• Journal for History of Mathematics
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• v.36 no.2
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• pp.21-34
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• 2023

Spherical trigonometry refers to the geometry related to spherical triangles. It has been an important tool for studying astronomy since ancient times. In trigonometry, concepts such as trigonometric functions naturally emerge from the relationship between arcs and chords of a circle. In this paper, we briefly examine the origin of spherical trigonometry. To introduce the basics of spherical trigonometry, we present fundamental and important theorems such as Menelaus's theorem, the law of sines and the law of cosines on a sphere, along with their proofs. Furthermore, we discuss the educational value and potential applications of spherical trigonometry.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.227-236
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• 2005

A chi-squared test of spherical symmetry is suggested. This test is easy to apply in practice since it is easy to compute and has a limiting chi-squared distribution under spherical symmetry. The result of Park(1998) can be used to show that it has the limiting chi-squared distribution. A simulation study is conducted to study the accuracy, in finite samples, of the limiting distribution. Finally, a simulation study that compares the power of our test with those of other tests of spherical symmetry is performed.

• Journal of Electrical Engineering and Technology
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• v.10 no.6
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• pp.2384-2392
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• 2015

The technical development and practical applications of big-data for health is one hot topic under the banner of big-data. Big-data medical image fusion is one of key problems. A new fusion approach with coding based on Spherical Coordinate Domain (SCD) in Wireless Sensor Network (WSN) for big-data medical image is proposed in this paper. In this approach, the three high-frequency coefficients in wavelet domain of medical image are pre-processed. This pre-processing strategy can reduce the redundant ratio of big-data medical image. Firstly, the high-frequency coefficients are transformed to the spherical coordinate domain to reduce the correlation in the same scale. Then, a multi-scale model product (MSMP) is used to control the shrinkage function so as to make the small wavelet coefficients and some noise removed. The high-frequency parts in spherical coordinate domain are coded by improved SPIHT algorithm. Finally, based on the multi-scale edge of medical image, it can be fused and reconstructed. Experimental results indicate the novel approach is effective and very useful for transmission of big-data medical image(especially, in the wireless environment).

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.182-184
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• 2005

In this study, we propose a chi-squared test of spherical symmetry. The advantage of this test is that the test statistic and its asymptotic p-value are easy to compute. A simulation study is conducted to study the accuracy, in finite samples, of the limiting distribution of the test statistic under spherical symmetry. The power of our test is compared with those of other tests for spherical symmetry in various alternative distributions via simulation.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2001.11a
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• pp.319-324
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• 2001

An anatomical head and a multi-layered spherical head with a half-wave handset antenna have been analysed and compared using the Finite-Difference Time-Domain (FDTD) and the Eigenfuntion Expansion Method (EEM), respectively. The analysis shows that results from a simple spherical head with a half-wave antenna can be used to predict the main antenna radiation patters as well as estimates of the peak SAR in a handset user's head. Various representative design data are presented using a six-layered spherical head with a half-wave antenna at 900 MHz

• Journal of Korean Clinical Health Science
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• v.8 no.1
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• pp.1386-1397
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• 2020

Purpose: To examine the effectiveness of various treatments; bifocal spectacles, orthokeratology, atropine, and time spent in outdoors; in slowing down the myopia progression for Asian adolescents (6-18age). Methods: The research focused on examining the most effective treatment in controlling myopia based on the literature sources that have been published. Through meta-analysis of various research papers that already has been done in this field, a lot of data was collected. For each treatment, the difference in axial length and spherical equivalent over time was measured and recorded. To quantitatively record the difference, both axial length and spherical equivalent was determined by value of control group value of treatment group. The paper compared the effectiveness of each treatment based on the data that was measured. Results: Adolescents who chose to spend time outdoors in order to slow down myopia progression had axial length difference of 0.03 mm and spherical equivalent difference of 0.17 D. Adolescents that used atropine had axial length difference of 0.36 mm and spherical equivalent difference of 0.92 D. Bifocal spectacle resulted in axial length difference of 0.21 mm and spherical equivalent difference of 0.59 D, and for orthokeratology 0.23 mm and 0.04 D, respectively. Axial length wise, myopia was most controlled by the atropine since there was a greatest difference between the group that got the treatment and the group that did not have the treatment. According to the spherical equivalent difference data, myopia was most controlled by atropine. Conclusion: Atropine showed the most effective result in controlling myopia among the four treatment. Again, compared to other three treatment, using atropine appeared to have greatest ability in slowing down myopia progression since adolescents who were treated with atropine had greatest difference from adolescents in the control group that had the same condition but didn't get the treatment. However, every treatment was only used for 2 or 3 years which is quite short time period to measure the long term effect of the four treatments. Also, since atropine is a pharmaceutical method to control myopia, it may harm adolescents' eyes compared to optical or environmental treatment.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.73-86
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• 2007

The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatial $C^1$ Hermite data, we construct a spatial PH curve on a sphere that is a $C^1$ Hermite interpolant of the given data as follows: First, we solve $C^1$ Hermite interpolation problem for the stereographically projected planar data of the given data in $\mathbb{R}^3$ with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in $\mathbb{R}^3$ using the inverse general stereographic projection.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.117-126
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• 2001

We provide a simple chi-squared test of multivariate normality based on rectangular cells on the spherical data. This test is simple since it is a direct extension of the univariate chi-squared test to multivariate case and the expected cell counts are easily computed. We derive the limiting distribution of the chi-squared statistic via the conditional limit theorems. We study the accuracy in finite samples of the limiting distribution and then compare the poser of our test with those of other popular tests in an application to a real data.

• The KIPS Transactions:PartD
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• v.8D no.2
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• pp.145-153
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• 2001

The Pyramid-Technique is based on mapping n-dimensional space data into one-dimensional data and expressing it as B-tree ; and by solving the problem of search time complexity the pyramid technique also prevents the effect \"phenomenon of dimensional curse\" which is caused by treatment of hypercube range query in n-dimensional data space. The Spherical Pyramid-Technique applies the pyramid method’s space division strategy, uses spherical range query and improves the search performance to make it suitable for similarity search. However, depending on the size of data and change in dimensions, the two above technique demonstrate significantly inferior search performance for data sizes greater than one million and dimensions greater than sixteen. In this paper, we propose a new index-structured PdR-Tree to improve the search performance for high dimensional data such as multimedia data. Test results using simulation data as well as real data demonstrate that PdR-Tree surpasses both the Pyramid-Technique and Spherical Pyramid-Technique in terms of search performance.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.29 no.9
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• pp.14-22
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• 2015

TIn this paper, a centering method for an unfocused input character using the spherical domain system and the centering character to use the shift invariant feature for the recognition system is proposed. A system for recognition is implemented using the centroid method with coordinate average values, and the results of an above 78.14% average differential ratio for the character features were obtained. It is possible to extract the shift invariant feature using spherical transformation similar to the human eyeball. The proposed method, which is feature extraction using spherical coordinate transform and transformed extracted data, makes it possible to move the character to the center position of the input plane. Both digital and optical technologies are mixed using a spherical coordinate similar to the 3 dimensional human eyeball for the 2 dimensional plane format. In this paper, a centering character feature using the spherical domain is proposed for character recognition, and possibilities for the recognized possible character shape as well as calculating the differential ratio of the centered character using a centroid method are suggested.