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2019/6, стр. 616 - 625

CONVERTER FROM MOODLE LESSONS TO INTERACTIVE EPUB EBOOKS

Martin Takev
E-mail: takevm@gmail.com
Computer Science Department
University of Plovdiv “Paisii Hilendarski”
24 Tzar Assen St.
4000 Plovdiv Bulgaria
Elena Somova
E-mail: eledel@uni-plovdiv.bg
Computer Science Department
University of Plovdiv “Paisii Hilendarski”
24 Tzar Assen St.
4000 Plovdiv Bulgaria
Miguel Rodríguez-Artacho
E-mail: miguel@lsi.uned.es
Languages and Systems Department
UNED University
14 Calle de Juan del Rosal
28040 Madrid Spain

Резюме: This article describes a software, that automatically converts already created Moodle Learning Resources of type “lessons” into interactive e-books, stored in EPUB format. The advantages of EPUB format to present learning content are discussed, as well as existing examples of its use in education. Emphasis is given to creating interactive EPUB lessons that enable tracking learners’ activities and saving their current progress with the help of xAPI statements and stateAPI implementation.

Ключови думи: EPUB; xAPI; e-learning environment; educational content modelling; educational authoring; Learning Analytics

1. Introduction

Modern learners are not the ones for whom the traditional education system was created. Students have other requirements and expectations from their education. They use various technologies, widely available to everybody. The use of mobile devices, smartphones, fablets and tablets is fully integrated into people’s natural life and social activities (Gaftandzhieva, Kasakliev & Doneva, 2016).

On one hand, learners have to interact with multiple learning objects (to view learning resources in the form of texts and video lectures, to complete assignments, take tests, experiment with physical or virtual objects, participate in discussions, etc.) and in most cases this requires them to switch to different learning environments (web browsers, video players, textbooks, physical or virtual laboratories, etc.). In recent years it has been worked considerably for the integration of these learning environments. There are many e-learning environments that offer an integrated set of services and resources for the different types of participators in the learning process (student, lecturer, author and administrator). Two of the most fundamental drawbacks of these e-learning environments are the relative complexity of the interface, due to the many opportunities, and the need for constant Internet access during learning.

On the other hand, the e-book market is currently in a strong upsurge. E-books offer easy access to educational content and learning activities using well-known mobile devices, without the need of constant Internet connection. The use of mobile devices fully transfers education anywhere and at any time.

The main goal of the article is to present a converter of existing Moodle lessons to interactive EPUB e-books.

Section 2 examines the advantages of the EPUB e-book format when it is used for educational content, and its structure is given in Section 3. Actual examples of EPUB use in education are shown in Section 4. Section 5 presents the authors’ Moodle lessons converter. The article ends with a conclusion, summarizing the authors’ work and some perspectives for development.

2. EPUB Advantages

The EPUB1) format is a standardized open e-book format that can be downloaded and read on different devices like smartphones, tablets, PCs or e-book readers. EPUB is the most widely supported vendor-independent XML-based e-book format and therefore it’s easily used.

EPUB introduces mechanisms to provide interactivity and multimedia integration using JavaScript and HTML5. In this way, EPUB can track learner’s activities in web-based learning environments.

(Chang & Hung, 2018) compares two content models – EPUB for e-books and SCORM for e-learning, in terms of their content presentation, metadata and packet structure. The authors identify the main advantages of EPUB:

– Content is easily shared and reused;

– Integration of multimedia and interactive components based on web technologies (despite limited media types);

– no special metadata related to the education;

– mechanism for automatic adjustment and content reformat for devices with small screen sizes;

– All resources can be used offline.

Tse (2013) shows as an advantage of using EPUB format for presenting learning content – the simplicity of downloading content, which puts the consumption of learning materials directly into the hands of the individual learner. According to Tse, the creation of educational content that captures and maintains learners’ focus is a great challenge.

Another advantage of the format is emphasized in (Murphy, Martin, & Farley, 2012) – providing access to an educational course’s electronic content without learners having permanent Internet access. (Murphy, Martin, & Farley, 2012) presents a pilot study on the use of e-readers in higher education by looking at the steps taken, as well as at the challenges and obstacles that have arisen from the EPUB conversion.

(Gailer, et al., 2014) focuses on the openness of EPUB, which promotes open learning and teaching in a meaningful way.

3. EPUB Structure

The EPUB format is a compressed ZIP file containing a package of files. There are the required structure and metadata files, located in the META-INF directory, and a mimetype file showing the actual file type to e-readers2).

Main component is the manifest file that structures and references the rest of the elements. EPUB content is structured by the OPF file, which determines the index, and the HTML files that describe the book content and formatting (using CSS files).

