Abstract
Calculate the area of a special spherical triangle, which is formed by intersecting of a sphere and three mutually perpendicular planes. The intersection point of the three planes lies inside of the sphere. The result of the calculation is not an approximate solution but an analytic one. The analytical expression shows that the area of spherical triangle, under the radius of a sphere being known, is only determined by the contact angles. The conclusion can be used in the research of nucleation theory of crystallography.
This paper was supported by the development fund of TangShan teacher’s college (No: 09D01).
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References
Yang, X.S., Hu, J.L., Chen, D.H., et al.: Verification of GRAPES unified global and regional numerical weather prediction model dynamic core. Chinese Science Bulletin 53(22), 3458–3464 (2008)
Zang, S.X., Zhou, H.L., Wei, R.Q., et al.: Structure and physical properties of the Earth’s interior. Acta Seismologica Sinica 16(5), 522–533 (2003)
She, C.L., Wan, W.X., Xu, G.R.: Climatological analysis and modeling of the ionospheric global electron content. Chinese Science Bulletin 53(2), 282–288 (2008)
Lu, X.R.: Geometry of broad line regions of active galactic nuclei. Chinese Journal of Astronomy and Astrophysics 8(1), 50–62 (2008)
Jiang, C.G., Jiang, Z.B., Liu, H., et al.: Accurate method to calculate curvature correction of the Earth in survey. Surveying and Mapping of Geology and Mineral Resources 20(3), 1–3 (2004)
Huang, X.J., Shen, L.: On the convergence of circle packings to the quasiconformal map. Acta Mathematica Scientia 29B(5), 1173–1181 (2009)
Dong, P.B., Liu, L.: Spherical triangle graphic methods based on the relation of spherical triangle and triangular pyramid. Journal of Engineering Graphics (2), 124–128 (2001)
Li, X.L., Chen, D.H., Peng, X.D., et al.: Implementation of the semi-lagrangian advection scheme on a quasi-uniform overset grid on a sphere. Advances in Atmospheric Sciences 23(5), 792–801 (2006)
Yang, D.H.: Some basic inequalities in higher dimensional non-Euclid space. Science in China Series A: Mathematics 50(3), 423–438 (2007)
Gong, X., Wang, B.X., Chen, L.P.: Solution to 3D constraint for solid model deformation. Journal of Huazhong University of Science and Technology (Natural Science Edition) 36(9), 75–78 (2008)
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Hao, X., Yan, M., Lu, X. (2010). Area of a Special Spherical Triangle. In: Zhu, R., Zhang, Y., Liu, B., Liu, C. (eds) Information Computing and Applications. ICICA 2010. Communications in Computer and Information Science, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16336-4_17
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DOI: https://doi.org/10.1007/978-3-642-16336-4_17
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