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The hamstrings are biarticular muscle group that plays an important role in the occupational performance of military personnel. The single leg hamstring bridge test (SLHBT) could be a good test to screen military personnel performance. The aims of our study were to assess the reproducibility of the SLHBT in the military population and to use receiver operating curve (ROC) analysis to examine the ability of the SLHBT to discriminate between soldiers with poor and good baseline fitness. A cross-sectional study was performed on 201 male members of the Slovenian Armed Forces (SAF). They undertook army physical fitness testing (APFT) and functional physical fitness testing (FPFT), which included the SLHBT. The SLHBT showed acceptable reproducibility in a military setting and had moderate predictive validity to discriminate between soldiers with poor and good overall physical fitness performance using a cut-off value of 20 repetitions. In conclusion, the SLHBT could be a good candidate test for the military population as the ROC analysis showed the ability of the SLHBT to discriminate between soldiers with poor and good baseline fitness. The SLHBT represents a simple and affordable test that can be used to evaluate performance and form preventive guidelines for military personnel.

Many enzymes are composed of several identical subunits which are arranged in some regular fashion and usually comply with some definite symmetry. [1] This symmetry may be approximate or exact and may or may not coincide with the symmetry of crystallographic packing. Purine nucleoside phosphorylases (PNP) are one class of oligomeric enzymes that show interesting properties connected with the interplay of symmetry. [2] There are two main classes of this enzyme: trimeric PNP or “low molecular mass” protein which can be found mostly in eukaryotic organisms, and hexameric PNP or “high molecular mass” protein which can mostly be found in prokaryotic organisms (Figure 1). [3] Interestingly, these two enzyme classes share only 20-30% sequence identity, but the overall fold of the single monomer is similar, and yet this similar monomeric building block makes a different quaternary structure. As part of the ALOKOMP project (alokomp.irb.hr) which tries to understand the allosteric communication between these monomeric subunits, the relational database of PNPs is constructed. As a special subset of this database, an all-to- all overlap of these structures is also made, which makes possible the assessment of symmetry relations in these enzymes using programmatic methods.

Glavna je ideja ovog rada da na postupan i srednjoškolcima prilagođen način predstavi simetriju kao temeljni pojam u fizici molekula i teoriju grupa kao moćan alat za prepoznavanje i klasifikaciju molekula. Uz obilje primjera, pokazano je kako naučiti učenike što su to simetrije u kontekstu molekule, kako dodijeliti simetrije molekularnim vibracijama te kako iskoristiti te simetrije za analizu i predviđanje molekularnog vibracijskog spektra. Također, kreiran je i tutorijal za učenike, korištenjem alata Webmo koji je slobodno dostupan na Internetu. Krajnji cilj je da sa usvojenim znanjima, učenici mogu primijeniti analizu vibracija molekule i procjenu spektra za molekule po želji., The main idea of this thesis is to present symmetry as a fundamental concept in molecule physics and group theory as a powerful tool for recognizing and classifying molecules in a gradual and student - friendly way. With plenty of examples, it is shown how to teach students what symmetries are in the context of a molecule, how to assign symmetries to molecular vibrations, and how to use those symmetries to analyze and predict the molecular vibrational spectrum. Also, there is created tutorial for students, using the Webmo tool, which is freely available on the Internet. The ultimate goal is that with the acquired knowledge, students can apply molecule vibration analysis and spectrum estimation for molecules as desired.

Циљ дисертације је да истражи основе на којима почива Костићево размишљање и његов естетицизам. Наиме, Костић је градио своју естетику на основама симетрије и хармоније, које обједињене укрштајем, касније чине и тежиште његовог поимања стварности. Костић излази из традиционалних оквира посматрања стварности и света, и у много чему, његово размишљање има велики број додирних тачака са размишљањима извесних филозофских претходника, као што су Платон, Хераклит и Хегел. Антика му јебила инспирација на више начина, а пре свега, он је инспирисан Хомеровом Илијадом, и то јасно показује кроз своје естетичке списе. Укрштај је симболичка представа не само света него и уметности, укрштај је првобитна мотивација, јер је само кроз судар опречних принципа и снага он видео и снагу стваралачког израза, те тако он повезује и поезију са филозофијом, утирући пут неким новим естетским параметрима, а и зато што је сматрао да поезија једино уз мисао може да оствари своју потпунију сврху. Хармонија није разумевана на типичан, већ сасвим другачији, антагонистички начин, јер ју је он видео као супротност симетрији, али у исти мах и њену елементарну неопходност за достизање савршенства. Потом је он своју теорију о укрштају применио у свом најзначајнијем песничком остварењу Santa Maria della Salute и о томе ћу посебно писати, као и о његовој мисаоној вези и сличности са бројним филозофима, уз акценат на повезаности са ОскаромВајлдом. Вајлд је, попут Костића, лепоту поставио у центар космоса и својихпромишљања, с тим што Костић лепоту повезује са светлошћу, што је и директан утицај грчке митолошке мисли. Костић види непрекидну борбу супротности као једини пут којим се долази до напретка, и то је типично Хераклитово размишљање, али је сам моменат јединства супротности, као нечег што је њима иманентно, Хегелово одређење. Хегелово јединство супротности је синоним за укрштај, а аутентична снага у борби Хераклитов и Ничеов моменат. На крају, његови естетски списи, укрштај као појам, борба супротности и вера у такво размишљање као основе самог стваралаштва, све то га је водило ка укрштају два опречна принципа- земаљског и небеског у песми Santa Maria della Salute., Cilj disertacije je da istraži osnove na kojima počiva Kostićevo razmišljanje i njegov esteticizam. Naime, Kostić je gradio svoju estetiku na osnovama simetrije i harmonije, koje objedinjene ukrštajem, kasnije čine i težište njegovog poimanja stvarnosti. Kostić izlazi iz tradicionalnih okvira posmatranja stvarnosti i sveta, i u mnogo čemu, njegovo razmišljanje ima veliki broj dodirnih tačaka sa razmišljanjima izvesnih filozofskih prethodnika, kao što su Platon, Heraklit i Hegel. Antika mu jebila inspiracija na više načina, a pre svega, on je inspirisan Homerovom Ilijadom, i to jasno pokazuje kroz svoje estetičke spise. Ukrštaj je simbolička predstava ne samo sveta nego i umetnosti, ukrštaj je prvobitna motivacija, jer je samo kroz sudar oprečnih principa i snaga on video i snagu stvaralačkog izraza, te tako on povezuje i poeziju sa filozofijom, utirući put nekim novim estetskim parametrima, a i zato što je smatrao da poezija jedino uz misao može da ostvari svoju potpuniju svrhu. Harmonija nije razumevana na tipičan, već sasvim drugačiji, antagonistički način, jer ju je on video kao suprotnost simetriji, ali u isti mah i njenu elementarnu neophodnost za dostizanje savršenstva. Potom je on svoju teoriju o ukrštaju primenio u svom najznačajnijem pesničkom ostvarenju Santa Maria della Salute i o tome ću posebno pisati, kao i o njegovoj misaonoj vezi i sličnosti sa brojnim filozofima, uz akcenat na povezanosti sa OskaromVajldom. Vajld je, poput Kostića, lepotu postavio u centar kosmosa i svojihpromišljanja, s tim što Kostić lepotu povezuje sa svetlošću, što je i direktan uticaj grčke mitološke misli. Kostić vidi neprekidnu borbu suprotnosti kao jedini put kojim se dolazi do napretka, i to je tipično Heraklitovo razmišljanje, ali je sam momenat jedinstva suprotnosti, kao nečeg što je njima imanentno, Hegelovo određenje. Hegelovo jedinstvo suprotnosti je sinonim za ukrštaj, a autentična snaga u borbi Heraklitov i Ničeov momenat. Na kraju, njegovi estetski spisi, ukrštaj kao pojam, borba suprotnosti i vera u takvo razmišljanje kao osnove samog stvaralaštva, sve to ga je vodilo ka ukrštaju dva oprečna principa- zemaljskog i nebeskog u pesmi Santa Maria della Salute.