EPUBs can be downloaded and read on different devices, because all modern devices have an e-book reading software. Thus, the EPUB resources can be used by students or teachers both off-line and on-line with the user’s favourite contemporary device and reading software.

4. Examples of Using EPUB

The research of (Gailer, et al., 2014) notes that EPUB is suitable for different types of exercises and is able to serve as the main format for upcoming digital textbooks. Gailer, et al. (2014) is developing a didactic and technical concept for implementing various exercises in an e-book. Such e-book prototype is created, consisting of a set of interactive exercises.

The authors of Sigarchian, et al. (2015) created e-Textbook – a prototype of a mobile learning environment, based on EPUB. In it they have integrated three interactive widgets that can interchange information and create semi-automatic new content: a report maker widget, a sine formula widget and a corresponding interactive graph maker widget. Objects, offering contextual content, and various sets of learning objects have been incorporated into the environment (including multimedia objects, objects with augmented reality features, i.e. digital objects that allow interaction with physical objects). E-TextBook also provides a unified mobile learning environment through interoperable packed semantically annotated learning content.

Lohr (2014) presents the attempt of an Austrian school to offer blended learning using personal computers and iPads. Science education is done through ebooks in pdf, epub and ibook format. They report that the ibook format, although better in integrating interactive elements, use of dictionaries and tagging tools, has a major drawback – it is only available for iPads, unlike the open pdf and epub formats. Seamlessly creating e-books with the software pages available for Mac OS and iOS is suited to the epub format, but the production of interactive ibooks can be done only with the available only for Mac OS iBooks Author software.

Although the undisputed advantages of gamification in learning, the gamified e-books and systems are few. The authors in (Heyvaert, Verborgh, Mannens, & Van De Walle, 2015) create the GEL (Gamification for EPUB, using Linked Data) framework, which allows embedding gamification concepts in a digital textbook using EPUB and Linked Data. They have created the ontology Gamification Ontology (GO), which presents the various concepts of gaming, and allows the discovery of other gamified е-books.

Figueiredo, Bidarra & Bostad (2016) show tools for expanding the classroom into a blended learning model, where e-books in EPUB standard incorporating lecture and problem-solving videos, teach mathematics to students in secondary education in a more comprehensive manner.

E-books in HTML and EPUB formats are more accessible than PDF books. This statement is proved by researchers at (Sun, et al., 2018), who are studying the availability of 140 publicly accessible electronic textbooks from the California Open Online Library for Education (COOL4ed). Each textbook is evaluated for compliance with 15 control points/accessibility points developed by the MERLOT (Multimedia Educational Resource for Learning and Online Teaching) project through an assessment system, specifically created for electronic textbooks. Furthermore, each textbook is evaluated in more than one format (EPUB, HTML or PDF).

Uosaki, Kiyota, Mouri, Ogata, & Choyekh (2016) present the use of EPUB in ubiquitous learning, which is applied to the Japanese language learning system SCROLL (System for Capturing and Reminding of Learning Log). They improve their system by adding EPUB functionality to increase the efficiency and enrich the content of their tests. The pilot assessment conducted shows sufficient results, despite the negative attitude shown by some learners.

5. Creating Lessons in EPUB Format

5.1. Moodle Lesson

One of the most usable and useful activities in the e-learning environment Moodle is the “lesson”3). It is composed of a series of HTML pages, consisting of learning content and a list of actions, each leading to one of the other pages of the lesson. Sometimes this navigation, created by the authors can be very complex, but it is the base that forms the adaptive nature of the lesson module and with correct planning and customization, each individual student’s learning path may differ.

There are two basic lesson page types: content pages and question pages. Question pages provide the option to place so-called in-text questions (ITQs), which evaluate the learning materials just passed and studied from the previous pages. Which in turn leads to different page navigation for the specific levels of knowledge, displayed by the learners and the lesson can be designed to be adaptive and use student’s choices to generate a self-directed lesson.

In the Moodle lesson module 6 types of questions are available4): Multichoice (or Multiple answer), Essay, Matching, Numerical, Short answer (incl. fill in the blank) and True/false.

5.2. Convert Moodle lesson to EPUB format

When converting a Moodle lesson to EPUB format, the same behaviour from the e-learning environment must be recreated into the EPUB document. This is done by generating an interactive EPUB file with JavaScript, delivering exactly identical learning process –visualization of lesson pages, page navigation, questions and their answers.

