki gaya belajar yang berbeda-beda.

Conditions for Rigid and Flat Foldability of Degree-n Vertices in Origami

In rigid origami, the complex folding motion arises from the rotation of strictly rigid faces around crease lines that represent perfect revolute joints. The rigid folding motion of an origami crease pattern is collectively determined by the kinematics of its individual vertices. Establishing a kinematic model and determining the conditions for the rigid foldability of a single vertex is thus important to exploit rigid origami in engineering design tasks. Today, there exists neither an efficient kinematic model to determine the unknown dihedral angles nor an intrinsic condition for the rigid foldability of arbitrarily complex vertices of degree n. In this paper, we present the principle of three units (PTU) that provides an efficient approach to modeling the kinematics of single degree-n vertices. The PTU is based on the notion that the kinematics of a vertex is determined by the behavior of a single underlying spherical triangle. The condition for the existence of this triangle leads to the condition for the rigid and flat foldability of degree-n vertices. These findings are transferred from single vertices to crease patterns, resulting in a simple rule to generate kinematically determinate crease patterns that can be designed to fold rigidly. Finally, we discuss the limitations of the PTU with respect to the global rigid foldability of a crease pattern.

New Formulae for Combined Spherical Triangles

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.