Virtuālās realitātes izmantošanai ir liels potenciāls telpiskās navigācijas pētīšanā, jo tā sniedz iespēju simulēt jebkuras telpas - gan reālas, gan imagināras, tajā pašā laikā lietotājam radot iegremdēšanās sajūtu virtuālajā vidē. Maģistra darbā virtuālās realitātes tehnoloģijas tika izmantotas, lai pārbaudītu, vai telpas spoguļsimetrija ietekmē spēju tajā orientēties. Simetrija ir viens no fundamentālajiem jēdzieniem cilvēka uztverē, tāpēc var sagaidīt, ka telpas simetrijas manipulēšana ietekmēs spēju atrast ceļu tajā. Eksperimenta veikšanai tika izstrādāta virtuālā vide, izmantojot Unity spēļu dzini. Pētījuma rezultātā tika novērota tendence uz to, ka ceļa atrašanai nepieciešamais laiks simetriskajās telpās ir īsāks, salīdzinot ar telpām, kurās simetrija ir izjaukta, kā arī subjektīvi tika uztverts, ka atrast ceļu tajās ir vieglāk., The use of virtual reality is very prospective for studying spatial navigation since it enables simulating any spaces, both real and imaginary, also providing an immersive virtual environment for the user. In the "Perception of spaces with different symmetry in virtual environment" Master's thesis, virtual reality technologies were used to verify that the reflection symmetry of space can influence the users' ability to navigate it. Symmetry is one of the fundamental concepts in human perception, so it can be expected that manipulating the symmetry of the environment can affect the wayfinding ability in it. For the experiment, a virtual environment was developed using the Unity game engine. It was observed that the time elapsed for wayfinding tasks was less in spaces with the reflection symmetry than in less symmetric spaces and that symmetric spaces were subjectively easier to navigate.

Članak tumači životopisne okolnosti nastanka i obilježja ustroja pjesme iz naslova. Interpretacija govori o elementima ljubavne poezije potrage, konzumacije i rastanka u tumačenu tekstu, a naglašena je promjena značenja nastala mijenom naslova. Glede ustroja, istaknut je smisao opetovnosti riječi (floor, hazel, lands…) te njihova povezanost sa Staigerovim tumačenje lirike. Objašnjena je uloga broja osam, svijetlih simbola i simetričnosti u sustavu magijskoga priziva. Tekst raspravlja i o stavu ženskoga elementa u pjesmi. Metodički pristup preporučuje motivacije čitanjem učeničkih sastavaka na temu povezanu s epigrafom iz Shakespeareove drame Antonije i Kleopatra. Prikaz osjećaja kazivača i s time povezane modulacije uz svaki stih pjesme koristan je pri interpretativnom čitanju. Tumače se i rasprave, učenički eseji ili pjesme u prozi o stavu djevojke., The article explains the biographical background and structure of Yeats’ poem, The Song of Wandering Angus. Although biography is significant to the poem, and the sources are well known, the final meaning of the poem, regarding the identification of the girl in the text, remains ambiguous. In the interpretation of the poem elements of the love poetry of quest, consummation and separation, are used stressing significant shifts revealed in changes in the title. As for the structure of the poem, the significance of repetition (floor, hazel, lands, fire…) is analyzed. The role of the symbols of light, symmetry and the number eight is also examined. In the classroom students may be motivated by reading their own short essays on lines from Shakespeare’s Anthony and Cleopatra – which also constitute the epigraph of this paper. It is useful to explore the poem, line by line, by assessing the subject’s feeling and voice modulation during the stage reading. Methodology could also include debates on the trout-girl’s attitude. The exercise may be consolidated in the writing of an essay or a prose poem by having students use motifs from the poem in their texts. Students could also read extracts from Yeats’ memoires and critical essays in their interpretation of the interrelation of motifs.