The main focus of the work is tracking learners’ actions throughout their use of EPUB lessons. The EPUB lesson files are located outside of the e-learning environment, which leads to the need of additional actions to track the activities, performed by learners – opening a lesson, reading a lesson or a page of a lesson, completing a lesson or answering lesson questions. This is achieved by using the xAPI specification5), JavaScript codes and the xAPIWrapper6) that carry out the communication between the EPUB file and the LRS (Learning record store).

The specification Experience API (or xAPI)5) is described as a next generation elearning standard, which combined with SCORM allows e-learning to use modern technologies in an interoperable way. А traditionally passive e-books are turned into interactive educational platforms, tracking learner activities by means of the Learning Record Store (LRS), that holds the structured interactions in a cloudbased model.

EPUB allows the use of JavaScript embedded code to describe user actions, following the guidelines of composing xAPI statements. The xAPI collects data about the wide range of experiences a person has done online or offline in statements in the form of “Noun, verb, object” (e.g. “I did this”). User activities are saved as statements in LRS. The LRS can exist on its own, or inside an LMS and it can share these statements with other LRSs.

When learners perform certain actions on the lesson, xAPI phrases are generated and sent to the LRS. From the student activity data recorded, different reports can then be made only for statistical purposes or as well for adapting the overall learning process.

Another key moment of the work is the ability to save users’ current progress or state (the stateAPI7)), i.e. where the student stands in terms of completing the learning material. EPUB lessons can be downloaded and opened by different devices. The lack of a single system to access the learning content (as is the case in Moodle) raises the problem of tracking how far a user has gone through the lesson and when the user is opening the same lesson on another device – continuing the studying from the exact position, reached on the previous device. This is accomplished with the xAPI specification and its stateAPI, that uses stored information in the LRS to detect what content a user has already read and what still has to be completed. The LRS needs to keep parameters8) like: the user (also references as an agent), who is reading the EPUB file, the ID of the activity, that this user is currently working on, the value, that needs to be saved as a state and optionally a unique identifier (timestamp) for this state.

Figure 1-a. Lesson content page preview in Moodle

Figure 1-b. Lesson content page preview in EPUB

For example, when reaching the 5th page of a lesson, a request is sent to the endpoint for the LRS (e.g. http://example.com/xAPI/activities/state) where this information is saved and the next time when the EPUB lesson is opened by the same user, even if this is done from another device – the lesson is opened right after the 5th page, so the learner can continue right where he had left.

5.3. Example EPUB lesson

The section provides an example lesson, containing both content and question pages, that is exported to an EPUB format file. In the EPUB lesson, the content is displayed to the learners one page at a time, similar to how the lesson is perceived in the e-learning environment. The rest of the pages are visualized after specific user actions have been undertaken – navigating to the appropriate part of the lesson or answering to a question.

As Moodle is an online learning environment and it uses HTML for visualization, after converting to EPUB format, there are hardly any differences in the displayed lesson (see Figure 1 and Figure 2). Figure 1 illustrates the preview of a content page in Moodle and in EPUB format, and Figure 2 – of a multichoice question page.

Figure 2-a. Lesson question page preview in Moodle

JavaScript code is used to check the learner’s answers to the question pages and, depending on the correctness of the answer, it is decided on which page to redirect the learner (analogous to the behaviour of Moodle).

Figure 2-b. Lesson question page preview in EPUB

When an EPUB file is opened, it is checked whether the user has already opened the lesson on another device. If yes, then the StateAPI takes the value that has been recorded as a session (which page of the lesson has the learner reached earlier) and opens the corresponding page to continue the lesson from where it was previously finished at the last opening of the file. If no session is found, the lesson opens from the first page.

To accomplish the tracking of the students and their activity onto the EPUB lesson, the following events can be specified: opening the lesson, going to a lesson page, answering a question and completing the lesson. For every event, requests are sent to the LRS with information about who, what and when they did in the lesson in the form of xAPI statements.

6. Conclusion

E-books provide easy access to learning content and activities without the need of constant internet access and using the well-known to users’ mobile devices. This article presented a Moodle plugin, capable of converting lesson modules to interactive EPUB e-books. It also highlighted the advantages of having learning materials in EPUB format and existing examples of its application in education. The creation of interactive EPUB lessons, tracking learners’ actions by sending xAPI statements to an LRS and saving their progress throughout different devices with session states (state API), is fully covered.

The developed software tool will be integrated with the mobile application – Mobile LAP (Gaftandzhieva, Doneva, Petrov & Totkov, 2018) that allows students to track their activity and success rate during training and compare them with the average level of activity and success rate of the other students, in order to increase their success, as well as to track whether they adhere to the learning schedule.

