China 
Africa 
Explore chapters and articles related to this topic
Numbers and Elementary Mathematics
Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018
If the positive integers A, B, and C satisfy A2 + B2 = C2, then the triplet (A, B, C) is a Pythagorean triple. A right triangle can be constructed with sides of length A and B and a hypotenuse of C. There are infinitely many Pythagorean triples.
Middle school students’ reasoning with regards to parallelism and perpendicularity of line segments
Published in International Journal of Mathematical Education in Science and Technology, 2023
This study is also important in terms of didactical and mathematical aspects. Many students use a wide range of types of reasoning-from linguistic to nonlinguistic or visual in organizing their thoughts, representing examples, and solving problems in school mathematics (Rivera, 2011). Understanding different types of reasoning regarding geometric concepts is critical for mathematics teachers to develop ‘an understanding of how visual thinking works in conjunction with language-based reasoning’ (Gooding, 2006, p. 41). Hence, they develop appropriate didactical opportunities for their students who have different reasoning types. Besides, there is a double characterization of geometric concepts in nature (Van der Waerden, 1975, 1983). Understanding parallelism and perpendicularity is critical to highlight the connections between Algebra, Arithmetic and Geometry that have dominated mathematical thinking. For example, the properties of perpendicularity explain the reasons why slopes of perpendicular lines are negative reciprocals of each other algebraically (Rivera, 2011). Similarly, Pythagorean triangles have both geometric aspects like perpendicularity in a right-angled triangle and arithmetical aspects referred to as Pythagorean triple of numbers like (3,4,5). Namely, the Theorem of Pythagoras that middle school students learn the theorem at school utilized perpendicularity of sides in right-angled triangles (Van der Waerden, 1983).