Inspirirani očitom simetrijom i ljepotom uzoraka ornamenata koje pronalazimo na drevnim zgradama, tkaninama, nakitu, posuđu itd., u ovom diplomskom radu tražit ćemo načine kako klasificirati te uzorke s gledišta matematičara. Matematički gledano, ornamenti su geometrijski ravninski uzorci čija se struktura ponavlja beskonačno mnogo puta u jednom smjeru. Ovisno o izometrijama koje komponiramo dobivamo različite uzorke, a ovisno o tome razlikovat ćemo grupe ornamenata. Grupa simetrija ornamenata naziva se grupa ornamenata i pokaže se da postoji točno sedam grupa ornamenata. Klasifikacija ornamenata po grupama temelji se na kompoziciji nekih od sljedećih izometrija: translacije duž fiksne horizontalne osi L, rotacije za 180° oko točke na osi L, osne simetrije s obzirom na horizontalnu os, osne simetrije s obzirom na vertikalnu os te klizne simetrije. Svaka od sedam grupa ornamenata potkrijepljena je primjerima. Također, prikazan je i primjer prepoznavanja grupe ornamenata na uzorcima na vazi i tradicionalnoj narodnoj nošnji. U posljednjem poglavlju predstavljene su mogućnosti upotrebe ornamenata u modernoj nastavi matematike kroz razne aktivnosti. Inspired by obvious symmetry and beauty of frieze patterns found on ancient buildings, fabrics, jewelry, pots etc., in this thesis we will look for possible ways for classification of those patterns from mathematical point of view. Mathematically speaking, friezes are geometrical planar patterns structured in such a way that they repeat themselves in one direction indefinitely. Depending on isometries combined we get various samples and based on that we discern frieze groups. The symmetry group of a frieze pattern is called a frieze group, and a proof that there are exactly seven types of frieze groups will be presented in the thesis. This classification is based on fact that the only possible motions for the frieze pattern are: translation along a fixed horizontal line L, 180 rotation about point on L, a horizontal mirror through L, vertical mirrors and glide symmetry. Examples will be provided for each of the seven groups. Further on, it will be shown how to recognize a type of group when one is presented with a pattern on an object such as a vase or a traditional Croatian dress. The final chapter considers the possibilities of various friezeusing activities in modern math class.

Inspiracija za diplomsko delo izhaja iz kalejdoskopa in simetričnih oblik, ki nastajajo v njem. V diplomskem delu je opisan proces oblikovanja in izdelave ženske kolekcije oblačil z elementi kalejdoskopa. V teoretičnem delu sem raziskovala sodobno modo in fuzijo med različnimi stili. Predstavila sem primere s podobno inspiracijo v modnem svetu. Opisala pa sem tudi računalniški program Tuxpi, s katerim sem klasične kose oblačil, kot so srajce, suknjiči in plašči, spremenila v simetrične vzorce, ki jih tvori kalejdoskop. V eksperimentalnem delu sem predstavila kolekcijo Kalejdoskop, barvno paleto kolekcije, uporabljene materiale in začetne kolaže. Prikazala sem proces od nastalih vzorcev po vzoru kalejdoskopa do tehničnih rešitev silhuet. Izdelani kosi pa so prikazani tudi s tehničnimi skicami ter fotografijami. Končni rezultat diplomskega dela je sodobna ženska kolekcija s pravilnimi simetričnimi kroji, ki ponazarjajo pogled skozi luknjo kalejdoskopa. The purpose of this bachelor’s thesis is to design women’s wear with kaleidoscope as inspiration. The inspiration for the collection came from the kaleidoscope and symmetric shapes that it makes. The theoretical part presents modern fashion and fusion between different styles. Following is research of already existing collections with the same inspiration. In this part, I also described computer program Tuxpi that helped me create kaleidoscope photos of pre-existing clothes such as blouses, blazers and coats. In the experimental part, I presented the Kaleidoscope collection, the colour palette of the collection, the materials used and the initial collages. I have shown the process from the pictures I created following the example of a kaleidoscope to the technical solutions of silhouettes. Final pieces are also shown in technical sketches and photographs. The final result of this diploma thesis is a women’s collection inspired by the symmetry of kaleidoscope reflections.

Učenici osnovnih škola gotovo redovito izvode pokus krstalizacije modre galice i kuhinjske soli. Modra galica je otrovna i štetna za okoliš, a veće kristale kuhinjske soli teško je dobiti. Umjesto pokusa kristalizacije modre galice i kuhinjske soli bolje je izvesti pokus kristalizacije limunske kiseline i običnoga šećera. Te su tvari jeftine, lako dostupne, biorazgradljive i nisu štetne za okoliš.

To investigate the level of bilateral symmetry or asymmetry between right and left foot center of pressure (COP) trajectory in the mediolateral and anteroposterior directions, this study involved 102 participants (54 females and 48 males). Ground reaction forces were measured using two Kistler force plates during two 45-s quiet standing trials. Comparisons of COP trajectory were performed by correlation and scatter plot analysis. Strong and very strong positive correlations (from 0.6 to 1.0) were observed between right and left foot anteroposterior COP displacement trajectory in 91 participants, 11 individuals presented weak or negative correlations. In the mediolateral direction, moderate and strong negative correlations (from &minus, 0.5 to &minus, 1.0) were observed in 69 participants, weak negative or weak positive correlations in 30 individuals, and three showed strong positive correlations (0.6 to 1.0). Additional investigation is warranted to compare COP trajectories between asymptotic individuals as assessed herein (to determine normative data) and those with foot or leg symptoms to better understand the causes of COP asymmetry and aid clinicians with the diagnosis of posture-related pathologies.

Bakalaura darbā “Saskarnes dizaina lietojamības un estētisko kritēriju analīze” izpētīts, kā cilvēki, ņemot vērā dažādus kritērijus - dzimumu, vecumu, izglītības līmeni un hobijus, mēra saskarnes un saskarņu lietojamību. Mērķis noteikt, vai simetriskas saskarnes vērtētas pozitīvāk par asimetriskām saskarnēm. Noskaidrojot simetrijas un asimetrijas ietekmi mūsdienu dizainā. Darbā ir apskatītas metrikas un metriku izcelsme, pēc kurām iespējams veikt saskarņu novērtēšanu. Darba ietvaros aprakstīta dizaina vēsture un lietojamība, un nozīme mūsdienās. Izzināta estētikas un lietojamības nepieciešamība mūsdienu saskarnēs, izprastas mūsdienu saskarņu pozitīvās īpašības un trūkumi. Bakalaura darba ietvaros, veicot pētījumu, veikta saskarņu analizēšanas rīka izstrāde, kurā atbilstoši noteiktas vērtēšanas metrikas un autora veidotas saskarnes. Izmantojot saskarņu analizēšanas rīku, ievākti dati, un balstoties uz tiem, veikta datu analīze. Saskarņu analīzes rīkā ievietotas autora veidotas saskarnes, kur īpaša uzmanība pievērsta simetrijai un asimetrijai. Izvērtēts, kādām saskarnēm, attiecīgi pēc noteiktajiem kritērijiem - dzimuma, vecuma, izglītības un hobijiem, cilvēki dod priekšroku. Izvērtēta saskarņu lietojamības nozīme., In my Bachelor’s thesis “Analysis of interface design usability and aesthetic criteria” research has been conducted on how people of different age, gender, education and hobbies evaluate interface designs and their usability. The aim is to determine whether symmetrical interfaces are rated more positively than asymmetric ones. Finding out the influence of symmetry and asymmetry in modern design. In this study, the rating metrics of interface designs and their origin are explained; further, the history of design and its usability and meaning nowadays are explored. The necessity of aesthetics and usability of modern interfaces is also studied and the advantages and disadvantages are discussed. In this Bachelor’s thesis, to perform the necessary research, an interface design analysis tool has been developed with proper evaluation metrics and author interfaces. By using this tool, the necessary data has been collected and then analyzed. In this interface evaluation tool, specific interface designs have been included with an emphasis on symmetry or asymmetry. Research results indicate preferred types of interface design according to user’s age, gender, education and hobbies. The importance of usability in interface design has also been explored.