The software would be further extended to convert other Moodle modules and to increase the range of generated statements, making the tracking of more student activities possible. Implementing the EPUB e-books in education could help in achieving greater accessibility of the learning material and encourage spending more time on it. All of this contributes to the possibility of making vast reviews on students’ behavior, which can be then analyzed to fully understand user’s participation in the learning process.

NOTES

1. International Digital Publishing Forum (IDPF). EPUB 3.0.1. http://idpf.org/ epub/301. Accessed 05.05.2019

2. edrLAB. https://www.edrlab.org/epub/anatomy-of-an-epub-3-file. Accessed 05.05.2019

3. Lesson Activity. https://docs.moodle.org/36/en/Lesson_activity. Accessed 05.05.2019

4. Building Lesson. https://docs.moodle.org/36/en/Building_Lesson. Accessed 05.05.2019

5. The Advanced Distributed Learning Initiative (ADL). Research & Development Experience xAPI. https://adlnet.gov/experience-api. Accessed 05.05.2019

6. xAPI Wrapper. https://github.com/adlnet/xAPIWrapper. Accessed 05.05.2019

7. Statement API. https://www.ht2labs.com/xapi-state-api/. Accessed 05.05.2019

8. xAPI Specification. https://github.com/adlnet/xAPI-Spec/blob/master/xAPICommunication.md#partthree. Accessed 05.05.2019

REFERENCES

Chang, H.-P. A. & Hung, J. C. (2018). Comparison of the features of EPUB e-book and SCORM e-learning content model. International Journal of Distance Education Technologies, 16 (2), 1 – 17.

Figueiredo, M., Bidarra, J. & Bostad, R. (2016). The development of an ebook for teaching and learning mathematics, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 10th International Conference on Universal Access in Human-Computer Interaction – UAHCI‘2016, 9739, pp. 49 – 56. Toronto, Canada.

Gaftandzhieva, S., Doneva, R., Petrov, S. & Totkov, G. (2018). Mobile Learning Analytics Application: Using Students’ Big Data to Improve Student Success. International Journal on Information Technologies & Security, 3 (10), 53 – 64. doi:1313 – 8251

Gaftandzhieva, S., Kasakliev, N. & Doneva, R. (2016). Mobile Application for Quality Evaluation of Learning. QED’16: Technology Advanced Quality Learning for ALL, (pp. 32 – 49). Sofia, Bulgaria. doi:978-619185-261-1

Gailer, C. A., Ebner, M. A., Kopp, M. B., Lackner, E. B., Raunig, M. B. & Scerbakov, A. A. (2014). Potential of EPUB3 for digital textbooks in higher education, Lecture Notes in Computer Science. European Conference on Technology Enhanced Learning, EC-TEL 2014, 8719, pp. 564 – 5659. Graz, Austria.

Heyvaert, P., Verborgh, R., Mannens, E. & Van De Walle, R. (2015). Linked data-enabled gamification in EPUB 3 for educational digital textbooks, Lecture Notes in Computer Science. 10th European Conference on Technology Enhanced Learning, EC-TEL 2015, 9307, pp. 587 – 591. Toledo, Spain.

Lohr, M. (2014). Ebooks as pdf files, in epub format or as interactive ibooks? Digital books in physics lessons of secondary education. Proceedings of the 10th International Conference on Mobile Learning – ML 2014, (pp. 11 – 18). Madrid, Spain.

Murphy, A., Martin, N. & Farley, H. (2012). Using e-readers to increase access to course content for students without internet access. ASCILITE 2012 – Annual conference of the Australian Society for Computers in Tertiary Education, (pp. 25 – 28). Wellington, New Zealand.

Sigarchian, H. G., De Meester, B., De Nies, T., Verborgh, R., Salliau, F., De Neve, W. & Van De Walle, R. (2015). Towards making EPUB 3-based e-TextBooks a first-class mobile learning environment. 10th International Conference on e-Learning – ICEL 2015, (pp. 270 – 278). Bahamas.

Sun, Y., Fritz, R. M., Yorba, L., Manabat, A. K., Katz, N. A. & Vu, K.-P. L. (2018). E-book accessibility evaluations. In Advances in Intelligent Systems and Computing (Vol. 596, pp. 328 – 336).

Tse, E. (2013, December). Special issue on child computer interaction. Personal and Ubiquitous Computing, 17 (8), 1573 – 1575.

Uosaki, N., Kiyota, M., Mouri, K., Ogata, H. & Choyekh, M. (2016). Onomatopoeia learning support for Japanese language learners using ubiquitous learning log system with eBook. Proceedings – IEEE 16th International Conference on Advanced Learning Technologies, ICALT 2016, (pp. 347 – 348). Austin, United States.

