This study aims to determine the response and potential effects of using a mathematics e-book on Pythagorean theorem material. The method used in development this ebook is ADDIE. research data was obtained through student questionnaires, learning outcomes test subjects were 15 grade VIII students SMP Negeri 3 Mesuji Raya, Kab. Ogan Komering Ilir, South Sumatra. Based results analysis, responses...

{3, 4, 5} is perhaps the most famous Pythagorean Triple with interest in such triples dating back many thousands of years to the ancient people of Mesopotamia. In this article, we shall consider such triples, with the restriction that the elements of these triples must not have any common factors they are Primitive Pythagorean Triples (PPTs). In particular, we shall consider the question of how...

Given a right triangle and two inscribed squares, we show that the reciprocals of the hypotenuse and the sides of the squares satisfy an interesting Pythagorean equality. This gives new ways to obtain rational (integer) right triangles from a given one. 1. Harmonic and Symphonic Squares Consider an arbitrary triangle with altitude α corresponding to base β (see Figure 1a). Assuming that the bas...

We formalized some basic properties of the Fibonacci numbers using definitions and lemmas from [7] and [23], e.g. Cassini’s and Catalan’s identities. We also showed the connections between Fibonacci numbers and Pythagorean triples as defined in [31]. The main result of this article is a proof of Carmichael’s Theorem on prime divisors of prime-generated Fibonacci numbers. According to it, if we ...

Given a right triangle and two inscribed squares, we show that the reciprocals of the hypotenuse and the sides of the squares satisfy an interesting Pythagorean equality. This gives new ways to obtain rational (integer) right triangles from a given one. 1. Harmonic and Symphonic Squares Consider an arbitrary triangle with altitude α corresponding to base β (see Figure 1a). Assuming that the bas...

This study aimed to develop STEM-based Mathematics learning devices equipped with worksheets. Devices developed based on STEM can make it easier for students follow the process of subject that are clear instructions in working all materials and assignments will be accepted by students. From results data analysis testing 30 class VIII at SMP Negeri 1 Torjun, Sampang Regency, was found this resea...

We prove ten necessary and sufficient conditions for a convex quadrilateral to have perpendicular diagonals. One of these is a quite new eight point circle theorem and three of them are metric conditions concerning the nonoverlapping triangles formed by the diagonals. 1. A well known characterization An orthodiagonal quadrilateral is a convex quadrilateral with perpendicular diagonals. The most...

In this paper we present a short but important summary of Pythagorean fuzzy sets. Especially we discuss several basic and important definitions of Pythagorean fuzzy sets, several operations on Pythagorean fuzzy sets, several algebraic laws of Pythagorean fuzzy sets. In the last we also present the concept of modal operators and normalization on Pythagorean fuzzy sets.