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Apollonea.com project: integrating geometry and collaboration in education
Full text linkThis article presents the Apollonea.com project, which aims to make the solutions to Apollonius’ problems accessible to students and teachers through modern technology. The web platform contains more than 150 interactive constructions created by students using GeoGebra, allowing for dynamic manipulation and visualization of solutions to various variants of Apollonius’ problems. The project combines classical geometric problems with an interdisciplinary approach, teamwork, and the use of modern technology. The article describes the process of developing the Apollonea.com website, the use of GeoGebra in the project, the structure and functions of the website, and its educational benefits in enhancing students’ geometric skills. The project demonstrates how traditional mathematics education can be connected with modern ICT tools.
Subject Classification: 97U50, 97G40, 51M04, 68U0
Termékenységi trendek vizsgálata Magyarországon és Svédországban
Full text linkThe aim of this study is to conduct a comparative analysis of fertility trends in Hungary and Sweden by examining demographic indicators (1980–2022) and the temporal evolution of structural factors. The first part of the study analyzes changes in fertility patterns based on demographic indicators. This is followed by an empirical investigation relying on trend analysis of time series data from 1995 to 2022, using international statistical databases. The trend analysis focuses on the temporal development of total fertility rates (TFR), as well as female employment rates, educational attainment, gender wage gaps, and the share of family benefits relative to GDP. The findings indicate that fertility trends often coincided with economic, social, and institutional changes. In Hungary, the TFR began to rise following its 2011 low point, while in Sweden fertility has remained relatively stable, supported by the expansion of in-kind family benefits and high female employment rates, which facilitate the reconciliation of childbearing and participation in the labour market. The analysis highlights that the impact of family policy measures is strongly conditioned by the broader structural environment.A tanulmány célja Magyarország és Svédország termékenységi trendjeinek összehasonlító elemzése demográfiai mutatók (1980-2022) és strukturális tényezők időbeli alakulásának vizsgálatával. A tanulmány elsőként demográfiai indikátorok alapján elemzi a termékenységi mintázatok változását. Az ezt követő empirikus vizsgálat 1995–2022 közötti idősorok trendelemzésén alapul, nemzetközi adatbázisokat felhasználva. A trendelemzés a teljes termékenységi arányszám, valamint a női foglalkoztatottság, iskolai végzettség, nemek közötti bérkülönbség és családtámogatások GDP-arányos szintjének időbeli változását vizsgálja. Az eredmények szerint a termékenység alakulása több esetben együtt változott gazdasági, társadalmi és intézményi tényezőkkel. Magyarországon a TTA 2011-es mélypont után emelkedni kezdett, Svédországban pedig a termékenység viszonylag stabil, ahol a természetbeni családtámogatások növekedése és a magas női foglalkoztatottság segítik a gyermekvállalás és munkavégzés összeegyeztetését. A vizsgálat rávilágít arra, hogy a családpolitikai intézkedések hatását a strukturális környezet nagymértékben meghatározza
Marktstädte in Ungarn an der Grenze zwischen Mittelalter und Früher Neuzeit: Die ungarischen Marktstädte
No full textIm Spätmittelalter gab es in Ungarn grundsätzlich zwei Haupttypen der Markt- und Ackerbürgerstädte: die Tieflandstädte mit großer Viehzucht (und großen dazugehörenden Grundstücken), und die Weinbaustädte in den Bergen. Die Wende des 15. und 16. Jahrhunderts, bzw. die Schlacht bei Mohács im Jahr 1526, als die Osmanen das mittelalterliche ungarische Königreich militärisch und politisch zerschlugen, bedeuteten für die meisten dieser Städte, insbesondere für diejenigen, die Viehzucht betrieben, nur wenige Veränderungen. Das 16. Jahrhundert verstärkte ihre bisherige Entwicklungsrichtung noch weiter. Das Bild war differenzierter als bei den Weinproduzierenden Marktstädten: Syrmien (ein hügeliges Gebiet um Fruska Gora, heute in Serbien), das wichtigste Weinbaugebiet des mittelalterlichen Ungarns, wurde zu einem Grenzgebiet des Türkischen Reiches, und wurde so das Ziel türkischer Einfälle. Aus dieser Gegend zogen die meisten Winzer und Weinproduzenten ins Landesinnere, was hier zum Niedergang der Weinproduktion und der Weinbaustädte führte. Viele Menschen aus Syrmien zogen in die weitere Umgebung der Stadt Tokaj, die sich dadurch ab dem 16. Jahrhundert schnell entwickelte und dort produzierten Weine sogar die Weine aus Syrmien übertrafen.In the late Middle Ages, two principal types of market and agrarian towns can be distinguished in the Kingdom of Hungary: on the one hand, the lowland settlements, characterized by extensive animal husbandry and the possession of large tracts of land; on the other, the viticultural towns situated in hilly regions. The transition from the fifteenth to the sixteenth century – particularly the watershed moment of the Battle of Mohács in 1526, when the Ottoman advance brought about the military and political disintegration of the medieval Hungarian kingdom – had comparatively little immediate impact on most of these urban centers, especially those oriented toward pastoral production. Indeed, the sixteenth century largely reinforced their established developmental trajectory.
