Symbolic geometry software and proofs

被引：0

作者：

Todd P.

Lyublinskaya I. ^{[1
]}

Ryzhik V. ^{[2
]}

机构：

[1] CUNY College of Staten Island, Staten Island

[2] Lycee Physical Technical High School, St Petersburg

来源：

International Journal of Computers for Mathematical Learning | 2010年 / 15卷 / 02期

关键词：

Computer Algebra System; Dynamic Geometry; Symbolic Expression; Geometry System; Dynamic Geometry Software;

D O I：

10.1007/s10758-010-9164-8

中图分类号：

学科分类号：

摘要：

Dynamic Geometry software has facilitated an inductive approach to geometry. The dynamic geometry allows students to discover results for themselves, formulate conjectures and intermediate results, examine special cases, and generate new ideas. The new symbolic geometry software, such as Geometry Expressions allows geometric and algebraic representations to coexist in the same model. Symbolic geometry measurements can be used in formulating purely geometrical proofs and also used as the link between the components of a hybrid geometric/algebraic proof. When proving that the incircle of a Pythagorean triangle has integer radius, the expression for the radius is taken as given by the symbolic geometry system, and further algebraic manipulation performed to prove that it is an integer. Displaying symbolic expressions for the length of the median along with coordinates of the triangle vertices and the foot of the median led to a proof path.

引用

页码：151 / 159

页数：8

共 50 条

[21] Exploratory teaching of geometry using dynamic geometry software and learning of mathematics teachers: A systematic review [J].

Gutierrez-Araujo, Rafael Enrique ;

Pazuch, Vinicius .

UNICIENCIA, 2023, 37 (01)

[22] Making versus observing manipulations of geometric properties of triangles to learn geometry using dynamic geometry software [J].

Bokosmaty, Sahar ;

Mavilidi, Myrto-Foteini ;

Paas, Fred .

COMPUTERS & EDUCATION, 2017, 113 :313-326

[23] Design of virtual scenarios for optimization problems in dynamic geometry software [J].

Villamizar Araque, Freddy Yesid ;

Rincon Leal, Olga Lucy ;

Vergel Ortega, Mawency .

LOGOS CIENCIA & TECNOLOGIA, 2018, 10 (02) :67-75

[24] A Dictionary of Gestures for Multitouch-based Interactive Geometry Software [J].

Reis, Helena M. ;

Isotani, Seiji ;

Gasparini, Isabela ;

Mizoguchi, Riichiro .

15TH IEEE INTERNATIONAL CONFERENCE ON ADVANCED LEARNING TECHNOLOGIES (ICALT 2015), 2015, :102-104

[25] Extending the technology acceptance model to evaluate teachers' intention to use dynamic geometry software in geometry teaching [J].

Pittalis, Marios .

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, 2021, 52 (09) :1385-1404

[26] Geometry Software Cabri 3D in Teaching Stereometry [J].

Vallo, Dusan ;

Zahorska, Julia .

2016 IEEE 10TH INTERNATIONAL CONFERENCE ON APPLICATION OF INFORMATION AND COMMUNICATION TECHNOLOGIES (AICT), 2016, :739-742

[27] Students" conceptions of congruency through the use of dynamic geometry software [J].

González G. ;

Herbst P.G. .

Int J Compur Math Learn, 2009, 2 (153-182) :153-182

[28] Visually Dynamic Presentation of Proofs in Plane Geometry Part 1. Basic Features and the Manual Input Method [J].

Ye, Zheng ;

Chou, Shang-Ching ;

Gao, Xiao-Shan .

JOURNAL OF AUTOMATED REASONING, 2010, 45 (03) :213-241

[29] DYNAMIC GEOMETRY SOFTWARE: THE TEACHER'S ROLE IN FACILITATING INSTRUMENTAL GENESIS [J].

Bretscher, Nicola .

CERME 6 - PROCEEDINGS OF THE 6TH CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION, 2010, :1340-1348

[30] Reduced GUI for an interactive geometry software: Does it affect students' performance? [J].

Borges, Simone S. ;

Reis, Helena Macedo ;

Marques, Leonardo B. ;

Durelli, Vinicius H. S. ;

Bittencourt, Ig Ibert ;

Jaques, Patricia A. ;

Isotani, Seiji .

COMPUTERS IN HUMAN BEHAVIOR, 2016, 54 :124-133

← 1 2 3 4 5 →