Pythagoras Research Articles

Creative Chronography in Early Christianity: John Malalas on the Deaths of King Cyrus of Persia

Abstract In this article, I use John Malalas’ account of Cyrus’ two deaths – which he claimed was based on Pythagoras of Samos and Julius Africanus – as a case study for historiographical creativity in early Christian chronography. First, I detect that one of Cyrus’ deaths is calqued on Xerxes’ death in the Greek historian, Ctesias of Cnidus, and thus an original interpretation of the event. Second, I place this death story in the greater context of Malalas’ account, showing the great extent to which Malalas, or his source, has rewritten the story of Cyrus. Third, I test the death story’s attribution to Julius Africanus, which I argue is false, based on the high level of chronographic accuracy required for Africanus’ Chronographiae. Fourth and finally, I examine how Malalas was using Africanus’ authority to authenticate the dubious death story of Cyrus.

Effects of a videogame in math performance and anxiety in primary school

The present paper describes the design and evaluation of a videogame developed to support math education and overcome math anxiety (MA) at the primary school level. The game narrative is based on the history of math. The player travels back on time and meets on-player characters such as Pythagoras of Samos and Ada Lovelace, learning about how math was used during their times. The player is invited to play a minigame where the concepts shared by the characters are used as a strategy to win. The game’s evaluation consisted of a pre and post-testing study that measured students’ math performance and MA levels. The experiment also included a group interview to collect students’ perceptions about the game. The experiment lasted five weeks, and 88 students from three primary schools played the game on weekly sessions 45-60 minutes long. Statistical analysis suggested the game significantly improves students’ math performance. However, the results indicated that female students from one of the classrooms had higher MA levels after playing the game. In addition, qualitative data shows students had a high level of engagement with the gameplay.

Philosophical models of cosmos of Pythagoras and Philolaus: from Antiquity until the beginning of Modern Age

This article determines the fundamental principles of the models of the Cosmos of Pythagoras of Samos (c. 570 – 500 BC) and Philolaus of Croton (c. 470 – c. 388 BC). The perception of Cosmos as “beauty” and “harmony” – one of the basic characteristics of Pythagorean approach towards cognition of the world; it “interweaves” with the rational perception of reality. The harmony of beauty is transformed into the harmony of numerical relations. The achievements of Pythagoreans, subsequently become one of the foundations of Plato's astronomical texts, who describes cosmology as exact scientific discipline. Nicolaus Copernicus resorts to Philolaus as his major predecessor. This article is first to analyze the symbolic elements of Philolaus’ model of Cosmos from the perspective of modern scientific knowledge. Based on the conducted analysis, the author advances a hypothesis on the noematic nature of the elements of Philolaus’ model of Cosmos, as well as indicates the significance of transposing the methods of practical geometry onto the theoretical fields of “celestial” space, independent from the direct measurements. The article describes the key principles of the model of the universe of Pythagoras of Samos and Philolaus of Croton; discusses reconstruction of Philolaus’ model of Cosmos by Ivan Nikolaevich Veselovsky and Sergey Viktorovich Zhitomirsky. Analysis is conducted on the continuity of the principles of the models of Cosmos of Philolaus and Nicolaus Copernicus.

Pythagoras’ LegacyEdited by Marcel Danesi

Pythagoras’ LegacyEdited by Marcel Danesi

Maor, Eli: Music by the Numbers. From Pythagoras to Schoenberg

Maor, Eli: Music by the Numbers. From Pythagoras to Schoenberg

Everything Flows: Continuous Micro-Flow for Pharmaceutical Production

Abstract The pre-Socratic philosophers made the first honest attempt, at least in the western world, to describe natural phenomena in a rudimentary scientific manner and to exploit those for technological application [1]. Pythagoras of Samos (570–495 BC) was an Ionian Greek philosopher and the first to actually call himself a “philosopher”. He was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, and the sphericity of the Earth. The Pythagorean triple is also well-known. Heraclitus of Ephesus (535–475 BC) was famous for his insistence on ever-present change as the fundamental essence of the universe, as stated in the famous saying “panta rhei” —everything flows.

Jubal, Pythagoras and the Myth of the Origin of Music - With some remarks concerning the illumination of Pit (It. 568)

At the end of the fourteenth century the iconography of Music shows a complex morphology based on the myth of the first founding father of the musical art. Its most sophisticated image appears in the opening illumination of Pit (Paris, Bibl. Nationale, It. 568), one of the most important manuscripts of the Italian Ars Nova. After reviewing the existing bibliography, the first part of the article traces the cultural context that produced this illumination. The second part reconstructs the whole history of the myth of the origin of music, its biblical tradition (Jubal), its pagan equivalent (Pythagoras), their association with the myth of translatio studii (the pillars of knowledge), and its syncretic form adopted from the twelfth century onward. The iconographic model was conceived in fourteenth-century Italy, and the illumination of Pit is its most complete form; it was later assimilated into the iconography of Saint Cecilia. The reconstruction of this stratification of myths aims to clarify how different musical traditions crossed each other, and at the same time proposes an earlier dating for the illumination of Pit (late fourteenth century) in connection with Silvestro dei Gherarducci’s Florentine workshop.

