Trójwymiarowe modele matematyczne na przykładzie obiektów ze zbiorów Muzeum Uniwersytetu Jagiellońskiego

This paper presents examples of mathematical models which have almost passed into oblivion, yet a few decades ago still played a significant role in the teaching of mathematics. In the late nineteenth century such devices started to be produced on a large scale for schools and universities. The Jagiellonian University Museum has three such models in perfect condition in its collections.W artykule podajemy przykłady modeli matematycznych, obecnie niemal zapomnianych, które jeszcze kilkadziesiąt lat temu odgrywały wielką rolę w dydaktyce matematyki. Z końcem XIX wieku powstała prężna produkcja tych modeli na użytek szkół i uczelni. W Muzeum UJ zachowały się w doskonałym stanie trzy takie modele. Three-dimensional mathematical models illustrated by objects from the collections of the Jagiellonian University Museum Abstract This paper presents examples of mathematical models which have almost passed into oblivion, yet a few decades ago still played a significant role in the teaching of mathematics. In the late nineteenth century such devices started to be produced on a large scale for schools and universities. The Jagiellonian University Museum has three such models in perfect condition in its collections

The divergent histories of Bose-Einstein statistics and the forgotten achievements of Władysław Natanson (1864–1937)

This article investigates the forgotten achievements of Władysław Natanson (1864–1937) related to the creation of Bose-Einstein statistics. The introductory part of the article presents considerations regarding the methodology of history and the history of exact sciences, and then the divergent research perspectives that can be taken in the description of the history of Bose-Einstein statistics, as well as the author’s integrated approach to this issue, which eliminates the disadvantages of these divergent views. This integrated approach is then used to describe the achievements of Władysław Natanson related to the creation of Bose-Einstein statistics. These achievements are presented against the background and in the context of discussions which – relatively sporadically – took place among various groups of researchers: historians and philosophers of science, physicists, sociologists of scientific knowledge in the 20th and 21st centuries. These discussions have now been reordered here. They are followed by a presentation of the complete list of Natanson’s publications regarding the subject. Also shown is his strategy to quote reliably the bibliography with regard to the explanation of the distribution of blackbody radiation and related issues. Additionally, a list of scientists who knew Natanson’s publications has been supplemented in the article and the precursorship of Natanson’s achievements is explained. This is followed by a rebuttal of many erroneous or simplified statements about him and his achievements. The already well-known terminological conventions have been recalled: “Bose statistics” and “Bose-Einstein statistics”, as well as recently introduced: “Planck-Bose statistics” (1984), “Natanson’s statistics” (1997)”, “Natanson-Bose-Einstein statistics” (2005), “Planck-Natanson-Bose-Einstein statistics” (2011), and “Natanson statistics” (2013). New terminological conventions have been introduced: “Boltzmann-Planck-Natanson statistics” and “Boltzmann-Planck-Natanson-Bose-Einstein statistics”. A side effect of this research is a discovery that Robert K. Merton – the author of the label ‘Matthew effect’ – chose the name of the effect using erroneous premises and the effect should therefore be named after its actual discoverer. The article is accompanied by four appendixes: the first presents reflections on the methodology of historiography and historiography of exact sciences, the second – a commentary on the use of the terms: “Bose statistics”, “Bose-Einstein statistics”, “Einstein-Bose statistics” and “Planck-Bose statistics”, the third – a very important letter by Max Planck to  Władysław Natanson (of 25 January 1913), and the fourth – the excerpts of two letters from Sommerfeld to Rubinowicz (of 1 October 1919 and 1 November 1919).This article investigates the forgotten achievements of Władysław Natanson (1864–1937) related to the creation of Bose-Einstein statistics. The introductory part of the article presents considerations regarding the methodology of history and the history of exact sciences, and then the divergent research perspectives that can be taken in the description of the history of Bose-Einstein statistics, as well as the author’s integrated approach to this issue, which eliminates the disadvantages of these divergent views. This integrated approach is then