• Journal for History of Mathematics
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• v.16 no.2
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• pp.43-54
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• 2003

In this article we study various proofs of Heron's formula, extract some didactical ideas from these proofs, and didactically enlarge Heron's formula. In this paper we in detail introduce five different proofs from various articles and textbooks, and suggest our proof of Heron's formula. Enlarging this proof we are able to prove Brahmagupta's formula and generalized convex quadrangle's area formula.

• Journal of Ecology and Environment
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• v.43 no.3
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• pp.282-288
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• 2019

We investigated the changes in the population size and inter-specific space usage for breeding in mixed breeding sites of the great cormorant (Phalacrocorax carbo), grey heron (Ardea cinerea), great egret (Ardea alba modesta) and intermediate egret (Egretta intermedia) in Gammul-myeon, Goesan-gun, Chungcheongbuk-do, South Korea, in 2016-2017. These species bred in two adjacent habitats (site A and site B). The number of breeding pairs of all species and the size of the breeding area at site B increased in 2017. In 2017, great cormorants at site B occupied the breeding sites previously occupied by the other species in 2016, while the grey heron and great egret occupied the sites around the great cormorant breeding site. The heights of nest trees and nests of great cormorant and grey heron did not differ temporally, but these heights in site B were significantly higher than those in site A for great cormorants. For great egrets, these greatly decreased in site B in 2017. Thus, the great cormorant either moved to favourable nest sites for breeding success or selected nest sites used by the herons in the previous year. Further studies of these two possibilities are necessary.

• Journal of Ecology and Environment
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• v.30 no.4
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• pp.341-346
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• 2007

Nest density was determined and tree and soil characteristics around Nycticorax nycticorax breeding sites and non-breeding sites on Bamsum Island in Seoul were analyzed from May 2005 to October 2006 to identify breeding site preferences of N. nycticorax and the effects of N. nycticorax nesting density on nesting tree structure and soil characteristics. N. nycticorax preferred trees of low height ($3.5{\sim}6$ m) and small diameter at breast height in high density Salix communities. Excrement of heron juveniles was dropped on the soil under the nests. The soil nutrient content under nests (P: 126.0 mg/kg, N: 202.8 mg/kg, EC: 549 ${\mu}S/cm$, pH 4.7) was much higher than that of control soils from Bamsum Island not enriched by heron excrement (P: 41.5 mg/kg, N: 42.0 mg/kg, EC: 342 ${\mu}S/cm$, pH 5.1). Formation of Salix communities on the shores of Bamsum Island is ongoing, and their structure has been directly influenced by annual flooding. After flooding, the nutrient content differences between heron-affected soils and control soils were not significant. This might be the reason that Salix communities on Bamsum were not affected by nesting herons as in other terrestrial communities where herons nest. This result indicates that flooding plays an important role in sustaining Salix communities on Bamsum Island where herons nest. The results of this study may increase understanding of N. nycticorax breeding behavior which may be useful for conservation planning.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4C
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• pp.254-264
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• 2011

In this paper, we propose two algorithm for improving the performance of wireless localization(Trilateration and Least Square) based on the range based approach method in indoor environment using RSSI for ranging distance. we propose a method to discriminate the case that has relatively large estimation errors in trilateration using Heron''s formula for the volume of a tetrahedron. And we propose the algorithm to process the discriminated types of distance using the absolute value calculated by Heron''s formula. In addition, we propose another algorithm for the case of which the number of anchor nodes larger than three. In this case, Residual Weighting Factor(RWGH) improves the performance of Least Square. However, RWGH requires many number of calculations. In this paper, we propose Iterative Weighted Centroid Algorithm(IWCA) that has better performance and less calculation than RWGH. We show the improvement of performance for two algorithms and the combination of these algorithm by using simulation results.

• Korean Journal of Environment and Ecology
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• v.21 no.1
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• pp.93-100
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• 2007

This study was based on the breeding process of the Pacific Reef Herons (Egretta sacra) bred in Aewol-eup, Jeju Island, for two years from February 2004 to June 2005. The clutch size of the pacific reef herons was $3.24{\pm}0.75$(N=17, range: $2{\sim}4$), and the egg-laying was at dawn or night intervals of one to three days. The major diameter of the egg(N=39) was $46.73{\pm}1.91mm$, the minor diameter thereof $34.06{\pm}0.83mm$, the weight thereof $27.67{\pm}3.12g$, and the thickness of the egg shell thereof $0.26{\pm}0.03mm$. In relation to the breeding cycles of the Pacific Reef Herons, the nesting or nest repairing was made from February to the end of April each year, the egg laying from the beginning of March to the beginning of May, the hatching from the beginning of April to the middle of May, and the nest departure from the middle of May to the end of July. The supplement brood was started immediately from May to June when the first brood had failed. The incubation period was $28.17{\pm}4.12(N=6)$ days, and hatched asynchronously. The fledgling period was $40.00{\pm}6.84(N=5)$ days, and bill, wing, tarsus and weight developments of early hatched nestlings were the fastest among the same brood. Compared with other egret species, the egg laying period of the Pacific Reef Heron was faster than that of the Black-crowned Night Heron, Little Egret and Great Egret, but later than that of Grey Heron, in Korea.

