• 한국학교수학회논문집
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• 제11권1호
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• pp.19-30
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• 2008

카발리에리는 아르키메데스의 구의 부피에 대한 연구결과를 재구성하는 과정에서 면적은 무한히 많은 평행한 선분으로, 부피는 무한히 많은 평행한 면적으로 구성된다고 하였다. 이것을 면적과 부피에 대한 불가분량이라 하고 이 원리를 발전시켜 카발리에리의 원리를 발견하였다. 본 연구에서는 영재학생들이 피라미드의 부피를 찾는 과정에서 카발리에리의 원리를 발견하고 이를 적용하고 일반화하는 교수 학습모형을 제시하였다.

• Journal of Korean Neurosurgical Society
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• 제58권5호
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• pp.454-461
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• 2015

Objective : In this study, we aimed to investigate the underlying ethiological factors in chiari malformation (CM) type-I (CMI) via performing volumetric and morphometric length-angle measurements. Methods : A total of 66 individuals [33 patients (20-65 years) with CMI and 33 control subjects] were included in this study. In sagittal MR images, tonsillar herniation length and concurrent anomalies were evaluated. Supratentorial, infratentorial, and total intracranial volumes were measured using Cavalieri method. Various cranial distances and angles were used to evaluate the platybasia and posterior cranial fossa (PCF) development. Results : Tonsillar herniation length was measured $9.09{\pm}3.39mm$ below foramen magnum in CM group. Tonsillar herniation/concurrent syringomyelia, concavity/defect of clivus, herniation of bulbus and fourth ventricle, basilar invagination and craniovertebral junction abnormality rates were 30.3, 27, 18, 2, 3, and 3 percent, respectively. Absence of cisterna magna was encountered in 87.9% of the patients. Total, IT and ST volumes and distance between Chamberlain line and tip of dens axis, Klaus index, clivus length, distance between internal occipital protuberance and opisthion were significantly decreased in patient group. Also in patient group, it was found that Welcher basal angle/Boogard angle increased and tentorial slope angle decreased. Conclusion : Mean cranial volume and length-angle measurement values significantly decreased and there was a congenital abnormality association in nearly 81.5 percent of the CM cases. As a result, it was concluded that CM ethiology can be attributed to multifactorial causes. Moreover, congenital defects can also give rise to this condition.

• 한국수학사학회지
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• 제27권2호
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• pp.127-138
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• 2014

In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.

• 한국초등수학교육학회지
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• 제13권1호
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• pp.115-140
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• 2009

Freudenthal은 수학화를 핵심 개념으로 하는 현실주의 수학 교육론을 주창하였다. 수학화란 현실 안에 있는 여러 현상들을 수학적인 수단을 사용하여 조직함으로써 현실에 질서를 부여하는 활동을 말한다. 본 연구에서는 Freudenthal의 수학화 이론을 바탕으로 제 7차 초등 수학 교과서 5-가 단계의 넓이 단원을 재구성하여 실험적인 지도만을 작성한 다음, 이를 통하여 교수 실험을 실시함으로써, 수학화를 통한 넓이의 지도 방안의 효과와 더불어 학생들의 넓이 개념과 공식에 대한 이해 실태를 분석하였다. 그 결과, 넓이의 개념 이해 측면에서는 실험반 학생들이 우수하였으나, 넓이의 계산 측면에서는 유의미한 차이가 없는 것으로 나타났다.

• Clinical and Experimental Reproductive Medicine
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• 제40권3호
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• pp.115-121
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• 2013

Objective: Letrozole and estradiol valerate are used to treat some hormonally-responsive symptoms and also in modeling of the polycystic ovary syndrome. However, the stereological analysis of the ovary has received less attention. Estimation of the whole ovary volume using the Cavalieri method can be applied in any orientation desired, but estimation of the mean volume of the oocytes requires isotropic uniform random sectioning. Here, a combined method was developed for estimating the parameters. To our knowledge, no comparison has been made of the effects of letrozole and estradiol on the ovary. Methods: Sixty rats were divided into 4 groups receiving estradiol (4 mg/kg), olive oil, letrozole (1 mg/kg), or normal saline. After 21 days, their ovaries were studied. Results: Relative to the control group, the total volume of the ovary and the cortex increased in the letrozole-treated and estradiol-treated rats. In addition, the number of the preantral, antral, and granulosa cells decreased by 43% to 56% in the letrozole- and estradiol-treated rats. On average, a 19% increase was observed in the atretic oocytes of the letrozole-treated and estradiol-treated rats, but the mean oocyte volume decreased by 29% to 44% in letrozole- and estradiol-treated rats. Furthermore, the letrozole-treated rats showed a 5-fold and 7-fold increase in the volume of the cysts and corpus luteum, respectively. A 3-fold increase was found in the volume of both the cysts and corpus luteum in the estradiol group. Conclusion: The structural changes of the ovary were most pronounced in the letrozole-treated animals.

• Journal of Periodontal and Implant Science
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• 제42권6호
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• pp.217-223
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• 2012

Purpose: Several parameters have been described for determining the success or failure of dental implants. The surface properties of transgingival implant components have had a great impact on the long-term success of dental implants. The purpose of this study was to compare the tendency of two periodontal pathogens to adhere to and colonize zirconia abutments and titanium alloys both in hard surfaces and soft tissues. Methods: Twelve patients participated in this study. Three months after implant placement, the abutments were connected. Five weeks following the abutment connections, the abutments were removed, probing depth measurements were recorded, and gingival biopsies were performed. The abutments and gingival biopsies taken from the buccal gingiva were analyzed using real-time polymerase chain reaction to compare the DNA copy numbers of Aggregatibacter actinomycetemcomitans, Porphyromonas gingivalis, and total bacteria. The surface free energy of the abutments was calculated using the sessile water drop method before replacement. Data analyses used the Mann Whitney U-test, and P-values below 0.05 find statistical significance. Results: The present study showed no statistically significant differences between the DNA copy numbers of A. actinomycetemcomitans, P. gingivalis, and total bacteria for both the titanium and zirconia abutments and the biopsies taken from their buccal gingiva. The differences between the free surface energy of the abutments had no influence on the microbiological findings. Conclusions: Zirconia surfaces have comparable properties to titanium alloy surfaces and may be suitable and safe materials for the long-term success of dental implants.