HISTORICAL AND EDUCATIONAL ASPECTS OF DISCOVERIES AND INVENTIONS THAT REVOLUTIONIZED MANKIND

This article presents discoveries and inventions from different periods of mankind, which played an important role in social and technological evolution. Thus, from the period of the Ancient World (prehistory - 400 AD), we present: the appearance of stone tools (which occurred in East Africa and belongs to the first hominids); pottery (appeared in 10500 BC); the development of metallurgy (began in the Middle East, around 6500 BC); the invention of the ox-drawn plow (which occurred around 4000 BC); the construction of the first pyramid in Egypt (2600 BC); the development of iron processing (as part of the development of metallurgy, it occurred around 1400 BC); modernization of papermaking technology (attributed to Tsai Lun, China, around 105 AD); Another historical period that we analyzed in terms of discoveries and innovations that revolutionized humanity was the Middle Ages (400 - 1500). Thus, from this period we presented the following discoveries and inventions: the discovery of the number zero (occurred in 520 and belongs to Indian mathematicians); woodcut printing (appeared in sixth century China); the first printed newspaper (year 700); the development of algebra (it belongs to the Greek mathematician Diophantos, 3rd century AD); gunpowder (it was discovered around 850); the establishment of the University of Bologna (made in 1088); The last period approached was the current one. From this period we presented the following discoveries: magnetism - a new form of electricity; devices controlled only by hand gestures.

The Effect of Phi on the Perception of Attractiveness

The ratio Phi, equal to approximately 1.618, is an observable phenomenon that Greek mathematician Euclid defined this relationship as a line in two parts, in which the ratio of the longer part to the shorter part is equal to the ratio of the total length over the longer part. The ancient Greeks thought of Phi as a mathematical representation of physical beauty. Although many studies have shown a correlation between Phi and perceived attractiveness, other studies have displayed no/very weak, correlation. The question, “Does the expression of Phi play a significant role in the attractiveness of a face?” was investigated. It was hypothesized that if the features of a face closely fit the proportions of Phi, then survey respondents will give that face a higher attractiveness rating than a face whose features do not. Landmark localization data was calculated for images of 14 different faces. Individual and average facial ratios were calculated for each photograph, and a survey was conducted in which 100 participants were asked to rate the attractiveness of each face on a scale of 1-10. The average attractiveness rating of each face was then compared to the variance/distance of its average facial ratio away from the numerical value of Phi. Based on the analysis of the data, faces with features whose proportions closely fit the ratio of Phi are perceived as more attractive than faces with features that do not. Faces with average facial ratios closer to Phi received higher average attractiveness ratings.

IS IT POSSIBLE TO SOLVE THE ANGLE TRISECTION PROBLEM WITH COMPASSSTRAIGHTEDGE CONSTRUCTION

If you pose the question given in the title of this note you will listen a negative answer. In the Google searcher you will receive about 6 million results. It means to find something new in the problem formulated by Greek mathematician is useless. This problem alongside with the circle squaring is considered as undecidable problem.

Art and Science Euclidean Geometry-The Five Axioms via Art

The major objective of this article is to demonstrate by artworks Euclid’s five axioms, which are the basis of his planar geometry. Euclid, a Greek mathematician and philosopher, lived between 325 BC and 265 BC where his image is demonstrated in (Figure 1). It was transplanted on an artwork of the Dutch painter Piet Mondrian (1872-1944) consisting of a grid of vertical and horizontal black lines which are the basis of Euclidean geometry.

LIVROS DIDÁTICOS DE MATEMÁTICA: O PONTO, A RETA E O PLANO DA GEOMETRIA EUCLIDIANA E A TRANSPOSIÇÃO DIDÁTICA

This study presents a discussion on the area of plane geometry or non-Euclidean geometry, having as focus the primitive ones of plane geometry: point, line and plane. As the name itself refers to this geometry is from the work of the Greek mathematician Euclid of Alexandria, whose work dates back to approximately 300 BC. As theoretical contribution was the theory of Didactic Transposition the French Yves Chevallard (1991), this theory refers briefly to the changes and transformations that you know suffers from your appearance in the scientific community to your entry in the living room class. A research on textbooks of mathematics 6th grade belonging to several times. On choice of textbooks of mathematics, were taken as the basis year of 1985, the date on which the creation of the National Textbook Program (PNLD) and the year of 1996 date of implementation of the new guidelines and Bases of Brazilian Education (LDB 9394/96). The textbooks of mathematics were chosen because they are one of the means used for the input of knowledge in the classroom. In this research paper was used qualitative research and documentation, the books were analyzed one by one, in order to understand how was the process of addressing the concepts of point, line and plane in math textbooks and the scientific community. The paper presents a theoretical discussion involving the textbooks, the PNLD and the work of Euclid-Elements.

Euclid. Optics

An annotated translation of Euclid’s Optics. The earliest systematic treatise by the famous Ancient Greek mathematician, which deals with the geometry of vision, is translated into Russian for the first time.

Eudoxus (c.390–c.340 BC)

Eudoxus of Cnidos was a Greek mathematician with wide-ranging philosophical and scientific interests. He was known in antiquity for his mathematical astronomy and his philosophical hedonism, and placed, if loosely, within the Pythagorean tradition. More recently, debate about the correspondence between mathematical models produced by astronomers and the physical motions of the astronomical bodies themselves has focused especially on Eudoxus, since he is generally regarded as the first to have used a mathematical model in astronomy.

Pythagoras Meets Paper Folding

One of the most well-known theorems in mathematics, the Pythagorean theorem and its proof are a standard part of the school mathematics curriculum. The theorem is named for Pythagoras, a Greek mathematician and philosopher, born around 570 BCE. More than 400 proofs of the theorem exist, and this number continues to grow (Maor 2007). A future American president, James Garfield, generated an original proof five years before being elected; another proof is credited to twelve-year-old Einstein.

Some Some properties of the certain \(P_t\)-sets

The problem of extendibility and characterization of \(P_t\)-sets is of big interest even though the problem is old, and it was started by Greek mathematician Diophantus. Let \(t\) be an integer. A set of \(m\) distinct positive integers \({a_1,a_2,\dots,a_m}\) is called a \(P_t\)-set if \(a_i a_j+t (1\leq i\leq j\leq m)\) is a perfect square whenever \(i\neq j\) In this paper, we will investigate several numerical \(P_k\)-sets and demonstrate that they cannot be widen. Also, we will determine some of their properties using reciprocity theorem.