The pattern proved more complex in the case of viticultural market towns. Syrmia (the hilly region around Fruška Gora, in present-day Serbia), which constituted the most important wine-producing area of medieval Hungary, was transformed into a frontier zone of the Ottoman Empire and thereby exposed to recurrent incursions. The ensuing insecurity prompted a significant outmigration of vintners and wine producers from the region into the interior of the kingdom. As a consequence, viticulture in Syrmia declined, while other centers, most notably the Tokaj region, experienced rapid expansion. From the sixteenth century onwards, Tokaj emerged as a leading center of Hungarian wine production, ultimately eclipsing Syrmia in both productivity and reputation
Diplomacy at the Time of the Breakthrough. Correspondence of King John I Albrecht (Jan Olbracht) with the Grand Masters of the Teutonic Order
No full textThis article discusses letters written by King John I Albert to the Grand Masters of the Teutonic Order and other recipients, preserved in the archives of the Teutonic Order. The first of these was sent by the prince, who sought the support of Grand Master Johann von Tiefen during the election of 1492. Most of the correspondence concerns the king’s relations with Tiefen’s successor, Duke Frederick of Saxony. The first problem was Frederick’s refusal to swear an oath of allegiance, which he consistently refused to do. The second important issue was the fight against the Turks, with the king demanding help from the Teutonic Order. The Grand Master’s brother, Duke Georg of Saxony, whose wife was the Polish king’s sister Barbara, was also involved in Polish diplomatic activities. Thirteen letters from the short reign of John Albrecht (1492–1501) were discussed, including their subject matter, form, and accompanying seals
Under the Shadow of Vendetta: Decision-making Situations in the Story of Anselmo and Angelica
No full textThe factional struggles for position and influence were truly defining historical events in medieval Italian towns for decades. Families such as the Uberti, Donati and Cerchi of Florence or the Bentivogli and Marescotti of Bologna fought each other. The background and the cause of these struggles were recorded in the thirteenth–fifteenth-century Italian narrative sources. The chapters on revenge (vendetta) and other acts of violence are very important and valuable parts of the mentality of that age. The descriptions, which inform us about the resolution of conflicts and reconciliation provide essential information about the authors’ views of the factional conflicts.