Greek Medicine Practice at Ancient Rome: The Physician Molecularist Asclepiades.

Background: In the pre-Hellenistic period, the concept of medicine was not well-defined. Usually, a disease was considered as a divine punishment and its treatment was devolved to the priests who asked for healing from the divinities. The only job that could be compared to medical practice was a kind of itinerant medicine, derived from the Egyptian therapeutic tradition based only on practical experience and performed by people that knew a number of remedies, mostly vegetable, but without any theoretical bases about the possible mechanisms of action. Opinions about the human nature (naturalistic thinking) and the origin of the illness and heal were the basis of Greek medicine practiced by ancient priests of Asclepius. However, with the evolution of the thought for the continuous research of “κόσμος” (world) knowledge, philosophy woulld become an integral part of medicine and its evolution. This close relationship between philosophy and medicine is confirmed by the Greek physician Galen in the era of the Roman Empire. Methods: Philosophical thought looked for world knowledge starting from mathematics, physics, astronomy, chemistry, medicine, psychology, metaphysics, sociology, and ethics. We must keep in mind that, according to the ancient people, the physicians could not heal the patients without the aid of a “divine God” until medicine, thanks to the Hippocratic practice, became more independent from the supernatural, and contemporary, ethical, and professional. Many physicians were philosophers, as confirmed by their views of life, such as Hippocrates of Cos, Aristotle (hailed as the father of comparative anatomy and physiology), Pythagoras of Samos, Alcmaeon of Croton, Empedocles, Praxagoras, Erasistratus, Galen, and others, including Asclepiades of Bithynia (atomists affinity). Asclepiades, a Greek physician born in Prusa, studied in Athens and Alexandria. His thought was influenced by Democritus’ theories, refusing extensively the Hippocratic ideas that diseases are a result of mood imbalance. Results: Differing from the current Hippocratic idea, only in extreme cases he prescribed medications and bloodletting, two of the most-used therapies of that time. He usually prescribed therapies based on the Epicurean thought, then consisting of walks and music, massages, and thermal baths. He anticipated the modern idea of the body consisting of atoms, and believed that between the atoms exist empty spaces called pores. As the founder of the so called Methodist School, he was the first to divide acute and chronic diseases, and thought that body weakness was dependent on the excessive width of the pores, while their excessive shrinkage determines fever. According to his student Caelius Aurelianus he was the first to adopt tracheotomy as an emergency therapy for diphtheria. Conclusions: Although it is very difficult to reconstruct the theories of Asclepiades of Bithynia because of the lack of original texts, this paper attempts to focus his role and his thought in affirming the Greek medical practice in ancient Rome and to highlight his modernity.

Un nuevo fragmento de Pitágoras

<p class='p1'>D.S. XVIII.1.1 contiene una cita de Pitágoras que no ha sido tomada en cuenta como fragmento, a pesar de que no puede haber dudas de que el autor se basaba en una obra considerada auténtica.</p>

Pythagoras on the rocks: A proof with bricks

In this short paper a practical and simple proof of the Pythagorean theorem is proposed. It uses colourful interlocking plastic bricks with two shapes: a cube that measures two centimeters on each side and a right prism where the base is a right-angled isosceles triangle and the two equal rectangular faces are the same as those of the cubic brick. The proof is designed for primary school children (but also for preschool children) and begins by telling the legend of Pythagoras, who discovered his theorem by looking at the floor tile pattern of Polycrates’ palace. This proof takes into account only right-angled isosceles triangle but it is possible to show the validity of Pythagorean theorem for all right-angled triangles by building a simple proof by rearrangement. Pitagora on the rocks. Una dimostrazione con i mattoncini In questo breve contributo viene proposta una semplice dimostrazione pratica del teorema di Pitagora, utilizzando mattoncini a incastro di plastica colorata di due forme: un cubo di due centimetri per lato e un prisma retto la cui base e un triangolo isoscele rettangolo e nel quale le due facce equivalenti sono uguali a quelle del mattoncino cubico. La dimostrazione e rivolta a bambini della scuola primaria (ma, eventualmente, anche in eta prescolare) e prende le mosse dalla leggenda secondo la quale Pitagora avrebbe scoperto il suo teorema mentre stava osservando il pavimento piastrellato del palazzo di Policrate, tiranno di Samo. Da questa dimostrazione – che prende in considerazione solo triangoli rettangoli isosceli – e poi possibile passare a una dimostrazione del teorema di Pitagora per tutti i triangoli rettangoli.

Some Pioneers of Mathematics:Biographical Accounts for the General Audience

This book is a compilation of biographies of 22 mathematicians from Pythagoras to Harish-Chandra. These pieces have earlier appeared in Vigyan Prasar's Dream -2047, a monthly newsletter. Hence mathematical expressions have been kept to a minimum. Since each essay has been written to be complete in itself, there are some boxed relevant quotations as an introduction and a short list of references at the end of each of them.