used to describe the achievements of Władysław Natanson related to the creation of Bose-Einstein statistics. These achievements are presented against the background and in the context of discussions which – relatively sporadically – took place among various groups of researchers: historians and philosophers of science, physicists, sociologists of scientific knowledge in the 20th and 21st centuries. These discussions have now been reordered here. They are followed by a presentation of the complete list of Natanson’s publications regarding the subject. Also shown is his strategy to quote reliably the bibliography with regard to the explanation of the distribution of blackbody radiation and related issues. Additionally, a list of scientists who knew Natanson’s publications has been supplemented in the article and the precursorship of Natanson’s achievements is explained. This is followed by a rebuttal of many erroneous or simplified statements about him and his achievements. The already well-known terminological conventions have been recalled: “Bose statistics” and “Bose-Einstein statistics”, as well as recently introduced: “Planck-Bose statistics” (1984), “Natanson’s statistics” (1997)”, “Natanson-Bose-Einstein statistics” (2005), “Planck-Natanson-Bose-Einstein statistics” (2011), and “Natanson statistics” (2013). New terminological conventions have been introduced: “Boltzmann-Planck-Natanson statistics” and “Boltzmann-Planck-Natanson-Bose-Einstein statistics”. A side effect of this research is a discovery that Robert K. Merton – the author of the label ‘Matthew effect’ – chose the name of the effect using erroneous premises and the effect should therefore be named after its actual discoverer. The article is accompanied by four appendixes: the first presents reflections on the methodology of historiography and historiography of exact sciences, the second – a commentary on the use of the terms: “Bose statistics”, “Bose-Einstein statistics”, “Einstein-Bose statistics” and “Planck-Bose statistics”, the third – a very important letter by Max Planck to  Władysław Natanson (of 25 January 1913), and the fourth – the excerpts of two letters from Sommerfeld to Rubinowicz (of 1 October 1919 and 1 November 1919).   Rozbieżne historie statystyki Bosego-Einsteina i zapomniane osiągnięcia Władysława Natansona (1864–1937) Abstrakt Artykuł bada zapomniane osiągnięcia Władysława Natansona (1864–1937) związane z powstaniem statystyki Bosego-Einsteina. W części wstępnej artykułuwskazano rozbieżne perspektywy badawcze, jakie przyjmowano w opisie historii statystyki Bosego-Einsteina, a także autorskie zintegrowane ujęcie tego zagadnienia, które eliminuje wady tych rozbieżnych perspektyw. Wspomniane zintegrowane ujęcie zastosowano następnie do opisania osiągnięć Władysława Natansona (1864–1937), związanych z powstaniem statystyki Bosego-Einsteina. Dokonania Natansona przedstawiono na tle i w kontekście dyskusji, jakie toczyły się (stosunkowo sporadycznie) wśród różnych grup badaczy: historyków i filozofów nauki, fizyków, socjologów wiedzy naukowej w XX i XXI w. Dyskusje uporządkowano oraz przedstawiono kompletną listę publikacji Natansona dotyczących omawianego zagadnienia. Wskazano także strategię rzetelnego cytowania przez Natansona bibliografii dotyczącej wyjaśnienia rozkładu promieniowania ciała doskonale czarnego i pokrewnych zagadnień; uzupełniono listę naukowców, którzy znali publikacje Natansona; skorygowano wiele błędnych lub uproszczonych stwierdzeń na temat Natansona i znaczenia jego publikacji, wyjaśniono kwestię prekursorstwa jego osiągnięć etc. Przypomniano już znane konwencje terminologiczne: „statystyka Bosego” i „statystyka Bosego-Einsteina”, jak również niedawno wprowadzone: „statystyka Plancka-Bosego” (1984), „statystyka Natansona” (1997, 2013), „statystyka Natansona-Bosego-Einsteina” (2005) oraz „statystyka Plancka-Natansona-Bosego-Einsteina” (2011). Wprowadzono nowe konwencje terminologiczne: „statystyka Boltzmanna-Plancka-Natansona” i „statystyka Boltzmanna-Plancka-Natansona-Bosego-Einsteina”. Skutkiem pobocznym tych badań jest odkrycie, iż socjolog Robert K. Merton – autor określenia „efekt św. Mateusza” – wybrał tę nazwę, posługując się błędnymi przesłankami i dlatego należy nazywać ten efekt nazwiskiem jego faktycznego odkrywcy. Do artykułu dołączone są cztery dodatki: pierwszy – przedstawia rozważania z zakresu metodologii historii i historii nauk ścisłych, drugi – komentarz dotyczący użycia terminów: „statystyka Bosego”, „statystyka Bosego-Einsteina”, „statytyska Einsteina-Bosego” oraz „statystyka Plancka-Bosego, trzeci – bardzo ważny list Maxa Plancka do Władysława Natansona z 25 stycznia 1913 r, a czwarty – fragmenty dwóch listów Sommerfelda do Rubinowicza z 1 października 1919 i 1 listopada 1919

