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TESELACIJE
TESSELLATION

Autor:МINА ŠЕKULАRАC I rаzrеd „Matematiĉka gimnazija”, Bеоgrаd
Меntоr:VЕSNА RАЈŠIĆ, prоfеsоrmаtеmаtikе Еlеktrоtеhniĉkа škоlа „Nikоlа Теslа”,
Bеоgrаd

REZIME
Prisustvo razliĉitih geometrijskih figura koje u pravilnom redu prekrivaju površine moguće je videti na podovima i
zidovima mnogih arhitektonskih objekata i spomenika kulture. Ovako dobijene šare nastale preciznim uklapanjem
geometrijskih oblika, bez meĊusobnog preklapanja i ostavljanja slobodnog prostora mogu se videti i na mozaicima,
vitraţima, kao i na šarama na posudama.
Ono što me je podstaklo na istraţivanje u ovoj oblasti jeste saznanje da je formiranje površina pomoću geometrijskih
šara, istraţeno u matematiĉkoj oblasti nazvanoj teselacije. Pojam teselacije definisan je u matematici tek u XVII veku,
iako se od antiĉkih dana ĉovek bavio geometrijskim figurama i njihovim kombinovanjem u cilju prekrivanja površina.
Primena teselacija prisutna je nа rаznim mеridiјаnimа, u mnоgim kulturаmа i krоz vrеmеnskе еpоhе pоlаzеći оd
nајјеdnоstаvniјih poploĉavanja pа dо fаntаstiĉnih geometrijskih kombinacija, prаtеći оdrеĊеni slеd i dоlаzеći dо istih
lоgiĉkih оbrаzаcа i istih rеzultаtа. Јеdаn оd rаzlоgа оdаbirа оvе tеmе је i njеna univеrzаlnоst u vrеmеnu i
prоstоru.Danas se princip teselacije primenjuje u mnogim oblastima, u tekstilnoj industriji, pri izradi raznih dezena
tekstila, u graĊevinarstvu, u dizajniranju elemenata podnih i zidnih obloga, u umetnosti, u mnogim naukama, u optici i
kristalografiji. Teselacije su prisutne i u društvenim igrama, u deĉijim igrama slagalica kao i u sloţenim
kompjuterskim igricama. U kompjuterskoj grafici i u dizajnu danas se u velikoj meri primenjuju teselacije.
Klјuĉnе rеĉi: teselacije,geometrijske figure, monoedarske teselacije, 1-uniformne teselacije, pravilne teselacije.

SUMMARY

There are numerous different geometric figures that in proper order cover surfaces of floors and walls of many
architectural structures and monuments. These patterns are made by precise geometrical shape matching, with neither
overlaps nor gaps, are included in various mosaics, stain glasses and pottery patterns.
What inspires me to research this area is finding out about various types of surface that can be created by applying
th
geometric patterns – which has been explored within a field of mathematics called tessellations. Not until the 17
century was the term tessellation defined in mathematics, in spite of the fact that ever since the ancient times men have
been dealing with geometric figures and their combination possibilities for the purpose of surface covering. The
application of tessellation has been used in many cultures all over the world, from the simplicity of tiling itself till
amazing geometric combinations, paying attention to specific order and reaching the same logical forms and
outcomes. One of the main reasons for choosing this very topic is its universal quality in time and space. Nowadays,
the principle of tessellation is applied in numerous fields, textile industry, textile patterns, construction, design
elements of both floor and wall cladding, art, science, optics and crystalgraphics. Also, tessellations are included in
various board games, children’s puzzle games and complex computer games. Computer graphics and design are based
on the application of tessellations.

Keywords: tessellations, geometric figures, monohedral tessellations, 1-uniform tessellations, regular tessellations.