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Краен срок за изпращане на решения: 0 юни 0 г.

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 1, 2021

Краен срок за изпращане на решения: 0 юни 0 г.

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СЕДЕМНАДЕСЕТА ЖАУТИКОВСКА ОЛИМПИАДА ПО МАТЕМАТИКА, ИНФОРМАТИКА И ФИЗИКА АЛМАТИ, 7-12 ЯНУАРИ 2021

Диян Димитров, Светлин Лалов, Стефан Хаджистойков, Елена Киселова

ОНЛАЙН СЪСТЕЗАНИЕ „VIVA МАТЕМАТИКА С КОМПЮТЪР“

Петър Кендеров, Тони Чехларова, Георги Гачев

2020 година
Книжка 6
ABSTRACT DATA TYPES

Lasko M. Laskov

Книжка 5
GAMIFICATION IN CLOUD-BASED COLLABORATIVE LEARNING

Denitza Charkova, Elena Somova, Maria Gachkova

NEURAL NETWORKS IN A CHARACTER RECOGNITION MOBILE APPLICATION

L.I. Zelenina, L.E. Khaimina, E.S. Khaimin, D.I. Antufiev, I.M. Zashikhina

APPLICATIONS OF ANAGLIFIC IMAGES IN MATHEMATICAL TRAINING

Krasimir Harizanov, Stanislava Ivanova

МЕТОД НА ДЕЦАТА В БЛОКА

Ивайло Кортезов

Книжка 4
TECHNOLOGIES AND TOOLS FOR CREATING ADAPTIVE E-LEARNING CONTENT

Todorka Terzieva, Valya Arnaudova, Asen Rahnev, Vanya Ivanova

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MATHEMATICAL MODELLING IN LEARNING OUTCOMES ASSESSMENT (BINARY MODEL FOR THE ASSESSMMENT OF STUDENT’S COMPETENCES FORMATION)

L. E. Khaimina, E. A. Demenkova, M. E. Demenkov, E. S. Khaimin, L. I. Zelenina, I. M. Zashikhina

PROBLEMS 2 AND 5 ON THE IMO’2019 PAPER

Sava Grozdev, Veselin Nenkov

Книжка 2
ЗА ВЕКТОРНОТО ПРОСТРАНСТВО НА МАГИЧЕСКИТЕ КВАДРАТИ ОТ ТРЕТИ РЕД (В ЗАНИМАТЕЛНАТА МАТЕМАТИКА)

Здравко Лалчев, Маргарита Върбанова, Мирослав Стоимиров, Ирина Вутова

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Йоана Христова, Геновева Маринова, Никола Кушев, Светослав Апостолов, Цветомир Иванов

A NEW PROOF OF THE FEUERBACH THEOREM

Sava Grozdev, Hiroshi Okumura, Deko Dekov

PROBLEM 3 ON THE IMO’2019 PAPER

Sava Grozdev, Veselin Nenkov

Книжка 1
GENDER ISSUES IN VIRTUAL TRAINING FOR MATHEMATICAL KANGAROO CONTEST

Mark Applebaum, Erga Heller, Lior Solomovich, Judith Zamir

KLAMKIN’S INEQUALITY AND ITS APPLICATION

Šefket Arslanagić, Daniela Zubović

НЯКОЛКО ПРИЛОЖЕНИЯ НА ВЪРТЯЩАТА ХОМОТЕТИЯ

Сава Гроздев, Веселин Ненков

2019 година
Книжка 6
DISCRETE MATHEMATICS AND PROGRAMMING – TEACHING AND LEARNING APPROACHES

Mariyana Raykova, Hristina Kostadinova, Stoyan Boev

CONVERTER FROM MOODLE LESSONS TO INTERACTIVE EPUB EBOOKS

Martin Takev, Elena Somova, Miguel Rodríguez-Artacho

ЦИКЛОИДА

Аяпбергенов Азамат, Бокаева Молдир, Чурымбаев Бекнур, Калдыбек Жансуйген

КАРДИОИДА

Евгений Воронцов, Никита Платонов

БОЛГАРСКАЯ ОЛИМПИАДА ПО ФИНАНСОВОЙ И АКТУАРНОЙ МАТЕМАТИКЕ В РОССИИ

Росен Николаев, Сава Гроздев, Богдана Конева, Нина Патронова, Мария Шабанова

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 1. Да се намерят всички полиноми, които за всяка реална стойност на удовлетворяват равенството Татяна Маджарова, Варна Задача 2. Правоъгълният триъгълник има остри ъгли и , а центърът на вписаната му окръжност е . Точката , лежаща в , е такава, че и . Симетралите