Raising public awareness of mathematics

This book arose from the presentations given at the international workshop held in Óbidos, 26–29 September 2010, as a result of a joint initiative of the Centro Internacional de Matemática and the Raising Public Awareness (RPA) committee of the European Mathematical Society (EMS). The objective was to provide a forum for general reflection with an international mix of experts on building the image of mathematics, ten years after the World Mathematical Year 2000 (WMY 2000). Óbidos, a charming town situated one hour by car to the north of Lisbon, Portugal, was also the site of the re-creation in the year 2000 of the international mathematics exhibition “Beyond the Third Dimension” (http://alem3d.obidos.org/en/) and a meeting of the EMS WMY2000 Committee. The opening of the workshop was also a public “mathematical afternoon” organised by the Portuguese Mathematical Society (SPM) in cooperation with the town of Óbidos. At this event mathematical films and lectures to the general public were presented. The first lecture was given by H. Leitão, from the University of Lisbon, on mathematics in the “Age of Discoveries”, and the second one by G.-M. Greuel, the current president of ERCOM (the EMS committee of the European Research Centres on Mathematics), on the topic “Mathematics between Research, Application and Communication”, which text is included in this book.info:eu-repo/semantics/publishedVersio

World Scientists’ Warning of a Climate Emergency

Scientists have a moral obligation to clearly warn humanity of any catastrophic threat and to “tell it like it is.” On the basis of this obligation and the graphical indicators presented below, we declare, with more than 11,000 scientist signatories from around the world, clearly and unequivocally that planet Earth is facing a climate emergency

Problem space of modern society: philosophical-communicative and pedagogical interpretations. Part I

This collective monograph offers the description of philosophical bases of definition of communicative competence and pedagogical conditions for the formation of communication skills. The authors of individual chapters have chosen such point of view for the topic which they considered as the most important and specific for their field of study using the methods of logical and semantic analysis of concepts, the method of reflection, textual reconstruction and comparative analysis. The theoretical and applied problems of modern society are investigated in the context of philosophical, communicative and pedagogical interpretations

The art and architecture of mathematics education: a study in metaphors

This chapter presents the summary of a talk given at the Eighth European Summer University, held in Oslo in 2018. It attempts to show how art, literature, and history, can paint images of mathematics that are not only useful but relevant to learners as they can support their personal development as well as their appreciation of mathematics as a discipline. To achieve this goal, several metaphors about and of mathematics are explored

Teaching/Learning Physics: Integrating Research into Practice

The GIREP-MPTL International conference on Teaching/Learning Physics: Integrating Research into Practice [GIREP-MPTL 2014] was held from 7 to 12 July 2014 at the University of Palermo, Italy. The conference has been organised by the Groupe International de Recherche sur l’Enseignement de la Physique [GIREP] and the Multimedia in Physics Teaching and Learning [MPTL] group and it has been sponsored by the International Commission on Physics Education [ICPE] – Commission 14 of the International Union for Pure and Applied Physics [IUPAP], the European Physical Society – Physics Education Division [EPS-PED], the Latin American Physics Education Network [LAPEN] and the Società Italiana di Fisica [SIF]. The theme of the conference, Teaching/Learning Physics: Integrating Research into Practice, underlines aspects of great relevance in contemporary science education. In fact, during the last few years, evidence based Physics Education Research provided results concerning the ways and strategies to improve student conceptual understanding, interest in Physics, epistemological awareness and insights for the construction of a scientific citizenship. However, Physics teaching practice seems resistant to adopting adapting these findings to their own situation and new research based curricula find difficulty in affirming and spread, both at school and university levels. The conference offered an opportunity for in-depth discussions of this apparently wide-spread tension in order to find ways to do better. The purpose of the GIREP-MPTL 2014 was to bring together people working in physics education research and in physics education at schools from all over the world to allow them to share research results and exchange their experience. About 300 teachers, educators, and researchers, from all continents and 45 countries have attended the Conference contributing with 177 oral presentations, 15 workshops, 11 symposia, and around 60 poster presentations, together with 11 keynote addresses (general talks). After the conference, 147 papers have been submitted for the GIREP-MPTL 2014 International Conference proceedings. Each paper has been reviewed by at least two reviewers, from countries that are different to those of the authors and on the basis of criteria described on the Conference web site. Papers were subsequently revised by authors according to reviewers’ comments and the accepted papers are reported in this book, divided in 8 Sections on the basis of the keywords suggested by authors. The other book section (actually, the first one) contains the papers that six of the keynote talkers sent for publication in this Proceedings Book. We would like to thank all the authors that contributed with their papers to the realization of this book and all the referees that with their criticism helped authors to improve the quality of the papers