Plane and Spherical Trigonometry

1942 ◽  
Vol 17 (3) ◽  
pp. 139
Author(s):  
Marion E. Stark ◽  
Frank A. Rickey ◽  
J. P. Cole
Keyword(s):  
Spherical Trigonometry

Aplikasi Teori Geodesi dalam Perhitungan Arah Kiblat: Studi untuk Kota Banjarnegara, Purbalingga, Banyumas, Cilacap, Kebumen

1970 ◽  
Vol 8 (2) ◽  
pp. 329-351
Author(s):  
Marwadi Marwadi
Keyword(s):  
Spherical Trigonometry

Para ulama sepakat bahwa menghadap kiblat menjadi syarat sahnya salat, tetapi mereka tidak sepakat bahwa  orang yang salat wajib menghadap ke bangunan Ka’bah atau ke arah Ka’bah. Untuk kesempurnaan ibadah, diperlukan usaha mencari arah kiblat yang tepat. Teori yang biasa digunakan untuk menghitung arah kiblat adalah teori ilmu ukur segitiga bola (spherical trigonometry). Sekarang, teori geodesi dengan rumus vincenty menjadi teori yang lebih akurat digunakan untuk menghitung arah kiblat daripada teori spherical trigonometry. Tulisan ini berusaha menggambarkan penggunaan teori geodesi dalam perhitungan arah kiblat untuk kota Banjarnegara, Purbalingga, Banyumas, Cilacap dan Kebumen. Teori geodesi menghasilkan arah kiblat untuk kota Banjarnegara 294°40’01.042”, Purbalingga 294°44’11.376”, Banyumas 294°45’25,582”, Cilacap 294°54’21.568”, dan Kebumen 294°44’16.752”. Jika arah kiblat tersebut dibandingkan dengan arah kiblat yang selama ini dipedomani, maka terdapat selisih rata-rata 0°7’32.74”. Dengan adanya hasil perhitungan yang mempunyai tingkat akurasi lebih tinggi, tentu akan menambah keyakinan dalam beribadah, walaupun arah kiblat yang selama ini menjadi pedoman juga masih dalam lingkup menghadap kiblat.

Mathematical models of Gauss – Kruger projection for calculation of meridians conversion on the plane and scale of the image

2018 ◽  
Vol 934 (4) ◽  
pp. 2-7
Author(s):  
P.A. Medvedev ◽  
M.V. Novgorodskaya
Keyword(s):  
Mathematical Models ◽  
Analytical Methods ◽  
Theoretical Studies ◽  
Spherical Trigonometry ◽  
Cylindrical Projection ◽  
Rectangular Coordinates ◽  
In Series ◽  
Observational Errors ◽  
The Difference

This work contains continued research carried out on improving mathematical models of the Gauss-Krueger projection in accordance with the parameters of any ellipsoid with the removal of points from the axial meridian to l ≤ 6° . In terms of formulae earlier derived by the authors with improved convergence for the calculation of planar rectangular coordinates by geodesic coordinates, the algorithms for determining the convergence of meridians on the plane and the scale of the image are obtained. The improvement of the formulae represented in the form of series in powers of the difference in longitudes was accomplished by separating spherical terms in series and then replacing their approximate sums by exact expressions using the formulae of spherical trigonometry. As in previous works published in this journal [7, 8], determining the sums of the spherical terms was carried out according to the laws of the transverse-cylindrical projection of the sphere on the plane. Theoretical studies are given and formulae are proposed for estimating the observational errors in the results of the derived algorithms. The maximum of observational errors of convergence of meridians and scale, proceeding from the specified accuracy of the determined quantities was established through analytical methods.

scholarly journals Qibla Direction Correction Test using a Digital Compass and Arduino Microcontroller

2019 ◽  
Vol 8 (2S7) ◽  
pp. 228-230
Keyword(s):  
Spherical Trigonometry ◽  
Arabic Word ◽  
Small Correction ◽  
Arduino Microcontroller ◽  
Yogyakarta City

Qibla is an Arabic word that refers to the direction in which a Muslim establishes prayer. In this study, we made a Qibla-based digital compass and Arduino microprocessor construction. The spherical trigonometry method is used to find out the direction of the Qibla by getting cross lines and longitude. While the direction of the qibla is obtained with the help of a digital compass. The testing of this tool was carried out at the mosque in Indonesia. The results showed that the direction of the Qibla for the Nur Asmaul Husna Mosque (Banten Province) is located at 295.2077026o with a correction of -0.06o . Gedhe Kauman Mosque is (Yogyakarta City) located at 294.7148437owith a correction of -0.35o and the Jami Nurul Muminin mosque is located at 294.0274353o with a correction of -9.74o . A small correction value indicates the accuracy of the Qibla direction

Stereographic Projection

2017 ◽  
Author(s):  
Glen Van Brummelen
Keyword(s):  
Stereographic Projection ◽  
Spherical Trigonometry ◽  
Arbitrary Triangle ◽  
Cesàro Method

This chapter deals with stereographic projection, which is superior to other projections of the sphere because of its angle-preserving and circle-preserving properties; the first property gave instrument makers a huge advantage and the second provides clear astronomical advantages. The earliest text on stereographic projection is Ptolemy's Planisphere, in which he explains how to use stereographic projection to solve problems involving rising times, suggesting that the astrolabe may have existed already. After providing an overview of the astrolabe, an instrument for solving astronomical problems, the chapter considers how stereographic projection is used in solving triangles. It then describes the Cesàro method, named after Giuseppe Cesàro, that uses stereographic projection to project an arbitrary triangle ABC onto a plane. It also examines B. M. Brown's complaint against Cesàro's approach to spherical trigonometry.

A pseudohedron

2004 ◽  
Vol 88 (512) ◽  
pp. 226-229
Author(s):  
H. Martyn Cundy
Keyword(s):  
The Other ◽  
Regular Polygons ◽  
Spherical Trigonometry ◽  
Equilateral Triangles ◽  
Infinite Set

The other day I received a long tube from a Canadian stranger containing a large poster featuring over a hundred polyhedra, including ‘all 92 Johnson polyhedra’. This term, though probably unfamiliar this side of the pond, was not completely unknown to me; it means convex polyhedra, excluding the regular and Archimedean ones, all of whose faces are regular polygons. Of course, as usual, we have to exclude those naughty polyhedra whose faces go around in pairs collecting squares (prisms) or equilateral triangles (antiprisms) and don’t know when to stop. The word convex is vital, otherwise there would be another infinite set. A lot of them are rather trivial, like sticking pyramids on the faces of a dodecahedron, but they include the deltahedra and many other interesting members. But they have at least one imitator who didn't quite make the grade. Trying to discover why, and how to coach him so that he would, I found that my spherical trigonometry was getting rather rusty so I set out to make one and see what was happening. I thought perhaps other readers would like to share this piece of antiresearch.

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