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Conference Proceedings EUROMATH & EUROSCIENCE 2019 Conference Proceedings European Student Conference in Mathematics & Science 13 – 17 March 2019 Paphos, Cyprus CONFERENCE PROCEEDINGS Editors Gregory Makrides, Yiannis Kalaitzis ISBN 978-9963-713-32-5 i EUROMATH & EUROSCIENCE 2019 Conference Proceedings ORGANIZERS Cyprus Mathematical Society Thales Foundation Cyprus www.cms.org.cy www.thalescyprus.com in cooperation with Cypus Ministry of Education and Culture Municipality of Paphos Le-MATH Project European Mathematical Society Mathematical Society of South Eastern Europe CERN The Cyprus Institute of Neurology & Genetics Bionformatics Cyprus Computer Society Robotex Cyprus Engino Digipro Education FUNecole ii EUROMATH & EUROSCIENCE 2019 Conference Proceedings ORGANIZING COMMITTEE CHAIR Gregoris A. Makrides President of the Cyprus Mathematical Society President of the Thales Foundation MEMBERS Andreas Philippou Andreas Skotinos Cyprus Mathematical Society Cyprus Mathematical Society Constantinos Papagiannis Theoklitos Paragyiou Cyprus Mathematical Society Cyprus Mathematical Society Soteris Loizias Andreas Savvides Cyprus Mathematical Society Cyprus Mathematical Society Savvas Antoniou Andreas Demetriou Cyprus Mathematical Society Cyprus Mathematical Society Tasos Evagorou Anastasia Eracleous-Theodorou Cyprus Mathematical Society Cyprus Mathematical Society Demetris Karantanos Stelios Kouzaris Cyprus Mathematical Society Cyprus Mathematical Society Kyriacos Matheou Theodosis Mourouzis Cyprus Mathematical Society Cyprus Mathematical Society Savvas Timotheou Pieros Faklamas Cyprus Mathematical Society Cyprus Mathematical Society George Chimonides Demetris Christofides Cyprus Mathematical Society Cyprus Mathematical Society CONTACT DETAILS Contact Email [email protected] Contact Phone 00 357 22 283 600 iii EUROMATH & EUROSCIENCE 2019 Conference Proceedings TABLE OF CONTENT PAGE STUDENT PRESENTATIONS IN MATHEMATICS ..................................................................................... 1 MP26. GEOMETRICAL STRUCTUR OF SANTUR AND BAGPIPE FROM VIEWPOINT OF MATHEMATICS ....................................................................................................................................... 1 MP39. THE AREA OF SURFACES WHICH ARE BOUNDED BY THE “BLACK HOLE” FUNCTIONS .................................................................................................................................................................. 8 MP40. SOME INFINITE PRODUCTS ................................................................................................... 17 MP41. MATHEMATIC APPLICATION IN MEDICAL SCIENCE ......................................................... 25 MP51. CONTINUED FRACTIONS ........................................................................................................ 30 MP52. TYPES OF SPACES AND TRANSFORMATIONS BETWEEN THEM ....................................... 37 MP54. MATHEMATICS IN CRYPTOGRAPHY ..................................................................................... 45 MP55. MATHEMATICS AND PHILOSOPHY ....................................................................................... 50 MP56. MATH AND PHYSICS IN BILLIARDS(POOL) .......................................................................... 61 MP65. A DEDUCTIVE DATABASE APPROACH TO AUTOMATED GEOMETRY THEOREM PROVING AND DISCOVERING WITH JAVA GEOMETRY EXPERT.................................................. 68 MP66. LINEARIZATION ........................................................................................................................ 77 MP73.HOW TO WIN A GAME OF PAC-MAN? .................................................................................... 85 MP74. MATHEMATICS IN CRYPTOGRAPHY ..................................................................................... 92 MP76. MATHEMATICS AND DANCE: A UNIVERSAL LANGUAGE .................................................. 99 MP82. THE REAL WORLD OF IMAGINARY NUMBERS .................................................................. 102 MP84. UNLIMITED CAPABILITIES: A REPORT ON VARIOUS SUBTYPES OF ARTIFICIAL INTELLIGENCE ................................................................................................................................... 111 MP86. EUCLIDIAN VS NON EUCLIDIAN GEOMETRY: IS GEOMETRY ONE SIDED? ................. 119 STUDENT PRESENTATIONS IN SCIENCE ............................................................................................ 125 SP4. NEUROLOGICAL DISEASES OF MANKIND AND ANIMALS: AN INSIGHT TO THE SOLUTION OF THE UNSOLVED ........................................................................................................................... 