Cilvēki izmanto saskarnes katru dienu, vairākas reizes dienā, ir svarīgi domāt ne tikai par saskarnes funkcionalitāti, bet arī par tās emocionālu pienesumu. Divi svarīgi aspekti, kas spēj ietekmēt lietotāju afektīvās reakcijas ir : saskarnē izmantotās formas un krāsu kombinācijas. Darba teorētiskajā daļā tiek apskatīta formu un krāsu kombināciju emocionālā ietekme : (1) Vai lietotāji pozitīvāk reaģēs uz simetriskām vai asimetriskām formām; (2) kādām krāsu shēmām lietotāji dos priekšroku; (3) kā afektīvās reakcijas atšķiras dažādu lietotāju vidū. Praktiskajā daļā tiek pētīts kādas, emocijas dažādām lietotāju grupām, izraisa saskarnes, kurās izmantotas simetriskas vai asimetriskas formas un harmoniskas vai nepatīkamas krāsu shēmas., People use interfaces daily which emphasizes the importance of thinking not only about the functionality of the interface but also about the emotional contribution the interface can bring to the user. Two important aspects, that can impact users’ affective reactions are shapes and color combinations that are used in the interface. The theoretical part of this work examines the emotional impact that shapes and color combinations can have on users: (1) impact of symmetrical or asymmetrical shapes on users’ affective reaction; (2)preferences in respect to color schemes; (3) affective reactions in different user groups. In empirical part impact of symmetrical or asymmetrical shapes and harmonious or unpleasant color schemes on emotions invoked in different user groups are studied.

Straipsnyje nagrinėjama simetrija kaip taktika spręsti įvairius matematinius uždavinius. Nors mokykliniame matematikos kurse, mokantis geometrijos temų, nagrinėjama ašinė ir centrinė simetrijos, sprendžiami su šiomis simetrijos rūšimis susiję nesudėtingi uždaviniai, tačiau simetrijos panaudojimas galėtų būti kur kas platesnis. Ji ypatingai padeda kaip taktika sprendžiant nestandartinius matematikos uždavinius. Straipsnyje pateikiami šios taktikos pritaikymo pavyzdžiai ir pristatomi simetrijos panaudojimo mokykloje tyrimo rezultatai. The article explores symmetry as tactics in solving various mathematical problems. Although in Mathematics curriculum while learning about Geometry, symmetry is taught and simple straightforward exercises are solved, it is argued that the application of symmetry could be much wider. It is especially useful as a strategy in solving non-standard math problems. The article presents examples of the use of such tactics as well as results from the experiment on the use of symmetry at school.

V raziskavi je predstavljen interdisciplinarni kreativni postopek oblikovanja ploskovnih vzorcev z matematičnimi funkcijami dveh spremenljivk. Na podlagi zasnovanih matematičnih enačb z linearnimi kombinacijami potenc sinusne funkcije smo z računalniškim algebrskim sistemom Wolfram Mathematica generirali trirazsežne grafe, ki smo jih presekali z izbranim številom k vodoravnih ravnin xy na enakomerno ali neenakomerno razmaknjenih nivojih. Dobljene preseke smo projicirali na ravnino z = 0, kjer so nastale ravninske disjunktne unije točkovnic. Z digitalnim prevodom abstraktnih matematičnih zapisov v vizualni medij smo dosegli nazorne vizualne podobe, ki smo jim v ustvarjalnem procesu postavili estetske zahteve. Kriteriji so obsegali likovni potencial periodične konfiguracije, izraznost prvin strukturnih gradnikov in skladnost odnosov v kompoziciji. V nadaljevanju smo ustreznim ravninskim disjunktnim unijam točkovnic z opcionalnimi parametri definirali barvne kombinacije za območja med točkovnicami in grafične atribute konturnih linij, s čimer smo ustvarili enoplastne ploskovne vzorce. Kompozicijsko raznovrstnost smo še povečali z medsebojnim nalaganjem in prekrivanjem različnega števila plasti, ki smo jih s sestavljanjem združili v večplastne konfiguracije. Rezultat raziskovalnega dela je oblikovana matematična kolekcije digitalnih vzorcev, v katero so vključeni enoplastni in večplastni ploskovni vzorci. S sistematično strukturno analizo smo referenčnim površinam vzorcev določili pripadajoče tapetne grupe na podlagi ploskovne organizacije, urejenosti modularnih strukturnih gradnikov in simetrijskih operacij. Realizirali smo tudi digitalno kolekcijo periodičnih vzorcev na osnovi 17 tapetnih grup, kjer smo iz nesimetrične celice izbranega ploskovnega vzorca, skladno z značilnostjo posamezne tapetne grupe, izvedli ustrezne simetrijske operacije in dobljeno simetrično jedrno enoto motiva, s ponavljanjem v pravilnih intervalih, nanizali z vzporednimi premiki znotraj elementarne mrežne strukture. V zaključku smo v galeriji Zeta v ospredje postavili likovno interakcijo gledalca z digitalnimi površinami ploskovnih vzorcev brez zapisa matematičnega ozadja. This research focuses on the creative interdisciplinary process of designing repetitive patterns stemming from periodic functions with two variables. By using Wolfram Mathematica, a computer algebra system, we generated 3D-graphs based on pre-set mathematical functions with linear combination of powers of sinusoidal functions. The latter were then cut by a selected number k on the horizontal xy plane on equal or unequal levels. The cuts were projected onto plane z = 0, where contour maps appeared. With a digital translation of abstract mathematical values onto a visual media, a visual image based on aesthetic concepts was created. The creative criteria were based on the artistic potential of periodic configurations, expressive properties of structural units and the congruence of various compositions. Colour combinations and contour lines were then applied to corresponding contour maps by means of optional parameters, thus creating one-layered repetitive patterns. An even greater diversity of composition was achieved by layering and combining planes into multi-layered configurations. Since the result of this research was to design a mathematical collection with one- and multi-layered repetitive digital patterns, a systematic structural analysis allowed us to define wallpaper groups based on planar distribution, disposition of modular structure units and symmetric operations. A digital collection of periodical patterns based on seventeen wallpaper groups was also created, in which symmetric operations were applied onto an asymmetric cell of a selected repetitive pattern in accordance with the characteristics of the various wallpaper groups. The symmetric unit of one motif which repeats itself in regular intervals was then applied in parallel rows within the elementary grid. Finally, we put up an exhibition at Zeta Gallery, where we focused on the artistic impact which the repetitive patterns, devoid of mathematical groundwork, had on visitors.

