Matematika ir muzika atrodo visiškai skirtingos sritys, tačiau yra glaudžiai susijusios. Matematiniai aspektai gali būti randami muzikoje, taipogi kūrybiniai požymiai gali būti rasti matematikoje, bet pastarųjų savo darbe aš nenagrinėju. Senovės Graikijoje muzika buvo laikoma griežta matematine disciplina. Pitagoriečių mokymo planas „quadrivium“ apėmė keturis mokslus: aritmetiką, muziką, geometriją ir astronomiją. Taipogi yra pastebėta, kad vaikai, besimokantys muzikos, yra gabesni sprendžiant galvosūkius, darant matematines išvadas, su tuo taipogi glaudžiai susijęs taip vadinamas „Mocarto efektas“, manoma, kad V. A. Mocarto kūrybos klausymas gerina žmonių matematinius bei erdvės suvokimo gebėjimus. Savo darbe, remiantis įvairiais šaltiniais, aš nagrinėju matematinius aspektus atsirandančius muzikoje. Darbas susideda iš tokių temų, kaip garso bangos, disonansas ir konsonansas, gamos ir temperacijos, simetrija muzikoje, aukso pjūvis muzikinėse kompozicijose. Paskutiniame skyrelyje aš aprašau L. van Bethoveno kūrinio „Švilpikas“ interpretaciją MadtTracker programoje. Darbas galėtų būti naudingas besimokant matematikos, atskleidžiant jos pritaikomumą muzikoje, tokiu būdu sudominant pačia matematika. / It may look odd that mathematics and music, which seem to be completely different areas, are closely related to each other. Mathematical aspects can be found in music and vice versa, mathematics contains many examples of creative work, however, the latter is not the object of interest in this theses. In ancient Greece music was considered strictly as a mathematical subject. Pythagoreans' teaching plan “quadrivium” involved four subjects: arithmetics, music, geometry and astronomy. It is also noticed that children who study music have better skills in solving puzzles, drawing mathematical conclusions. This is also closely related to so called „Mozart effect“: it is believed that listening to W. A. Mozart improves one's mathematical skills. In this theses mathematical aspects obtained in music are analyzed with reference to various sources. Theses includes such topics as sound waves, dissonance and consonance, scales and temperaments, symmetry in music, golden mean in musical compositions. Last chapter provides an interpretation of “Ground-hog” by L. van Beethoven with MadTracker software. The thesis could be useful in studying mathematics and applying it in music. Such application might as well increase interest in mathematics itself.

After amputation possibilities of human body motion are very limited. Amputation usually changes inert characteristics of human body parts and asymmetry of gait is visible. After prosthetics, gait with prosthesis remains asymmetric in relation with impaired body balance control. Loss of proprioreception in amputated side reduces regulation of stance. To retrieve stance skills and to train body balance pneumatic prosthesis is usually applied. The aim of this investigation was to assess influence of pneumatic prosthesis to stance and walking characteristics. To achieve this aim there were two main objectives 1) to evaluate influence of pneumatic prosthesis to stance symmetry in early period of prosthetics; 2) to evaluate influence of pneumatic prosthesis to gait symmetry in early period of prosthetics. Investigation was conducted using computerised pedobarograph „Parotec System“. Changes of weight center position were analyzed at the beginning and the end of rehabilitation period, time characteristics of weight bearing phases were assessed, vertical force and index of gait asymmetry were calculated. Investigation was performed at the department of Physical medicine and rehabilitation of Joint-stock company „Ortopedijos technika“. Patients who underwent below knee amputation were included. Testing was performed twice for every patient: at the beginning and the end of prosthetics. Weight center position in regard to both lower limbs was analyzed. At the end of prosthetics gait... [to full text]