TRIANGLES WITH EQUAL AREAS, GENERATED BY TWO TRANSFORMATIONS IN THE TRIANGLE PLANE

被引：0

作者：

Stefanov, Ivan ^{[1
]}

Dimitrov, Deyan ^{[1
]}

Borisov, Borislav ^{[1
]}

机构：

[1] Math High Sch Lovech, 1 Acad Urumov Str, Lovech 5500, Bulgaria

来源：

MATHEMATICS AND INFORMATICS | 2018年 / 61卷 / 01期

关键词：

triangle; area; isotomic transformation; isogonal transformation; polynomial root;

D O I：

暂无

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

The paper is an elaboration by high school students under the scientific advices of Assoc. Prof. Dr. Veselin Nenkov. The new results in it were estimated highly during its presentation at the International competition "Methodology and Information Technologies in Education" in 2018 and the work was awarded first prize. It is dedicated to a well-known problem for triangle and quadrilateral areas determined by triangle secants. A general formula is found for the area of one of the triangles. The areas of triangles are determined when obtained by isotomic and isogonal transformations in the plane of a given triangle. What is investigated is the question for equal areas of the obtained triangles and the generating ones.

引用

页码：60 / 72

页数：13

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