• Proceedings of the Korean Society of Environment and Ecology Conference
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• 2008.10a
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• pp.46-48
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• 2008

• Journal of Veterinary Clinics
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• v.30 no.1
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• pp.49-52
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• 2013

A wild black-crowned night heron (Nycticorax nycticorax) with dehydration and a non-weight bearing lameness of the left leg was rescued. On physical examination, the left knee was displaced laterally at almost a $90^{\circ}$ angle with firm swelling and crepitus in the area of the coxofemoral joint. Radiographs confirmed cranio-dorsal coxofemoral luxation. A closed reduction attempt failed. The coxofemoral joint luxation was reduced surgically by placement of the femoral neck next to the pelvis with a suture. Ten days after surgery, radiographs and computed tomography showed the femoral neck and head were positioned well within the acetabulum. At 20 days, the bird was using the affected limb normally, and could hunt and forage for food in a rehabilitation housing unit with a small pond. The bird was successfully released into the wild. The placement of the femoral neck adjacent to the pelvis with a suture can be successfully performed for cases of avian coxofemoral joint luxation. Furthermore, this procedure can provide sufficient stabilization of the coxofemoral joint and acceptable limb function.

• Proceedings of the Korean Society of Environment and Ecology Conference
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• 2006.10a
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• pp.86-96
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• 2006

To provide some ecological informations for protection and management of mixed heronries, their distribution, breeding species and individuals, and site characteristics that may be important to heron ecology were investigated in Jeollanam-do during 2005 breeding season. During the study, 17 mixed heronries, containing a total of six ardeid species were found. Of them, Great Egret(Egretta alba) and Grey Heron(Ardea cinerea) bred in most sites(both 92%) and were most numerous(36.3%, 31.0% respectively). Many of heronries(53.3%) were located within the bamboo forest. Other site characteristics were as follows: the mean area of heronry was $2346m^2$ with range of $500-7,000m^2$, the mean distance between nearest two heronies was 18.1km with range of 5.6-40.4km, the mean distance to nearest village was 297m with range of 10-2,000m, the mean gradient of the topography was $18^{\circ}$ with range of $2^{\circ}{\sim}40^{\circ}$, and 40.0% of heronries were located in the eastern slope.

• School Mathematics
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• v.8 no.3
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• pp.327-339
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• 2006

In this study, a teaching units for teaching and learning of secondary preservice teachers' mathematising is designed, focusing on reinvention of Bretschneider's formula. preservice teachers can obtain the following through this teaching units. First, preservice teachers can experience mathematising which invent a noumenon which organize a phenomenon, They can make an experience to invent Bretscheider's formula as if they invent mathematics really. Second, preservice teachers can understand one of the mechanisms of mathematics knowledge invention. As they reinvent Brahmagupta's formula and Bretschneider's formula, they understand a mechanism that new knowledge is invented Iron already known knowledge by analogy. Third, preservice teachers can understand connection between school mathematics and academic mathematics. They can understand how the school mathematics can connect academic mathematics, through the relation between the school mathematics like formulas for calculating areas of rectangle, square, rhombus, parallelogram, trapezoid and Heron's formula, and academic mathematics like Brahmagupta's formula and Bretschneider's formula.

• Journal of Ecology and Environment
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• v.31 no.2
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• pp.147-151
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• 2008

Feeding methods of five species of herons and egrets were studied in an agricultural landscape in Asan city, Chungcheongnam-do, Korea in 2006. Grey herons primarily hunted while standing, whereas great egrets fed while walking slowly. Two smaller species, little and cattle egrets, were active foragers, feeding both while walking quickly and walking slowly. Little egrets were the only species using the foot stirring method. The medium-sized heron, intermediate egrets, foraged mainly while walking slowly or leaning. For grey herons, great egrets and little egrets, the frequency of use of different feeding methods was different between habitats: these species used the leaning method more frequently in rice fields than in reservoirs and ditches. Also, most herons (all species other than great egrets) showed seasonal changes in their feeding methods that are related to changes in habitat condition.