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 1, 2019

Задача 1. Да се намерят всички цели числа , за които

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ДЪЛБОКО КОПИЕ В C++ И JAVA

Христина Костадинова, Марияна Райкова

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 1. Да се намери безкрайно множество от двойки положителни ра- ционални числа Милен Найденов, Варна

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 6, 2018

Задача 1. Точката е левият долен връх на безкрайна шахматна дъска. Една муха тръгва от и се движи само по страните на квадратчетата. Нека е общ връх на някои квадратчета. Казва- ме, че мухата изминава пътя между и , ако се движи само надясно и нагоре. Ако точките и са противоположни върхове на правоъгълник , да се намери броят на пътищата, свърз- ващи точките и , по които мухата може да мине, когато: а) и ; б) и ; в) и

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THE REARRANGEMENT INEQUALITY

Šefket Arslanagić

АСТРОИДА

Борислав Борисов, Деян Димитров, Николай Нинов, Теодор Христов

COMPUTER PROGRAMMING IN MATHEMATICS EDUCATION

Marin Marinov, Lasko Laskov

CREATING INTERACTIVE AND TRACEABLE EPUB LEARNING CONTENT FROM MOODLE COURSES

Martin Takev, Miguel Rodríguez-Artacho, Elena Somova

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

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РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 5, 2018

Задача 1. Ако и са съвършени числа, за които целите части на числата и са равни и различни от нула, да се намери .

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RESULTS OF THE FIRST WEEK OF CYBERSECURITY IN ARKHANGELSK REGION

Olga Troitskaya, Olga Bezumova, Elena Lytkina, Tatyana Shirikova

DIDACTIC POTENTIAL OF REMOTE CONTESTS IN COMPUTER SCIENCE

Natalia Sofronova, Anatoliy Belchusov

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Краен срок за изпращане на решения 30 ноември 2019 г.

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 4, 2018

Задача 1. Да се намерят всички тройки естествени числа е изпълнено равенството: а)

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ЕЛЕКТРОНЕН УЧЕБНИК ПО ОБЗОРНИ ЛЕКЦИИ ЗА ДЪРЖАВЕН ИЗПИТ В СРЕДАТА DISPEL

Асен Рахнев, Боян Златанов, Евгения Ангелова, Ивайло Старибратов, Валя Арнаудова, Слав Чолаков

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Борислав Борисов, Деян Димитров, Николай Нинов, Теодор Христов

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Веселин Ненков, Станислав Стефанов, Хаим Хаимов

A TRIANGLE AND A TRAPEZOID WITH A COMMON CONIC

Sava Grozdev, Veselin Nenkov

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Христо Лесов, Казанлък Задача 2. Окръжност с диаметър и правоъгълник с диагонал имат общ център. Да се докаже, че за произволна точка M от е изпълне- но равенството . Милен Найденов, Варна Задача 3. В изпъкналия четириъгълник са изпълнени равенства- та и . Точката е средата на диагонала , а , , и са ортоганалните проекции на съответно върху правите , , и . Ако и са средите съответно на отсечките и , да се докаже, че точките , и лежат на една права.

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 3, 2018

Задача 1. Да се реши уравнението . Росен Николаев, Дико Суружон, Варна Решение. Въвеждаме означението , където . Съгласно това означение разлежданото уравнение придобива вида не е решение на уравнението. Затова са възможни само случаите 1) и 2) . Разглеж- даме двата случая поотделно. Случай 1): при е изпълнено равенството . Тогава имаме:

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PROBLEM 6. FROM IMO’2018

Sava Grozdev, Veselin Nenkov

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 2, 2018

Задача 1. Да се намери най-малкото естествено число , при което куба с целочислени дължини на ръбовете в сантиметри имат сума на обемите, рав- на на Христо Лесов, Казанлък Решение: тъй като , то не е куб на ес- тествено число и затова . Разглеждаме последователно случаите за . 1) При разглеждаме естествени числа и , за които са изпълнени релациите и . Тогава то , т.е. . Освен това откъдето , т.е. .Така получихме, че . Лесно се проверява, че при и няма естествен

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 1. Да се намерят всички цели числа , за които

2018 година
Книжка 6
„ЭНЦИКЛОПЕДИЯ ЗАМЕЧАТЕЛЬНЫХ ПЛОСКИХ КРИВЫХ“ – МЕЖДУНАРОДНЫЙ СЕТЕВОЙ ИССЛЕДОВАТЕЛЬСКИЙ ПРОЕКТ В РАМКАХ MITE

Роза Атамуратова, Михаил Алфёров, Марина Белорукова, Веселин Ненков, Валерий Майер, Генадий Клековкин, Раиса Овчинникова, Мария Шабанова, Александр Ястребов