Simetrija se može pomoću vizualnog osjeta pronaći u svemu što nas okružuje. Osnovne su vrste simetrije: središnja simetrija, osna simetrija i ravninska simetrija. Provedenim istraživanjem željelo se utvrditi jesu li djeca predškolske dobi sposobna dovršiti simetrične oblike, hoće li djeca starije dobne skupine uspješnije likovno izrazit simetriju od mlađe dobne skupine te utvrditi postoji li značajna razlika između dvodimenzionalnog i trodimenzionalnog likovnog izražavanja simetrije kod djece predškolske dobi. Istraživanje je provedeno u Dječjem vrtiću „Ivana Brlić Mažuranić“ u Slavonskom Brodu. Sudjelovala su djeca iz mlađe i starije odgojne skupine pri čemu je ukupan broj ispitanika bio 20. Prikupljeno je 59 likovnih radova koji su analizirani u radu. Utvrđeno je da su djeca predškolske dobi sposobna dovršiti simetrične oblike, ali su imala poteškoće oko dovršavanja istih. Djeca starije odgojne skupine bila su uspješnija u izražavanju simetrije od mlađe odgojne skupine. Također je utvrđena značajna razlika između dvodimenzionalnog i trodimenzionalnog likovnog izražavanja simetrije kod djece predškolske dobi. Symmetry can be found by visual sensation in everything around us. The ground types of symmetry are: central symmetry, axial symmetry and planar symmetry. The goal of research was to determine whether preschool children are able to complete symmetrical shapes and whether older children will be more successful in expressing symmetry than preschool children and to establish that there is no significant difference in cognition between two-dimensional and three-dimensional symmetry by preschool children. The research was guided by Kindergarten "Ivana Brlic Mazuranic" in Slavonski Brod. Children from the younger and older educational groups participated, with the total number of respondents being 20. There were 59 collected and analyzed art work. Conclusion was that preschool children were able to complete symmetrical forms, that children of the older educational group were more successful in expressing symmetry than preschool children, and that there was a significant difference between two-dimensional and three-dimensional visual expressions of symmetry at preschool children.

Učenici osnovnih škola gotovo redovito izvode pokus krstalizacije modre galice i kuhinjske soli. Modra galica je otrovna i štetna za okoliš, a veće kristale kuhinjske soli teško je dobiti. Umjesto pokusa kristalizacije modre galice i kuhinjske soli bolje je izvesti pokus kristalizacije limunske kiseline i običnoga šećera. Te su tvari jeftine, lako dostupne, biorazgradljive i nisu štetne za okoliš. Ovo djelo je dano na korištenje pod licencom Creative Commons Imenovanje 4.0 međunarodna., Middle school students almost regularly perform experiments of crystallization of copper(II) sulphate pentahydrate and kitchen salt. Copper(II) sulphate pentahydrate is poisonous and harmful to the environment, and larger crystals of kitchen salt are difficult to obtain. Instead of experimenting with the crystallization of copper(II) sulphate pentahydrate and kitchen salt, it is better to carry out crystallization of citric acid and common (table) sugar. These materials are inexpensive, easily accessible, biodegradable, and not environmentally hazardous. This work is licensed under a Creative Commons Attribution 4.0 International License.

Stereokemija je grana kemije koja se bavi proučavanjem prostorne organizacije molekula te istražuje njihovu trodimenzijsku strukturu koja je iznimno važna za određivanje svojstava, ponajprije bioloških karakteristika. Stereokemija se bavi proučavanjem kiralnosti, optičke aktivnosti, te utjecajem prostorne strukture na reaktivnost molekula. Kiralnost je svojstvo predmeta ili molekule koje se očituje u tome da, zbog svoje nesimetričnosti prostornog rasporeda atoma ili molekula, izvorna molekula se ne može preklopiti sa svojom zrcalnom slikom. Molekule mogu biti kiralne ili akiralne. Stereoizomeri se dijele na konformacijske i konfiguracijske od kojih će se više govoriti o konfiguracijskim optičkim stereoizomerima: enantiomerima i dijastereoizomerima. Stereokemija kao znanstvena disciplina usko je povezana s pojmom simetrije. Simetrija se može općenito definirati kao razmjernost i skladnost u rasporedu točaka ili nekih dijelova predmeta u prirodi pa sve do malih molekula. Simetričnim predmetom smatra se onaj koji posjeduje određene elemente simetrije. Te geometrijske veličine mogu biti točka (centar inverzije), pravac ( os simetrije) ili ravnina ( ravnina simetrije). S obzirom na pripadajuće elemente simetrije koje posjeduje određena molekula može se svrstati u određenu točkinu grupu. Točkine grupe mogu se okarakterizirati kao kiralne ili akiralne ovisno o elementima simetrije koji joj pripadaju. Poznavanje simetrija i kiralnosti kao dva usko povezana pojma od velike su važnosti s obzirom na svoju raširenost u svakodnevnom životu.