In medieval Siena, the Salimbeni were one of the most powerful families. During the fourteenth century they fought against the Tolomei, the Malavolti and the Piccolomini factions. In the meantime, the Senese popolo excluded these clans – the so called casati – from the main officies to insure the pax urbana. In my presentation, I will examine the fight between the Salimbeni and Montanini families as well as the turning-points in the story of the reconciliation of this struggle. According to the Annali sansei, a bloody, factional conflict broke out between these two influential families in 1394. This chronicle describes that the struggle led to many casualties, leaving only one young man, Carlo, in the male line of the Montanini family. Instead of continuing to fight, the two sides made peace the following year. According to the fifteenth century author of the chronicle of Siena, the solution to the conflict was a marriage between the members of the opposing families, Anselmo Salimbeni and Carlo’s sister Angelica Montanini. Anselmo’s choice between vendetta and peace symbolised a turning point in the city’s politics. In my lecture, I will examine how this case might be interpreted by analysing its particular features
The Papal State and the Birth of the Modern Fortress: Innovation in Military Construction between the Late Middle Ages and the Early Modern Period
No full textTransformations from the fifteenth to the sixteenth centuries, particularly focusing on the emergence of the angular bastion trace. It argues that this “modern style” of fortification was not merely a response to advances in weaponry but a generative force that reshaped political communities, especially evident in the Papal States. Drawing on Paolo Prodi’s seminal work, the study highlights how these military innovations contributed to the Papal States becoming a prototype of the early modern State. The analysis traces the evolution of papal fortification policy from the mid-fourteenth century, examining initiatives under Cardinal Albornoz and subsequent popes, including significant projects like Rocca Pia and Matteo Nuti’s designs. The “Borgia moment” under Alexander VI is emphasized as a period of unprecedented quantitative and qualitative innovation, characterized by a centralized defensive network and cutting-edge architectural advancements, notably at Nettuno. The essay then details the continuity of this strategic vision under Julius II and Clement VII, despite periods of conflict, illustrating the ongoing integration of military infrastructure with broader state-building objectives. Finally, it notes that this intense period of design and construction preceded the formal codification of fortification treatises, underscoring a unique channel of knowledge transmission
Wirtschaftliche Ungleichheit oder ausgewogene Beziehungen. Das Königreich Ungarn im europäischen Wirtschaftssystem
No full textThe economic division of labour in Europe from the second half of the fifteenth century onwards is clearly visible. Western European historiography focuses primarily on the Atlantic region and Western Europe in its portrayal of the globalising economic system, while Central Europe is very often treated as peripheral. However, this cannot be confirmed by the relevant historical sources. The regions of the Carpathian Basin participated in the continental economic cycle mainly with raw materials, live animals and semi-finished products. Nevertheless, at the beginning of the early modern period, Central Europe and the Hungarian regions were indispensable partners of the Western European regions rather than vulnerable markets.The period from the second half of the fifteenth century to the first half of the seventeenth century was the last period of (early) modern history in which a more or less balanced system of relations still connected the regions above mentioned. This does not, of course, contradict the part of the classic centre-periphery model that states that the regions of Western and Central Europe had different production profiles from the fifteenth century onwards. While the former had a clear advantage in craft production, the latter concentrated mainly on agricultural products and mining raw materials. Nevertheless, it should be emphasised that in the first half of the early modern period, every region was still able to participate in multilateral trade with numerous goods that other regions needed. None of the regions became the exclusive consumer market for the other. Mutual dependence can be demonstrated in almost all bilateral interregional relationships
TEHETSÉG AZONOSÍTÓ, KOMPLEX TELJESÍTMÉNYDIAGNOSZTIKAI PROTOKOLL A KOSÁRLABDÁZÁSBAN
Full text linkIf we want to gain a competitive advantage over our domestic and international competitors in continuous competition, the first task is to filter and select the sport or the given sport correctly. Later based on the current results of sports science, it is necessary to consistently, consciously, complete the complex, time-consuming process of talent management. Selection process requires a lot of patience and perseverance. The aim of talent identification is to select children in sports with specific skills that can be systematically transformed into practice.. It is necessary to measure complex, sport-specific components of performance. Researchers in a meta-analysis of talent identification protocols in team sports found that physical parameters such as height, body weight, body composition, and physiological capacities such as aerobic capacity, anaerobic strength, strength, coordination, and agility play a role. On the other hand, the quality of specific psychological-mental skills is also critical in identifying talents.