A NEW MEANING OF THE NOTION “EXPANSION OF A NUMBER”

Rosen Nikolaev, Tanka Milkova, Radan Miryanov

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ИТОГИ ПРОВЕДЕНИЯ ВТОРОЙ МЕЖДУНАРОДНОЙ ОЛИМПИАДЬI ПО ФИНАНСОВОЙ И АКТУАРНОЙ МАТЕМАТИКЕ СРЕДИ ШКОЛЬНИКОВ И СТУДЕНТОВ

Сава Гроздев, Росен Николаев, Мария Шабанова, Лариса Форкунова, Нина Патронова

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Mariya Gachkova, Martin Takev, Elena Somova

УЛИТКА ПАСКАЛЯ

Дарья Коптева, Ксения Горская

КОМБИНАТОРНИ ЗАДАЧИ, СВЪРЗАНИ С ТРИЪГЪЛНИК

Росен Николаев, Танка Милкова, Катя Чалъкова

Книжка 4
ЗА ПРОСТИТЕ ЧИСЛА

Сава Гроздев, Веселин Ненков

ИНЦЕНТЪР НА ЧЕТИРИЪГЪЛНИК

Станислав Стефанов

ЭПИЦИКЛОИДА

Инкар Аскар, Камила Сарсембаева

ГИПОЦИКЛОИДА

Борислав Борисов, Деян Димитров, Иван Стефанов, Николай Нинов, Теодор Христов

Книжка 3
ПОЛИНОМИ ОТ ТРЕТА СТЕПЕН С КОЛИНЕАРНИ КОРЕНИ

Сава Гроздев, Веселин Ненков

ЧЕТИРИДЕСЕТ И ПЕТА НАЦИОНАЛНА СТУДЕНТСКА ОЛИМПИАДА ПО МАТЕМАТИКА

Сава Гроздев, Росен Николаев, Станислава Стоилова, Веселин Ненков

Книжка 2
TWO INTERESTING INEQUALITIES FOR ACUTE TRIANGLES

Šefket Arslanagić, Amar Bašić

ПЕРФЕКТНА ИЗОГОНАЛНОСТ В ЧЕТИРИЪГЪЛНИК

Веселин Ненков, Станислав Стефанов, Хаим Хаимов

НЯКОИ ТИПОВЕ ЗАДАЧИ СЪС СИМЕТРИЧНИ ЧИСЛА

Росен Николаев, Танка Милкова, Радан Мирянов

Книжка 1
Драги читатели

където тези проценти са наполовина, в Източна Европа те са около 25%, в

COMPUTER DISCOVERED MATHEMATICS: CONSTRUCTIONS OF MALFATTI SQUARES

Sava Grozdev, Hiroshi Okumura, Deko Dekov

ВРЪЗКИ МЕЖДУ ЗАБЕЛЕЖИТЕЛНИ ТОЧКИ В ЧЕТИРИЪГЪЛНИКА

Станислав Стефанов, Веселин Ненков

КОНКУРСНИ ЗАДАЧИ НА БРОЯ

Задача 2. Да се докаже, че всяка от симедианите в триъгълник с лице разделя триъгълника на два триъгълника, лицата на които са корени на урав- нението където и са дължините на прилежащите на симедианата страни на три- ъгълника. Милен Найденов, Варна Задача 3. Четириъгълникът е описан около окръжност с център , като продълженията на страните му и се пресичат в точка . Ако е втората пресечна точка на описаните окръжности на триъгълниците и , да се докаже, че Хаим Х

РЕШЕНИЯ НА ЗАДАЧИТЕ ОТ БРОЙ 2, 2017

Задача 1. Да се определи дали съществуват естествени числа и , при които стойността на израза е: а) куб на естествено число; б) сбор от кубовете на две естествени числа; в) сбор от кубовете на три естествени числа. Христо Лесов, Казанлък Решение: при и имаме . Следова- телно случай а) има положителен отговор. Тъй като при число- то се дели на , то при и имаме е естестве- но число. Следователно всяко число от разглеждания вид при деление на дава ос

2017 година
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A SURVEY OF MATHEMATICS DISCOVERED BY COMPUTERS. PART 2

Sava Grozdev, Hiroshi Okumura, Deko Dekov

ТРИ ИНВАРИАНТЫ В ОДНУ ЗАДА

Ксения Горская, Дарья Коптева, Асхат Ермекбаев, Арман Жетиру, Азат Бермухамедов, Салтанат Кошер, Лили Стефанова, Ирина Христова, Александра Йовкова

