tag:blogger.com,1999:blog-83846545996739516102024-03-13T16:04:39.955-07:00Ádám AnitaTanár - képzőművészÁdám Anitahttp://www.blogger.com/profile/11736367907214966643noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-8384654599673951610.post-46869634723376809122015-08-07T05:44:00.006-07:002016-01-24T05:35:24.652-08:00<div style="text-align: center;">
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<span style="color: #ffd966; font-weight: normal;">SZÖGHARMADOLÁS / TRISECTIO</span></h2>
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Egy híres ókori probléma újszerű megközelítése és megoldása </span></h4>
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<span style="font-family: inherit; font-weight: normal; text-indent: -18pt;">The new approach and solution of a
famous ancient problem</span></h4>
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<span style="line-height: 24px; text-align: justify;">A kör </span><span style="line-height: 24px; text-align: justify;">és a hozzátartozó</span><span style="line-height: 24px; text-align: justify;"> </span><span style="line-height: 24px; text-align: justify;">ortogonális rendszer ( 'r' </span><span style="line-height: 24px; text-align: justify;">egyenlő oldalú, centrális kereszt) </span><span style="line-height: 24px; text-align: justify;">szerkezeti kapcsolata által </span><span style="line-height: 24px; text-align: justify;"> </span><span style="line-height: 24px; text-align: justify;"> különleges szögeket is kaphatunk, mint pl. 20⁰, 40 ⁰... stb., valamint nem-euklideszi szerkesztéssel a szögharmadolás is megoldható.</span><br />
<span lang="EN-GB" style="font-family: inherit; line-height: 150%;">With the structural connection of the circle and the relevant orthogonal
system ('r' equal side-length central cross) we can get special angles,
such as 20</span><span lang="EN-GB" style="font-family: inherit; line-height: 150%;">⁰</span><span lang="EN-GB" style="font-family: inherit; line-height: 150%;">, 40 </span><span lang="EN-GB" style="font-family: inherit; line-height: 150%;">⁰</span><span lang="EN-GB" style="font-family: inherit; line-height: 150%;">... etc., and the trisection can be
solved by non Euclidean drawing.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">copyright </span><span style="line-height: 24px;">© 2014. 07.10. </span></div>
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<span style="line-height: 24px;">Lektorálta: Ruff Feremc </span></div>
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<span style="line-height: 24px;"> matematika - fizika szakos egyetemi tanár</span></div>
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<span style="line-height: 24px;">Translated by Tímea Rezsnyák</span></div>
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Ádám Anitahttp://www.blogger.com/profile/11736367907214966643noreply@blogger.com0tag:blogger.com,1999:blog-8384654599673951610.post-82260137525548136362014-10-07T11:04:00.000-07:002018-07-21T21:38:57.823-07:00<div style="text-align: center;">
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TERMÉSZETI ALAPFORMÁK </span></h4>
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<span style="font-size: medium; font-weight: normal;">BASIC SHAPES OF NATURE</span></h4>
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<span style="line-height: 150%;">A természeti törvények
kölcsönhatásai következtében környezetünk különböző színterein </span><span style="line-height: 150%;">párhuzamosan ismétlődő formai struktúrák figyelhetők meg, melyek megjelenésében
az </span><span style="line-height: 150%;">ív</span><b style="line-height: 150%;"> </b><span style="line-height: 150%;">szerepe </span><span style="line-height: 150%;">és előfordulása meghatározó jelentőségű.</span><span style="line-height: 150%;"> </span><br />
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<span style="line-height: 150%;">A gömb egyetemessége folytán számos természeti forma kiindulási alapja. </span><span style="line-height: 150%;">Módosulatai, metszetei, részletei, geometriai rendszerei </span><span style="line-height: 150%;">természeti formakincsünk fontos alkotórészei. </span></div>
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<span style="line-height: 150%;">A természeti formák elemzése során </span><span style="line-height: 150%;">gyakran találkozhatunk dinamikus formakapcsolatokkal - melyek további morfológiai
tulajdonságaikat vizsgálva - </span><span style="line-height: 150%;"> </span><span style="line-height: 150%;">áramvonalas </span><b style="line-height: 150%;"> </b><span style="line-height: 150%;">alakzatokra egyszerűsíthetők.</span></div>
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<span style="line-height: 150%;">A formai redukciók </span><span style="line-height: 150%;">szimmetrikus és aszimmetrikus </span><span style="line-height: 150%;">formákat eredményezhetnek, melyek szerkezeti felépítésében spirális elrendeződések </span><span style="line-height: 150%;">fedezhetők fel.</span></div>
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<span style="line-height: 150%;">Spirális rendszerek az
egyetemes fizikai törvényeknek köszönhetően számtalan esetben jöhetnek létre az
anyag -és energia áramlás különböző szintjein, ezért az áramvonalas befoglaló alakzatok </span><span style="line-height: 150%;">univerzális </span><span style="line-height: 150%;"> </span><span style="line-height: 150%;">alapformáknak is
felfoghatók.</span><o:p></o:p></div>
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<span style="line-height: 150%;"><span style="line-height: 150%;">Alaktani jellegzetességeiket a tartalmi sajátosságaiban rejlő dinamikai tulajdonságok és a külső erők </span><span style="line-height: 150%;">együttesen alakíthatják.</span></span></div>
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<span style="line-height: 150%;">Térdinamikai szempontból a rész-egész-viszonyrendszer tükrében meghatározó szerepet játszanak a </span><span style="line-height: 150%;">folyamatosan változó formai kölcsönhatásokban.</span></div>
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<span style="line-height: 150%;">Vizuális és esztétikai
értelemben sokszínű megjelenésüknek köszönhetően összhangot képesek </span><span style="line-height: 150%;">teremteni az egymástól függetlenül létező és funkcionálisan is eltérő
természeti struktúrák között.</span></div>
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<i>Ádám Anita<o:p></o:p></i></div>
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<span lang="EN-GB" style="font-family: "times" , "times new roman" , serif; line-height: 115%;"><br /></span>
<span lang="EN-GB" style="font-family: "times" , "times new roman" , serif; line-height: 115%;">Due to natural
interaction of the rules of the nature, side by side repeated shape structures
can be seen on different levels of our environment and the role and occurrence
of arch is of crucial significance in their appearance.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: "times" , "times new roman" , serif; line-height: 115%;">Glob is the
starting points of several natural shapes because of their universalities.
