• The Mathematical Education
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• v.45 no.3 s.114
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• pp.367-373
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• 2006

This study suggests that it is necessary to prove that the values of three areas of a triangle, which are obtained by the multiplication of the respective base and its corresponding height, are the same. It also seeks to deeply understand the meaning of Area formula of triangles by exploring some questions raised in the analysis of the proof. Area formula of triangles expresses the invariance of congruence and additivity on one hand, and the uniqueness of parallel line, one of the characteristics of Euclidean geometry, on the other. This discussion can be applied to introducing and developing exploratory learning on area in that it revisits the ordinary thinking on area.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.2
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• pp.161-180
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• 2005

The purpose of this study is to delve into how elementary mathematics textbooks deal with the areas of triangles and quadrilaterals from a viewpoint of the Didactic Transposition Theory. The following conclusion was derived about the teaching of the area concept: The area concept started to be taught perfectly in the 7th curricular textbook, and the focus of area teaching was placed on the area concept, since learners were gradually given opportunities to compare and measure areas. As to the area formulae of triangles and quadrilaterals, the following conclusions were made: First, the 1st curricular, the 2nd curricular and the 3rd curricular textbooks placed emphasis on transposition by textbooks, and the 4th curricular, the 5th curricular and the 6th curricular textbooks accentuated transposition by teachers. The 7th curricular textbooks put stress on knowledge construction by learners; Second, the focus of teaching shifted from a measurement of area to inducing learners to make area formula. Namely, the utilization of area formula itself was accentuated, while algorithm was emphasized in the past; Third, the way to encourage learners to produce area formula changed according to the curricula and in light of learners' level, but a wide range of teaching devices related to the area formulae were removed, which resulted in offering less learning chances to students; Fourth, what to teach about the areas of triangles and quadrilaterals was gradually polished up, and the 7th curricular textbooks removed one of the overlapped area formula of triangle.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.695-704
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• 2023

Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.

• Anatomy and Cell Biology
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• v.56 no.3
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• pp.350-359
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• 2023

The suboccipital triangle (ST) is a clinically relevant landmark in the posterior aspect of the neck and is used to locate and mobilize the horizontal segment of the third part of the vertebral artery before it enters the cranium. Unfortunately, this space is not always a viable option for vertebral artery exposition, and consequently a novel triangle, the inferior suboccipital triangle (IST) has been defined. This alternative triangle will allow surgeons to locate the artery more proximally, where its course is more predictable. The purpose of this study was to better define the anatomy of both triangles by measuring their borders and calculating their areas. Ethical clearance was obtained from the University of Pretoria (reference number: 222/2021) and both triangles were subsequently dissected out on both the left and right sides of 33 formalin-fixed human adult cadavers. The borders of each triangle were measured using a digital calliper and the areas were calculated using Herons Formula. The average area of the ST is 969.82±153.15 mm², while the average area of the IST is 307.48±41.31 mm². No statistically significant differences in the findings were observed between the sides of the body, ancestry, or sex of the cadavers. Measurement and analysis of these triangles provided important anatomical information and speak to their clinical relevance as surgical landmarks with which to locate the vertebral artery. Of particular importance here is the IST, which allows for mobilisation of this artery more proximally, should the ST be occluded.