GAMES WITH MODIFIED DICE

Aldiyar Zhumashov

SOME NUMERICAL SQUARE ROOTS (PART TWO)

Rosen Nikolaev, Tanka Milkova, Yordan Petkov

ЗАНИМАТЕЛНИ ЗАДАЧИ ПО ТЕМАТА „КАРТИННА ГАЛЕРИЯ“

Мирослав Стоимиров, Ирина Вутова

Книжка 5
ВТОРОЙ МЕЖДУНАРОДНЫЙ СЕТЕВОЙ ИССЛЕДОВАТЕЛЬСКИЙ ПРОЕКТ УЧАЩИХСЯ В РАМКАХ MITE

Мария Шабанова, Марина Белорукова, Роза Атамуратова, Веселин Ненков

SOME NUMERICAL SEQUENCES CONCERNING SQUARE ROOTS (PART ONE)

Rosen Nikolaev, Tanka Milkova, Yordan Petkov

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ГЕНЕРАТОР НА ТЕСТОВЕ

Ангел Ангелов, Веселин Дзивев

INTERESTING PROOFS OF SOME ALGEBRAIC INEQUALITIES

Šefket Arslanagić, Faruk Zejnulahi

PROBLEMS ON THE BROCARD CIRCLE

Sava Grozdev, Hiroshi Okumura, Deko Dekov

ПРИЛОЖЕНИЕ НА ЛИНЕЙНАТА АЛГЕБРА В ИКОНОМИКАТА

Велика Кунева, Захаринка Ангелова

СКОРОСТТА НА СВЕТЛИНАТА

Сава Гроздев, Веселин Ненков

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НЯКОЛКО ПРИЛОЖЕНИЯ НА ТЕОРЕМАТА НА МЕНЕЛАЙ ЗА ВПИСАНИ ОКРЪЖНОСТИ

Александра Йовкова, Ирина Христова, Лили Стефанова

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Сава Гроздев, Росен Николаев, Веселин Ненков

СПОМЕН ЗА ПРОФЕСОР АНТОН ШОУРЕК

Александра Трифонова

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ИЗКУСТВЕНА ИМУННА СИСТЕМА

Йоанна Илиева, Селин Шемсиева, Светлана Вълчева, Сюзан Феимова

ВТОРИ КОЛЕДЕН ЛИНГВИСТИЧЕН ТУРНИР

Иван Держански, Веселин Златилов

Книжка 1
ГЕОМЕТРИЯ НА ЧЕТИРИЪГЪЛНИКА, ТОЧКА НА МИКЕЛ, ИНВЕРСНА ИЗОГОНАЛНОСТ

Веселин Ненков, Станислав Стефанов, Хаим Хаимов

2016 година
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ПЕРВЫЙ МЕЖДУНАРОДНЫЙ СЕТЕВОЙ ИССЛЕДОВАТЕЛЬСКИЙ ПРОЕКТ УЧАЩИХСЯ В РАМКАХ MITE

Мария Шабанова, Марина Белорукова, Роза Атамуратова, Веселин Ненков

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Ксения Горская, Дарья Коптева, Даниил Микуров, Еркен Мудебаев, Казбек Мухамбетов, Адилбек Темирханов, Лили Стефанова, Ирина Христова, Радина Иванова

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Веселин Ненков, Станислав Стефанов, Хаим Хаимов

FUZZY LOGIC

Reinhard Magenreuter

GENETIC ALGORITHM

Reinhard Magenreuter

Книжка 5
NEURAL NETWORKS

Reinhard Magenreuter

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АКТИВНО, УЧАСТВАЩО НАБЛЮДЕНИЕ – ТИП ИНТЕРВЮ

Христо Христов, Христо Крушков

ХИПОТЕЗАТА В ОБУЧЕНИЕТО ПО МАТЕМАТИКА

Румяна Маврова, Пенка Рангелова, Елена Тодорова

Книжка 3
ОБОБЩЕНИЕ НА ТЕОРЕМАТА НА ЧЕЗАР КОШНИЦА

Сава Гроздев, Веселин Ненков

Книжка 2
ОЙЛЕР-ВЕН ДИАГРАМИ ИЛИ MZ-КАРТИ В НАЧАЛНАТА УЧИЛИЩНА МАТЕМАТИКА

Здравко Лалчев, Маргарита Върбанова, Ирина Вутова, Иван Душков

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Румяна Маврова, Пенка Рангелова

Книжка 1
EDITORIAL / КЪМ ЧИТАТЕЛЯ

Сава Гроздев

STATIONARY NUMBERS

Smaiyl Makyshov

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Сава Гроздев, Веселин Ненков

2015 година
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