Uvod: Proteze se uporabljajo kot nadomestilo amputiranega uda. Funkcija proteze je lahko zgolj estetski pomen, v večini pa je namenjena, da se posamezniku vrnejo funkcionalna mobilnost in sposobnost opravljati vsakodnevne naloge. Značilnost proteze neposredno vplivajo na vzorec hoje, zato je potrebno posvetiti veliko pozornosti izbiri primerne proteze za vsakega posameznika. Namen: Namen diplomskega dela je pregled strokovne literature na področju protetičnih stopal. V prvem delu bomo opisali posamezne kategorije, v katere jih uvrščamo, nato pa predstavili njihov vpliv na hojo. Metode dela: Za pisanje diplomskega dela smo uporabili deskriptivno metodo. Iskanje strokovnih člankov je potekalo po podatkovnih bazah Google Scholar, Science Direct in PubMed v mesecu oktober 2017 in v mesecu junij 2018. Članke smo iskali v angleškem in slovenskem jeziku. Izbrali smo članke objavljene v obdobju 2004 do 2018. Vključitveni kriterij pri iskanju: TT enostranska amputacija, obstoječa proteza, primerjava med protetičnimi stopali. Rezultati: Na področju merjenja dolžine koraka, kadence in hitrosti hoje v literaturi med različnimi protetičnimi stopali ni bilo statistično pomembnih razlik. Med povprečnimi vrednostmi SEW se je pokazalo nekaj razlik med posameznimi stopali. Stopalo Talux in Proprio sta v splošnem dosegala višje vrednosti v primerjavi s SACH in SAFE stopali. Primerjave med SACH in SAFE niso pokazale statistično pomembnih razlik, prav tako ne Talux in Proprio med seboj. Razprava in zaključek: Metode analize hoje se običajno ocenjujejo kot časovne, prostorske, kinetične in kinematične spremenljivke med ciklom hoje. Raziskave, ki so primerjale učinkovitost protetičnih stopal glede na dolžino koraka, niso uspele dokazati funkcionalnih razlik. Pri merjenju SEW vrednosti se je pokazalo, da stopala Talux in Proprio rahlo izstopata v primerjavi s SACH in SAFE vendar so razlike med njimi še vedno majhne. Menimo, da lahko razlike v rezultatih v veliki meri pripišemo k različnim spremenljivkam kot so ležišče, razlike v funkcionalnih nivojih med amputiranci in izbor ustreznega merilnega orodja. Introduction: Prostheses are used as a replacement for amputated limbs. The function of the prosthesis can be purely aesthetic, and in most cases, it is intended to return functional mobility to the individual and the ability to perform daily tasks. The feature of the prosthesis directly affects the pattern of walking, so a lot of attention needs to be paid to choosing the appropriate prosthesis for each individual. Purpose: The purpose of this undergraduate thesis is to review professional literature in the field of prosthetic feet. In the first part, we will describe the individual categories in which they are classified, and then present their impact on walking. Methods: The descriptive method was used to write this undergraduate thesis. The search for professional articles was carried out using Google Scholar, Science Direct and PubMed databases in October 2017 and in June 2018. We searched for articles in English and Slovene. We selected articles published in the period from 2004 to 2018. Inclusion criteria in search: TT unilateral amputation, existing prosthesis, comparison between prosthetic feet. Results: When measuring the step length, cadence and walking speed, there were no statistically significant differences in the literature between various prosthetic feet. Among the SEW average values, there were some differences between the individual feet. Talux and Proprio feet generally achieved higher values compared to SACH and SAFE feet. Comparisons between SACH and SAFE did not show statistically significant differences, nor did the comparisons between Talux and Proprio. Discussion and conclusion: Methods of walking analyses are usually evaluated as time, space, kinetic and kinematic variables during a walking cycle. Studies that compared the effectiveness of prosthetic feet with respect to step length have failed to demonstrate functional differences. When measuring the SEW value, Talux and Proprio feet were slightly standing out compared to SACH and SAFE, but the differences between them are still minor. We believe that differences in results can be largely attributed to different variables such as prosthetic socket, differences in functional levels between the amputees and the selection of the appropriate measuring tool.

U ovom Završnom radu je objašnjena teorijska podloga i načelo rada Fluxgate magnetometara i gradiometara te su opisane neke od njihovih primjena. Istaknute su prednosti Fluxgate magnetometara te su uspoređena svojstva različitih izvedbi. Provedena je analiza postojeće izvedbe te je utvrđeno kako postoji značajna asimetrija između sondi i napon pomaka. Bitno je istaknuti važnost smanjenja napona pomaka i otklanjanja asimetrije jer je uređaj namijenjen za mjerenje bioloških magnetskih polja gdje je potrebna visoka osjetljivost. Asimetrija je otklonjena izradom novog para sondi Fluxgate gradiometra i prilagodbom ulazne impedancije. Napon pomaka je smanjen spajanjem promjenjivih otpornika na predviđena mjesta i ugađanjem te pravilnim razvođenjem mase. Sve izmjene na uređaju su detaljno opisane i izneseni su razlozi za njihovu provedbu te je prokomentiran učinak svake od izmjena na rad cijelog uređaja. Na kraju rada je iznesen prijedlog nove izvedbe Fluxgate gradiometra koja bi se mogla primijeniti u magnetokardiografiji i magnetomiografiji. In this BSc Thesis theoretical background and operating principle of Fluxgate magnetometer and gradiometer are explained. Some applications of Fluxgate gradiometer and magnetometer are described. The advantages of Fluxgate gradiometer are described and performances of different implementations are compared. Existing prototype was analyzed and there was found significant asymmetry between two probes and offset voltage. It is important to reduce offset voltage and eliminate asymmetry because device is intended to measure biological magnetic fields (high sensitivity is required). Asymmetry was eliminated by developing a new pair of Fluxgate gradiometer probes and adapting input impedance. The offset voltage was reduced by connecting trimmer resistors and properly connecting ground wires. Every modification on the device is described in detail and the reasons for their implementation are explained. New implementation of Fluxgate gradiometer which could be applied in magnetocardiography and magnetomyography is suggested at the end of the assignment.

In this paper I discuss the phenomenon of mirror image properties in human languages. I give examples from English, Polish, Malay, Gothic, Latin and Classical Greek. Although I take into consideration only a few languages, my paper has further implications, namely, that mirror image properties exist in any language of the world. I start with a description of the natural phenomenon of mirror image and then extend my discussion to language. I talk about mirror image sentences, reduplication, and palindromes. Avtor na podlagi primerov iz angleščine, poljščine, malajščine, gotščine, latinščine in klasične grščine razpravlja o lastnostih zrcalnih podob v človeških jezikih. Kljub upoštevanju omejenega števila jezikov ugotavlja, da je lastnost zrcalne podobe značilnost vseh jezikov sveta. Razprava, ki se začenja z opisom naravnega pojava zrcalne slike in se nadaljuje z opazovanjem tega pojava v jeziku, prikazuje lastnosti zrcalne podobe na primeru stavkov, podvojitev in palindromov.