Ha a folyamatos versengésben versenyelőnyt akarunk szerezni a hazai és nemzetközi vetélytársainkkal szemben, akkor – stratégiai szinten mindenképpen – az első feladat a sportra, illetve az adott sportágra, később az adott posztra helyesen szűrni, kiválasztani, majd konzekvensen, tudatosan, tervszerűen, a sporttudomány eredményeit felhasználva végig vinni a tehetséggondozás hosszú, sok türelmet és kitartást igénylő folyamatát. A tehetség-azonosítás célja a sportban is azon gyermekek kiválasztása, akik az adott sportág eredményes űzéséhez szisztematikusan fejleszthető képességekkel rendelkeznek. Ennek érdekében komplex, a teljesítmény minden lehetséges, sportág specifikus összetevőit szükséges mérni. Kutatók a csapatsportok tehetségazonosító protokolljainak meta-analízise során arra jutottak, hogy fizikai paraméterek, mint magasság, testtömeg, testösszetétel, a fiziológiai kapacitás, mint aerob kapacitás, anaerob erő, erő, a motorikum oldalán a koordináció, és az agilitás játszik meghatározó szerepet. Ugyanakkor bizonyos pszichés mentális képességek megléte, a stressztűrő-képesség, a döntéshozó képesség megfelelő színvonala mind fontos tényezők egy-egy sporttehetség azonosításakor
Pathogenic fungal pathogens and diseases: a mini review of effects on maize production
Full text linkMaize, the most important cereal globally in terms of nutrition and income, is highly susceptible to biotic stresses caused by various pathogens, including fungi, bacteria, viruses, nematodes, and parasitic plants. This review gives an account of the epidemiology, diversity, and effect of fungal diseases on maize, with a focus on common pathogens, namely Ustilago sp. and Fusarium sp. Additionally, the review explores the major contributors to the pathogen and disease development, namely: soil quality, temperature, and humidity. Clarity is made herein about the damages and effects on maize growth, including development, yield, and grain quality, with marked economic losses recorded annually. The increasing threat of climate change escalates the dangers, pointing out the urgency for sustainable control strategies of the diseases. Conventional methods of using chemicals have been rendered inadequate for maize fungal disease control, underscoring the need for applying biopesticides and natural products obtained from microorganisms as innovative, remediation strategies. Together with these innovations are biocontrol agents that provide better solutions for reducing the reliance on chemical formulations as well as strengthening a healthier agricultural environment. Finally, a comprehensive understanding of the interaction between maize pathogens and environmental determinants is vital for the development of more effective integrated pest management strategies to enhance maize productivity and subsequent food safety
Mesterséges intelligencia alkalmazása az oktatásban
No full textArtificial intelligence has integrated itself into our everyday lives. The use of AI in education is not a new topic. The research aimed to explore the attitudes, experiences and potential applications of professionals working with children in the use of artificial intelligence (AI) in education. A questionnaire method was used in the research. The survey included 122 participants (n=122). The results showed that the majority of respondents have a positive opinion of AI, even if they do not actively use it in their daily lives. Among the application areas of AI, data collection stands out in terms of popularity, while in other areas (e.g. preparing presentations, preparing for class, preparing assignments, searching for scientific literature), its uptake is more moderate but significant among respondents. Results show that AI is mostly used for tasks that facilitate information gathering and content creation. Most respondents think that AI can be used in certain areas, and there is a significant minority that is positive about its future use. There is great potential for future applications in education, although current experience and applications have not yet triggered a full-scale transformation.A mesterséges intelligencia a mindennapi életünk elengedhetetlen részévé integrálta magát. Az MI alkalmazása az oktatásban sem újkeletű téma. A kutatás arra irányult, hogy feltárja a gyermekekkel foglalkozó szakemberek hozzáállását, tapasztalatait és alkalmazási lehetőségeit a mesterséges intelligencia (MI) oktatásban való felhasználásával kapcsolatban. A kutatásban kérdőíves módszert alkalmaztunk. A vizs-gálatban 122 fő vett részt (n=122). Az eredmények azt mutatták, hogy a válaszadók többsége pozitív véleménnyel van az MI-ről, még ha nem is használják aktívan a mindennapokban. A mesterséges in-telligencia alkalmazási területei közül az adatgyűjtés kiemelkedik a népszerűség tekintetében, míg más terü-leteken (pl. prezentációkészítés, órára való felkészülés, beadandók készítése, szakirodalmak keresése) a válaszadók körében mérsékeltebb, de jelentős az elterjedtsége. Az eredmények azt mutatják, hogy az MI-t leginkább olyan feladatokhoz veszik igénybe, amelyek megkönnyítik az információgyűjtést és a tartalomkészítést. A legtöbb válaszadó szerint az MI hasznosítható bizonyos területeken, és vannak olyanok akik pozitívan tekintenek a jövőbeli felhasználásra. A jövőbeli alkalmazások szempontjából az oktatásban nagy potenciál rejlik, bár a jelenlegi tapasztalatok és alkalmazások még nem indítottak el teljes körű átalakulást