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

2021 ◽  
Vol 47 ◽  
Author(s):  
Evaldas Gečiauskas
Keyword(s):  
Spherical Trigonometry ◽  
Integral Calculus ◽  
Analytical Geometry ◽  
Vilnius University ◽  
School Books

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.

The determination of true orientations of fractures in rock cores

1983 ◽  
Vol 20 (2) ◽  
pp. 221-227 ◽  
Author(s):  
J. S. O. Lau
Keyword(s):  
Stereographic Projection ◽  
Management Program ◽  
Reference Line ◽  
Spherical Trigonometry ◽  
Mathematical Methods ◽  
Analytical Geometry ◽  
Deep Boreholes ◽  
Nuclear Fuel Waste ◽  
Apparent Orientation

Determination of the true orientations of fractures in diamond drill cores obtained from deep boreholes in plutonic bodies is an essential requirement of the geoscience component of the Canadian Nuclear Fuel Waste Management Program. A reference line can be painted on the entire length of the rock core, indicating the orientation of the core, and the apparent orientation of the fracture can be measured from this reference line. This paper describes three methods that have been developed to convert the apparent orientation to true orientation, namely, stereographic projection, spherical trigonometry, and analytical geometry. The results obtained from these techniques were compared to assess their relative accuracy. Whereas the graphical method is more readily adaptable for use in the field, the mathematical methods can be computer-programmed and the programs GEOCORE and ORIENTC are available from the Geological Survey of Canada to facilitate the calculation of large volumes of data. Keywords: true orientation, fracture, rock core, stereographic projection, spherical trigonometry, analytical geometry.

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.

Women Welfare Measures Implemented During DMK Regime

Think India ◽  
2019 ◽  
Vol 22 (3) ◽  
pp. 772-779
Author(s):  
T.Vinsela Jeev
Keyword(s):  
Police Department ◽  
Small Scale ◽  
Economic Activities ◽  
The Poor ◽  
Small Scale Industry ◽  
Poor Women ◽  
The Government ◽  
Physically Challenged ◽  
Self Help Groups ◽  
School Books

During the DMK regime many welfare schemes for implemented for women especially. This schemes for developments for socio and economic activities for women. The poor women, widows, physically challenged were benefited their schemes. The government allotted lot of sewing machines, Free school books, Midday meal schemes, Small scale Industry, Self help groups, Boating supply for fisher mans and many women teachers were appointed in Elementary school, Middle school, High schools. Women’s were appointed in police Department and also so many schemes for the development of socio and economic condition of the poor women people.

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.

The method of sweeping tangents

2008 ◽  
Vol 92 (525) ◽  
pp. 396-417 ◽  
Author(s):  
Tom M. Apostol ◽  
Mamikon A. Mnatsakanian
Keyword(s):  
Integral Calculus ◽  
Visual Approach

What is the area of the shaded region between the tyre tracks of a moving bicycle such as that depicted in Figure 1 ? If the tracks are specified, and equations for them are known, the area can be calculated using integral calculus. Surprisingly, the area can be obtained more easily without calculus, regardless of the bike’s path, using a dynamic visual approach called the method of sweeping tangents that does not require equations for the curves.

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