Knjiga tematizira ružno kao estetičku kategoriju i to na način obrata u odnosu na metafizičku ideju ljepote izraženu skladom, simetrijom i proporcijom koje su postavljene samom idejom kao formom. Autorova je teza kako estetika, koja jest nauk o lijepome, nastaje kao svijest o ružnome, kao misaona, kao misaona, a ne samo osjetilna kategorija kojom filozofija emancipira svijest od zadanosti metafizičkim idealima sklada, simetrije i proporcije. Teza je stoga istaknuta na način da ružno nije više negacija lijepoga nego ima zasebnu bitkovnu odrednicu. U knjizi je tako teza razrađena kroz zasebne pojmove koji bilježe ideju ružnoga poput grotesknoga, disonantnoga, lažnoga, neidentičnoga, neformnoga, zlog, ludoga, bučnoga, dekonstruiranoga, nesuglasnoga i suvišnoga iskazanih u pozicijama Diderota, Schopenhauera, Nietzschea, Adorna, Bataillea, Foucaulta, Attalija, Deridaa, Rancièrea i Nouvela. Autor pokazuje kako se o lijepome nema što misliti jer ono ima privlačnu snagu neovisnu o mišljenju, odnosno ono se bespojmovno i bezinteresno sviđa, dok ružno tjera um na napor mišljenja kako u filozofiji tako i u umjetnosti. Tako estetika ružnoga bilježi jedan emancipacijski smisao u odnosu na dominaciju i imperativ lijepoga kroz kategorije sklada, simetrije i proporcije kojima je opterećen i time neslobodan suvremeni čovjek.

We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2)[superscript 3]×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. The construction suggests a generalization to U(1)[superscript k] factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups., United States. Dept. of Energy. Office of High Energy Physics (Award DE-SC00012567)

Tema ovog rada je simetrijski zasnovana analiza sistema čiji atomi (čvorovi) imaju nenulte magnetne momente (spinove), a čija je dinamika diktirana Hamiltonijanima kvadratne forme po spinovima, tj. spin-spin interakcija je zadata tenzorom drugog reda. U ovoj oblasti se obično koristi isključivo translaciona periodi ˇcnost kristala, dok se ostale simetrije naknadno razmatraju. Stoga je osnovni cilj ove studije uključivanje kompletne simetrije sistema, pre svega u modeliranje magnetnih Hamiltonijana, a potom i u nalaženje njihovih mogućih rešenja u smislu kvazi-klasičnih osnovnih stanja i odgovarajućih nisko-energijskih (heli)magnonskih spektara. Da bi se to efikasno postiglo, rad je metodološki zasnovan na strogom formalizmu koji tretira sisteme čije su geometrijske konfiguiracije invarijantne na podgrupe Euklidske grupe, a interakcije obuhvataju proizvoljan nivo susedstva. Polazeći od osobina Lijeve algebre ugaonih momenata, u kvantno-mehaničkom prostoru stanja definiše se dejstvo grupe, koje, usled principa invarijantnosti hamiltonijana, izdvaja aksijalno-vektorsku reprezentaciju uz odgovarajuća ograničenja na tenzorsko polje interakcije. Zajedno sa tim, hermitičnost hamiltonijana omogućava generalizaciju Morijinih pravila na sve dozvoljene komponente interakcije. Zbog velike dimenzije kvantnog prostora stanja, koja se skalira eksponencijalno sa brojem čvorova, rešenja ovakvih modela su, osim u najjednostavnijim slučajevima, aproksimativna. Tako, ograničavanjem probnog skupa varijacionog problema na separabilna stanja energija postaje funkcional po klasičnim vektorima (na čvorovima), koji, u opštem slučaju, nemaju med¯usobno jednake dužine. Kako je potonji uslov podrazumevan u aproksimaciji srednjeg polja, u radu se razmatraju mogu´cnosti da ovako nad¯eno osnovno stanje bude regularno, tj. invarijantno na neku spinsku grupu. U tu svrhu se pokazuje da se klasifikacija spinskih grupa može izvršiti korišćenjem realnih trodimenzionalnih reprezentacija (spinske reprezentacije) kojima se direktno određuju i sva regularna uređenja (međusobno jednakih dužina). Polazeći dalje od pretpostavke da je model takav da je optimizovan regularno ured¯enim klasičnim spinovima na ˇcvorovima, a ˇcuvaju´ci njihovu prirodu ugaonog momenta, izvedeno je preslikavanje u bozonsku sliku otklona od osnovnog stanja. Time se dinamika niskoenergijskih pobuda svodi na svojstveni problem odgovarajuće beskonačno dimenzione dinamičke matrice koji se, opet zahvaljujući simetriji, lako rešava metodom modifikovanih grupnih projektora. Kako, međutim, u opštem slučaju grupa simetrije može biti smanjena, predlaže se algoritam za rešavanje svojstvenog problema dinami čke matrice koji efektivno koristi celu grupu. Za monoperiodične sisteme koji su opisani jednom od 13 familija linijskih grupa detaljno se analiziraju transformaciona svojstva tenzora interakcije i Morijina pravila, dok se pojmovi izotropnosti i homogenosti prilagođavaju kvazi-jednodimenzionalnoj geometriji. Izdvaja se prototipni Hamiltonijan koji pored XXZ Hajzenbergovog člana ima i Džalošinski- Morijin vektor usmeren duž ose sistema. Pored tenzora, podrobno se klasifikuju spinske reprezentacije i uređenja prve (najvažnije) familije linijskih grupa; uređenja ostalih familija se dobijaju iz prve, u radu predloženim algoritmom. Konačno, navedeni teorijski koncepti se primenjuju na nedavno sintetisanim 13C nanotubama čiji su nuklearni spinovi putem lutajućih elektrona spregnuti dugo-dometnom Ruderman- Kitel-Kasuja-Josida interakcijom. Dobijena raznolikost helimagnetnih faza koje se kontrolišu naponom, osim toga što ukazuje na univerzalno ponašanje svih nanotuba, kandiduje ih, takođe, za spintroničke uređaje. Subject of this work is symmetry based analysis of systems whose atoms (sites) have non-vanishing magnetic moments (spins), and whose dynamics is governed by Hamiltonians of quadratic forms in spins, i.e. spin-spin interaction is given by the second rank tensor. Commonly, in this field, the translational periodicity of a crystal is used only, while the other symmetries are considered afterwards. Therefore, the main aim of this study is inclusion of the full symmetry of systems in the modeling of the magnetic Hamiltonians first, and then in finding their possible solutions, in particular the quasi-classical ground states and the corresponding low-energy (heli)magnons spectra. To achieve this efficiently, the work is methodologically based on rigorous formalism treating the systems whose geometrical configurations are invariant under the subgroups of the Euclidean group, and whose interactions involve arbitrary levels of neighbours. Starting from the properties of the angular momentum Lie algebra, in quantum-mechanical state space group action is defined, which, due to the invariance principle for Hamiltonian, singles out the axial-vector representation and its constrains on the interaction tensor field. Together with that, the hermiticity of Hamiltonian enables us to generalize the Moria’s rules on all of the allowed components of the interaction. Because of the large dimension of the quantum state space, which is exponentially scaled by the numbers of sites, the solutions of such models are approximate, except in the simplest cases. Thus, restricting the trial set of the variational problem to the separable states, the energy becomes a functional over the site classical vectors, which, in general case, do not have mutually equal lengths. Since, in the mean-field approximation the latter condition is defaulted, in this work, the possibilities that the ground state found in this way is regular, i.e. invariant under a spin group, are considered. For this purpose, it is shown that the classification of the spin groups can be performed using orthogonal three-dimensional real representations (spin representations), by which all the regular arrangements (of mutually equal lengths) are directly determined also. Further on, starting from the assumption that a model is optimized by the regularly arranged classical site spins, and preserving their angular momentum nature, the mapping in the bosonic picture of deviations from the ground state is derived. Thereby, the dynamics of the low-energy excitations is reduced to the eigenproblem of the corresponding infinite-dimensional dynamical matrix, which, owing to symmetry again, is easy to solve by the modified group projectors technique. However, since in general case the symmetry group can be lowered, the algorithm for solving the dynamical matrix eigenproblem, which effectively uses the whole group is proposed. For monoperiodic systems, described by one of the 13 families of the line groups, the transformational properties of interaction tensors are analysed in detail, while the notions of isotropy and homogenity are accommodated to the quasi-one-dimensional geometry. The Hamiltonian prototype, which besides the XXZ Heisenberg term has also the Dzyaloshinskii-Moria vector directed along the system axis, is singled out. In addition to the tensors, spin representations and arrangements of the first (the most important) family line groups are classified thoroughly; the arrangements of the rest of the families are to be obtained from these by the algorithm proposed in the work. Finally, the specified theoretical concepts are applied to the recently synthesized 13C nanotubes, whose nuclear spins are coupled by the long-ranged Ruderman-Kittel- Kasuya-Yosida interaction via itinerant electrons. Besides the obtained diversity of the gate-voltage controlabille helimagnetic phases reveals a universal behaviour of all the nanotubes, it makes them to be the candidates for spintronic devices, too.