125 SP5. THE EFFECT OF RADON AND RADIOACTIVITY.................................................................... 133 SP7. DRIVING ON A RAINY DAY........................................................................................................ 137 SP16. SPECTROPHOTOMETRY ......................................................................................................... 141 SP17. STEM CELLS .............................................................................................................................. 148 SP19. CHROMATOGRAPHY ............................................................................................................... 155 WORKSHOPS ........................................................................................................................................... 161 WS23. PLAYING WITH FAIR AND BIASED COINS ........................................................................... 161 iv EUROMATH & EUROSCIENCE 2019 Conference Proceedings STUDENT PRESENTATIONS IN MATHEMATICS MP26. GEOMETRICAL STRUCTUR OF SANTUR AND BAGPIPE FROM VIEWPOINT OF MATHEMATICS Parnian Shojaei, Parmida Azizi, Ava Ilami Farzanegan Highschool, Bushehr, Iran ABSTRACT This project is devoted into the two most important sections. Firstly, plenary description of Bagpipe, such as: History, the components of constituent its modulation involves voice leading, specifically discusses on some kinds of topological metrics of musical data related to bagpipe, an abridged history and introduction of the Iranian version of bagpipe called Ney-anban. Secondly one of the eldest classical instruments called Santour which is of the main instruments of Iranian classical music is introduced and some of the mathematical points of its structure are showed. BAGPIPE The Highland bagpipe, considered ‘the national instrument of Scotland, is one of the most recognized and celebrated icons of traditional music in the world. It is also among the least understood by Western musicians and ethnomusicologists alike. But this is beginning to change: Scottish bagpipe music and tradition – particularly, but not exclusively, the Highland bagpipe – has enjoyed an unprecedented surge in public visibility and scholarly attention over the past two decades. Founded mainly on the work of Robin Lorimer, Peter Cooke and Francis Collinson of the Edinburgh school in the 1960s and 1970s, an increasingly eclectic and practice-based corps of scholarship has emerged, bringing to light, as never before, treatment of evidence subject to the performer’s own grasp of his craft. Scholarship has also become increasingly international and reflexive in scope. Bagpipes have been promoted as ‘national’, ‘cultural’ or ‘regional’ instruments – in Scotland, Galician Spain, Brittany, Bulgaria and Ruthenia – and the meanings and political overtones of this need to be more deeply explored. Bagpipe revivals, where an instrument has become extinct. NEY_ANBAN The Iranian version of bagpipe which names Ney_anban, is played in southern Iran. This version of bagpipe even does not have a complete octave (!) but this instrument has a warm sound and most of people enjoy hearing its sound. When old sailors were in a far distance from their home and family, ney_anban and traditional songs and dances helped them to be strong. Obviously 1 EUROMATH & EUROSCIENCE 2019 Conference Proceedings this instrument is not so famous and there is not a regular method for it but musicians are attracting to this instrument more than before. There is a picture of ney_anban below. SANTOUR Santour is an originally Iranian instrument and it is one of the eldest instruments of Asia. This instrument was traded and travelled to different parts of the world and each country customized and designed their own versions to adapt to their musical scales and tunings. The original Santour was made with tree bark, stones and stringed with goat intestines. Santour is also the father of the harp, the Chinese Yangqin, the harpsichord, the Qanun, the cimbalom and the American and European hammered dulcimers. Santour has accepted many changes in different periods of time. And the instrument we call Santour today is the instrument which has been used since about a century ago. The oval-shaped Mezrabs (mallets) are feather-weight and are held between the thumb, index and middle fingers. A typical Persian Santour has two sets of bridges, providing a range of approximately three octaves. The right-hand strings are made of brass or copper, while the left- hand strings are made of steel. Two rows of 9 bridges a total of 18 vaults divide the Santour into three positions. Over each vault cross four strings tuned in unison, spanning horizontally across the right and left side of the instrument. There are three sections of nine pitches: each for the bass, middle and higher octave
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