[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588810-105":59,"doc-detail-588810-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","traditional-patterns-of-easter-eggs-in-the-carpathian-basin-and-spherical-symmetries","TRADITIONAL PATTERNS OF EASTER EGGS IN THE CARPATHIAN BASIN AND SPHERICAL SYMMETRIES","","Analyzing wax-resist Easter egg decorations from the Carpathian Basin, the article identifies which spherical symmetry groups occur and which do not, and explores why these symmetry decorations appear. It first reviews the history of egg decorating and the wax-resist technique, then frames egg motifs through spherical symmetry group classification. Eggs are treated as topologically homeomorphic to the sphere, enabling comparison between egg patterns and spherical symmetry structures.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/traditional-patterns-of-easter-eggs-in-the-carpathian-basin-and-spherical-symmetries/588810/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/traditional-patterns-of-easter-eggs-in-the-carpathian-basin-and-spherical-symmetries/588810.png","ImageObject",300,407,{"name":92,"@type":93},"Chumphorn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Which spherical symmetry groups are studied in the Carpathian Basin Easter egg patterns?","Question",{"text":112,"@type":113},"The article analyzes which spherical symmetry groups can be found among wax-resist decorated eggs in the Carpathian Basin, and which groups cannot be found.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the article connect egg decoration patterns to mathematical symmetry?",{"text":117,"@type":113},"It compares egg motifs with spherical symmetries by using the classification system of spherical symmetry groups, supported by the fact that eggs are topologically homeomorphic to a sphere.",{"name":119,"@type":110,"acceptedAnswer":120},"Why does the article mention both dissymmetry and imperfect symmetry?",{"text":121,"@type":113},"It explains that patterns cannot be completely perfectly symmetrical, partly due to the egg’s geometry and partly due to the nature of human creation.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},588810,1792273275,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":46,"preview_page_count":4},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","TRADITIONAL PATTERNS OF EASTER EGGS IN THE CARPATHIAN BASIN AND SPHERICAL SYMMETRIES  \nEleonóra STETTNER, Rózsa NIENHAUS  \nAbstract: In this article we are analyzing which spherical symmetry groups can be found and which ones cannot among the eggs with wax-resist patterns most frequently used in the Carpathian Basin. We are also trying to answer the question why exactly these symmetry decorations can be found. Before that, we are providing a review on the history of decorating eggs and of the abovementioned decoration technique. By publishing this article, our unconcealed aim is also to make this tradition and the related precious patterns more widely known. The author of the second chapter of the article is Rózsa Nienhaus, the founder of the Egg Art Museum.  \nKey words: spherical symmetry, symmetry group, patterns of easter eggs  \n1. Introduction  \nThe concept of symmetry is inevitable in the relationship between mathematics and art. While preparing for my classes on Mathematics and Art, or for the activities of the Experience Workshop, I was surprised by the richness of symmetries applied in the old, several hundred or sometimes even several thousand-year-old works of folk art. The study of the works and life of the Dutch painter, M.  \nC. Escher leads one inevitably to the patterns of the Alhambra tiles. Surprisingly, all 17 wallpaper groups can be found here (Pérez-Gómez, 1987) . The patterns of the Alhambra were created in the thirteenth-fifteenth centuries A.D. Mathematicians provided a complete classification of the plane crystal groups at the turn of the 19th and 20th centuries. In mathematics it often happens that several mathematicians prove a theorem, independently of one another, almost at the same time. The same happened here. ’In the E2 Eucledean plane there are 17 crystal groups. Their first complete list was published by Fjodorov (1890) along with the 219+11 spatial crystal groups, which were discovered atthe same time by Schoenflies (1891) . Fricke and Klein also dealt with plane crystal groups in 1897, and then György Pólya as well, in 1924. Nowacki described crystal groups in an abstract way.’(Stettner, 2004) .  \nAll 17 groups can be found on authentic Hungarian folk art embroidery works, which were not created in the last 200 years, either (Hargittai & Lengyel, 1985) . Moreover, Szaniszló Bérczi draws attention to the fact that the 7 frieze symmetries can also be found in Hungarian ornamental art from the time of the Hungarian conquest (Bérczi, 2010) . All these frieze symmetries can be found on Hungarian folk art embroidery (Hargittai & Lengyel, 1984), what is more, all of them come up if we only examine embroidery made using a special technique, cross-stitch.  \nA good example of spherical symmetries is the one thousand-year-old Japanese technique of temari. Originally it was a simple toy ball made for children, but nowadays anyone can learn how to create the amazing patterns with the help of several Youtube videos ([http://temari.com/](http://temari.com/)). The article written by Carolyn Yackel and presented at the greatest mathematical art world conference also draws attention to the relationship between art and the mathematical content of temari balls (Yackel, 2011) .  \nI first met egg decorating patterns put in a systematic form in the article of Erzsébet Györgyi (Györgyi, 1974) . Thanks to my relationship with the founder of the Egg Art Museum (Zengővárkony), among several thousands of decorated eggs I had the opportunity to meet various decorating techniques, and to examine and analyze them thoroughly related to our topic. I found that eggs that were made using  \nthe wax-resist technique have the richest symmetry. Thus, the present article studies these ones, and illustrates occurring spherical symmetries using items from the photo collection of the museum.  \n’The vast majority of egg decorations (considered archaic by character) were created with this process, and we have reason to believe that this ","cbCaisbc2tJ8VFNX","https://ap.wps.com/l/cbCaisbc2tJ8VFNX","pdf",727189,"English","# Introduction\n## Symmetry in mathematics and art\n## Plane crystal groups and frieze symmetries\n## Spherical symmetries and technique background\n# From the Bare Egg to the Decorated One","[{\"question\":\"Which spherical symmetry groups are studied in the Carpathian Basin Easter egg patterns?\",\"answer\":\"The article analyzes which spherical symmetry groups can be found among wax-resist decorated eggs in the Carpathian Basin, and which groups cannot be found.\"},{\"question\":\"How does the article connect egg decoration patterns to mathematical symmetry?\",\"answer\":\"It compares egg motifs with spherical symmetries by using the classification system of spherical symmetry groups, supported by the fact that eggs are topologically homeomorphic to a sphere.\"},{\"question\":\"Why does the article mention both dissymmetry and imperfect symmetry?\",\"answer\":\"It explains that patterns cannot be completely perfectly symmetrical, partly due to the egg’s geometry and partly due to the nature of human creation.\"}]","TRADITIONAL PATTERNS OF EASTER EGGS IN THE CARPATHIAN BASIN AND SPHERICAL SYMMETRIES | PDF",1792065980]