Number Symbolism in the Vedas

Numbers became very sacred to all cultures since the time man started feeling the need to use numbers in daily life and started observing that the events related to nature/cosmos had a preference for certain numbers. Thus came a stage when mathematics started evolving along with philosophy. All this activity ultimately led to the evolution of the modern ‘numerology’ (science of numbers), the credit for which goes to Pythagoras. During this process, all cultures, independent of each other, had shown preference for certain numbers in their religious beliefs and activities. Similarly, in the Vedas too, one finds numbers such as 1, 3, 7 and 10 as the most used numbers; at least on a few hundred or perhaps even more than a thousand occasions to describe various events. {The other single digit numerals like 4 and 5 etc. are also preferred although to a lesser extent (Murthy, 2003)}. The symbolism associated with the single digit numerals was very well established in virtually all cultures, since counting began on the ten fingers.

Pythagoras's biggest disappointment

Pythagoras's biggest disappointment

Pythagoras plays his lyre

Pythagoras plays his lyre

Does Pythagoreanism Really Belong to Greek?

Pythagoras of Samos was the founder of the religious movement called Pythagoreanism and also well known Philosopher and mathematician. We have very little reliable information about Pythagoras from the secondary sources because he personally wrote nothing though hecould inspire legends. That is why Aristotle also often referred to the Pythagoreans but not to Pythagoras as such. Historically Pythagoras is being treated as the first mathematician, the first philosopher and the first metempsychosist. But there are certain doubts on the authorship of Pythagoreanism. Is it really proposed by Pythagoras? Some believes that he was not the author of Pythagoreanism because the Pythagorean principle was very much present in 10^th century BC in China and 9^th century BB in India. This paper examines the evidences and tries to analyze the authorship of Pythagoreanism.

A slowly converging sequence via Pythagoras

A slowly converging sequence via Pythagoras

Pythagoras by Integral

(2015). Pythagoras by Integral. The American Mathematical Monthly: Vol. 122, No. 8, pp. 792-792.

Review and evaluate the role of holy Figures in architecture

Abstract. Pythagoras and his followers believed that all aspects of the universe, the earth and sky are reflected in the numbers. AfllaTvn terms of numbers represent the harmony of the universe and of Aristotle, the number of the origin and essence of everything. In Greek philosophy the odd numbers and even numbers of males and females, and this means that the numbers have saxhorn in other words, it is assumed they have intelligence. Filolaes language that Pythagoras was a great student, who said that anything that can recognize the number, it may not be possible without the understanding or knowing something. Another discussion about the value of their belief in the auspicious or unlucky. Sacred and religious value in the numbers or at different times in different nations was different. Christians, for example, four and seven are considered sacred and the Babylonians and the Persians have preferred number sixty and sixty multiples. In this paper, the numbers and the sanctity of the buildings proposed to be studied. And the sanctity of the sacred numbers can be addressed. Zero, one, two, three, four, five, six, seven, eight, ten, and the number pi on a number of sacred buildings Zanbil ziggurat, respectively, Hegmataneh, Hanging Gardens of Babylon, the Mausoleum of Cyrus, Maya temples, set pyramids of Giza, the Kaaba, the shrine of Imam Khomeini, the building of the Palace of the Sun, thirty-three bridges in Isfahan, Imam Mosque in Isfahan, are examined. Four in the Kaaba and Zanbil ziggurat, referring to the four directions, integrity, discipline, wisdom. Seven in the Hanging Gardens of Babylon, the Mausoleum of Cyrus, referring to seven of the Koran, the Seven Fountains of Paradise, and Hell has seven floors.

The complex planetary synchronization structure of the solar system

The complex planetary synchronization structure of the solar system, which since Pythagoras of Samos (ca. 570-495 BC) is known as the music of the spheres, is briefly reviewed from the Renaissance up to contemporary research. Copernicus' heliocentric model from 1543 suggested that the planets of our solar system form a kind of mutually ordered and quasi-synchronized system. From 1596 to 1619 Kepler formulated preliminary mathematical relations of approximate commensurabilities among the planets, which were later reformulated in the Titius-Bode rule (1766-1772) that successfully predicted the orbital position of Ceres and Uranus. Following the discovery of the ~11 yr sunspot cycle, in 1859 Wolf suggested that the observed solar variability could be approximately synchronized with the orbital movements of Venus, Earth, Jupiter and Saturn. Modern research have further confirmed that: (1) the planetary orbital periods can be approximately deduced from a simple system of resonant frequencies; (2) the solar system oscillates with a specific set of gravitational frequencies, and many of them (e.g. within the range between 3 yr and 100 yr) can be approximately constructed as harmonics of a base period of ~178.38 yr; (3) solar and climate records are also characterized by planetary harmonics from the monthly to the millennia time scales. This short review concludes with an emphasis on the contribution of the author's research on the empirical evidences and physical modeling of both solar and climate variability based on astronomical harmonics. The general conclusion is that the solar system works as a resonator characterized by a specific harmonic planetary structure that synchronizes also the Sun's activity and the Earth's climate.

97.21 Some more on Estermann and Pythagoras

97.21 Some more on Estermann and Pythagoras