Hoja in tek sta najosnovnejši in najbolj pogosti obliki gibanja pri ljudeh in pomenita premik od ene točke do druge. Prav tako predstavljata ena izmed najbolj kompleksnih vsakdanjih opravil, pri katerem se ob aktivaciji mišic, potrebnih za gibanje, aktivirajo tudi stabilizatorji trupa, ki skrbijo za vzravnano držo med gibanjem. Na prvi pogled človeško telo izgleda bilateralno simetrično, ko pa pogledamo bolj natančno, naletimo na opazne razlike, ki kažejo na nesimetrijo človeškega telesa. Ta nesimetrija človeškega telesa se kaže tudi v oblikah gibanja, ki navzven izgledajo simetrično. Analiza merjenja gibanja ima dolgo zgodovino, a s pojavom instrumentaliziranih tekalnih stez in snemanjem kinematike gibanja so te raziskave postale bolj natančne in enostavnejše za izvedbo. Namen diplomske naloge je primerjava reakcijskih sil podlage med bosonogim tekom in tekom v supergah pri različnih hitrostih teka, izračun indeksov simetrije in nesimetrije silami podlage in pokazati, da obutev ali hitrost teka ne vpliva na simetrijo oziroma nesimetrijo in njeno velikost med tekom. Walking and running are the most basic and also most common forms of human movement from one point to another. Walking and running are also one of the most complex everyday tasks in which the required muscles for movement also trigger torso stabilizers for upright posture during movement. From a superficial point of view, the human body has a bilaterally symmetrical shape, but examined more precisely, we find noticeable differences that indicate human body asymmetry. This asymmetry of the human body is also mirrored in the form of movement, which externally appears symmetrical. Analysis and measurement of the gait cycle has an extensive history, but with the emergence of instrumented treadmills and recording of movement kinematics, these studies have become more precise and simpler to execute. The purpose of this thesis is the comparison of the reaction ground forces between barefoot and shoe running at different speeds, calculating indices of symmetry and asymmetry based on ground reaction forces and to show that shoes or running speed does not affect the side or size of symmetry or asymmetry between legs.

The presented review on chirality is dedicated to the centennial birth anniversary of Nobel laureate Vladimir Prelog and 160 years of Pasteur's discovery of chirality on tartrates. Chirality has been recognized in nature by artists and architects, who have used it for decorations and basic constructions, as shown in the Introduction. The progress of science through history has enabled the gathering of knowledge on chirality and its many ways of application. The key historical discoveries about the rotation of polarized light as a consequence of molecular chirality and findings of Pasteur and Lord Kelvin are described. Chirality can be found in physics of elementary particles and in many fields of chemistry: analytical and organic chemistry, chemistry of natural compounds, medicinal and pharmaceutical chemistry, biochemistry and biotechnology, and molecular biology. The development of knowledge about chirality and its physical background are briefly described. Definitions for geometrical, topological, and conformational chirality are given accompanied by numerous examples of molecules exhibiting such features. The relations between symmetry and chirality in crystallography are exposed. X-ray crystallography is a method of choice for unambiguous determination of molecular architecture, including the absolute configuration of the molecule using Bijvoet's approach. Two methods of determination of absolute configuration by X-ray diffraction and circular dichroism are briefly discussed. To mark two significant jubilees, the essay is dedicated to the role of chirality in stereochemistry. Stereochemistry is not a branch of chemistry but rather a view at chemistry, as considered by E. L. Eliel; this approach is respected in the essay presented. This very approach leads to various aspects of chirality and brings to the consistency of many definitions. The future will bring us knowledge on the role of chirality in communications among molecules, which guide our life processes. The synthesis of various dynamically chiral supramolecules from achiral molecules and preparations of conjugated homochiral polymers will offer new types of biosensors, artificial enzymes and some sophisticated materials. Theresearch of isotopic chirality by quantum-chemical methods reveals some parity-violating effects and shed more light on the physical bases of molecular chirality.

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