The Archives Speak: International Contests in Informatics
Pavel Azalov
Penn State, Hazleton, U.S.A.
Abstract. The main theme of this article centers on the international contests in Informatics. The article details the key events preceding the initiation and organization of the First International Olympiad in Informatics (IOI), held in Bulgaria in 1989, and provides supporting documentation. The path, leading to this Olympiad and the events between the First National Olympiad in Informatics (NOI) and the First IOI are discussed as well. An outline of the international contests in informatics held in Sofia (1987), Bratislava (1987), Varna (1988), and Nova Gorica (1988) is offered. In the beginning of 1989, in Netherlands, UNESCO held a consultative meeting to discuss various issues related to international Olympiads. The invited participants were the leaders of the well-established International Olympiads in Mathematics, Physics, and Chemistry. The author was invited to introduce the Olympiads in Informatics and to present the plan for the organization and inauguration of the First IOI in Bulgaria. Next the paper discusses the progress of our talented students, winners of the Bulgarian NOIs. Subsequently, a few, as university students, participated in the world’s most reputable completion - the ACM International Collegiate Contest (ACM ICPC). There is a brief presentation of the student team from Sofia University “St. Kl. Ohridski”, which participated in this contest in 1996 and placed first in Europe and fourth overall, among the 1001 teams from universities around the world. Due to its factual nature, the article contains an extensive list of references, including text excerpts, citations, photos, and other relevant materials, supporting the historical facts related to the competitions in Informatics.
Keywords: programming contests; international olympiad in informatics; IOI; history of IOI; ACM ICPC
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Electronic Textbook in Overview Lectures for State Examination in DisPel
Asen Rahnev,
Boyan Zlatanov,
Evgeniya Angelova,
Ivaylo Staribratov,
Valya Arnaudova,
Slav Cholakov
University of Plovdiv “Paisii Hilendarski”
Abstract. The paper presents the design, authoring and implementation of an electronic textbook in the Overview Course for the preparation of the written state examination for students from program „Information technologies, Mathematics and Educational Management“ in Plovdiv University „Paisii Hilendarski“, Branch Smolyan. The textbook is created in the Distributed e-Learning Platform – DisPeL. The paper describes the specifics of the course, the adaptation of the learning content and the implementation of the learning process in DisPeL.
Keywords: electronic textbook; electronic learning content; DisPeL
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Experimental Mathematics as Environment for the Preparation of Students for Research in the Form “Science 2.0”
1) Larisa Udovenko, 2) Maria Shabanova, 3) Magomedhan Nimatuliev
1) Moscow State Pedagogical University – Moscow (Russian Federation)
2) Northern (Arctic) Federal University Named after M. V. Lomonosov – Moscow (Russian Federation)
3) Financial University under the Government of the Russian Federation – Moscow (Russian Federation)
Abstract. The paper presents the experimental mathematics as a problem environment for students’ research activities. Such an area is available to students who have different level of mathematical competence. The organization of students’ research activities in experimental mathematics environment is a basis for their preparation for work in the form “Science 2.0”. Students will learn the following main characteristics of Science 2.0: working on a project, participation in crowd-sourcing, research network, computer supported research.
Keywords: experimental mathematics; network research project; crowdsourcing; dynamical mathematics software; inquiry-based education
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Loci, Generated by Equilateral Triangles with Vertices Lying on a Circle
Borislav Borisov,
Deyan Dimitrov,
Nikolay Ninov,
Teodor Hristov
Mathematics High School – Lovech
Abstract. The article is a scientific work of student under the supervision of Associate Professor Dr. Veselin Nenkov. The new results in it were awarded first prize at the International Competition “Methodology and Information Technology in Education” in 2019. The article refers to loci determined by notable points in a triangle, generated by equilateral triangles with vertices on a constant circle. The construction of the triangle is similar to the initial one from the First International “Network research project” with the participation of Bulgaria, Kazakhstan, and Russia. The main difference between those two constructions consists in the location of two pairs of vertices of the two equilateral triangles – in the initial problem they are on a constant line, but in the present one – on a circle. The loci are circles, ellipses, and curves of fourth order.
Keywords: equilateral triangle; circle; ellipse; curve of fourth degree
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Geometric Modeling in Combinatoric Problems
Nataliya Pavlova
Episkop Konstantin Preslavski Shumen University
Abstract. The article presents the changes in the mathematics curriculum. The place of Combinatorics in new curriculum is considered. An idea for geometric modeling application is proposed for solving combinatory problems. Three different types of models are suggested. The proposed idea is applicable for differentiation on training, for implementation on a project-based approach, and for working in the extracurricular education.
Keywords: combinatorics; modeling; geometry; student; extracurricular education
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One Generalization of the Geometric Problem from 19th Junior Balkan Mathematical Olympiad
1) Ivaylo Staribratov, 2) Radka Todorova
1) University of Plovdiv “Paisii Hilendarski” (Bulgaria)
2) Mathematical School “Academic Kiril Popov” – Plovdiv (Bulgaria)
Abstract. We present one possible generalization, inspired by the usage of the Dynamic Geometry Software GeoGebra, of the geometric problem from the 19th Junior Balkan Mathematical Olympiad. We have presented the process of the generalization in front of students about 16 – 17 years of age from the Mathematical School “Academic Kiril Popov” – Plovdiv. We have use the technique of tree diagrams to ease students’ understanding of the solution and to help them in the steps of the generalization.
Keywords: Math Olympiad; Dynamic geometry software; Experiment; Tree diagram
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Extremal Properties of the Lemoine Point in the Quadrilateral
1) Veselin Nenkov, 2) Stanislav Stefanov
1) “Nikola Vaptsarov” Naval Academy – Varna
2) Technical University Sofia
Abstract. Proofs are presented of some extremal properties of a notable point in a convex quadrilateral.
Keywords: quadrilateral; notable point; extremal properties
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Some Simple Interest Models
Tanka Milkova
University of Economics – Varna (Bulgaria)
Abstract. In this paper some aspects of financial mathematics and in particular some problems for simple interest are examined. As we know, the classical formula for simple interest is based on the assumption for constant initial investment and constant interest rate. The present study is mainly methodological and it examines three additional simple interest models – constant investment and variable interest rate, variable investment and constant interest rate, variable investment and variable interest rate. Some formulas are outlined – they can be used for educational purposes and for solving practical problems.
Keywords: simple interest; financial calculations; percentages
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A Triangle and a Trapezoid with a Common Conic
1) Sava Grozdev, 2) Veselin Nenkov
1) University of Finance, Business and Entrepreneurship – Sofia (Bulgaria)
2) „Nikola Vaptsarov“ Naval Academy – Varna (Bulgaria)
Abstract. The aim of the present note is to propose a generalization of Problem 1 on the IMO’2018 paper. The International Mathematical Olympiad (IMO) is the most prestigious scientific Olympiad for high school students. Its 59th edition took place in Cluj-Napoca, Romania, 3–14 July 2018. The problem 1 on the paper was solved fully (7 points) by 381 participants, 7 students were marked with 6 points, 7 with 5 points, 10 with 4 points, 15 with 3 points, 24 with 2 points, 54 with 1 point and 96 with 0 points. The mean result of all the 594 participants in the Olympiad from 107 countries is 4, 934, which shows that the problem is easy and has not bordered most of the contestants. Nevertheless it turns out to be interesting and originates rich in content ideas.
Keywords: Olympiad; problem solving; triangle; trapezoid; conic
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Contest Problems of this Issue
Veselin Nenkov
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Solutions of the Contest Problems from Issue 3, 2018
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