Its alterations, geometric systems and details are major elements of our natural
shape treasure.<o:p></o:p></span></div>
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<span lang="EN-GB" style="font-family: "times" , "times new roman" , serif;">In the course of natural shape analysis, dynamic shape relations can often
be seen, which can be simplified as symmetrical and unsymmetrical streamline
shapes after further examinations of their morphologic features.<o:p></o:p></span></div>
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<span style="font-family: "times" , "times new roman" , serif;">In the most typical projections
of streamline shapes spiral arrangements can be found.</span></div>
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<span style="font-family: "times" , "times new roman" , serif;">Owing to the universal physical laws helical or spiral systems can be
created in many cases on the different levels of material and energy flows,
therefore the streamline overall shapes can be regarded as universal basic
shapes.</span></div>
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<span style="font-family: "times" , "times new roman" , serif;">Their typical shape features can be formed collectively by their dynamic
features hidden in their base feature and outer forces. </span><br />
<span style="font-family: "times" , "times new roman" , serif;">Space dynamically, they have major roles in the continuously changing shape
interactions, in the mirror of part-total relationship system,</span></div>
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<o:p></o:p></span>
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<span lang="EN-GB" style="font-family: "times" , "times new roman" , serif; line-height: 150%;">In visual and aesthetic sense,
they can provide harmony between the independently existing and also
functionally independent natural structures due to their multi-coloured
appearance.<o:p></o:p></span><br />
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<i><span lang="EN-GB" style="font-family: "times new roman" , serif;"><span style="font-family: "times" , "times new roman" , serif;">Anita Adam</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></span></i></div>
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A természeti formák egyedi megjelenésük folytán geometriailag nem tökéletesek, ezért a befoglaló alakzatok csupán közelítő jellegűek és elsősorban formai karakterként értelmezendők. <br />
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;">The natural shapes due to
their unique appearance are not perfect geometrically; therefore the overall
shapes are only approximate and can be defined mostly as shape characters.<o:p></o:p></span></div>
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<i> </i><span style="line-height: 150%;">A gömb és a kör mint a középpontosan
szimmetrikus elrendeződések befoglaló alakzata</span></div>
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;">The
globe and circle as the overall shapes of centrally symmetric arrangements <o:p></o:p></span><br />
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<span style="line-height: 150%;">A körből eredeztethető szimmetrikus
és aszimmetrikus természeti alapformák és dinamikus formai kapcsolatok<b><o:p></o:p></b></span><br />
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">Symmetrical and unsymmetrical natural </span><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">basic shapes originated from
circles, and dynamic shape relations<span style="font-size: 13.5pt;"><o:p></o:p></span></span></div>
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<span style="line-height: 150%; text-align: justify;"><b>SPIRÁLIS ELRENDEZŐDÉSEK KÖZVETLEN MEGJELENÉSE</b></span><br />
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">THE IMMEDIATE APPEARANCE OF SPIRAL ARRANGEMENTS</span></div>
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<span style="text-align: justify;"><span style="line-height: 150%;">Spirális rendszerek az egyetemes fizikai törvényeknek köszönhetően számtalan esetben jöhetnek létre az anyag -és energia áramlás különböző szintjein. </span></span><br />
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<span lang="EN-GB">Owing to the
universal physical laws spiral systems can be created in many cases on the
different levels of material and energy flows.<span style="font-size: 13.5pt;"><o:p></o:p></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfTeGiCxYqMETy-8Zrx7uDxaCc0sU_wUYLutCOyrIRDZeatmAkzEsOon2HXpvnfApRcteMAG_ZuH66dm8MzhbtpDojwzUpIfwZjhyOCSviZX8cIofQjGj7653BqcLW66TsEYIoN89ug9k/s1600/N%C3%A9vtelen-5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfTeGiCxYqMETy-8Zrx7uDxaCc0sU_wUYLutCOyrIRDZeatmAkzEsOon2HXpvnfApRcteMAG_ZuH66dm8MzhbtpDojwzUpIfwZjhyOCSviZX8cIofQjGj7653BqcLW66TsEYIoN89ug9k/s1600/N%C3%A9vtelen-5.jpg" width="640" /></a></div>
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<b>ÁRAMVONALAS ALAPFORMÁK</b></div>
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<span style="font-family: "times new roman" , serif; line-height: 150%;">STREAMLINE BASIC SHAPES </span></div>
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<v:oval id="_x0000_s1035" style="height: 51.05pt; left: 0; margin-left: 15.8pt; margin-top: 9.4pt; position: absolute; text-align: left; width: 51.05pt; z-index: 251763712;"><v:shape alt="tengericsillag_11.jpg" id="Kép_x0020_14" o:spid="_x0000_s1043" style="height: 77.45pt; left: 0px; margin-left: 354.4pt; margin-top: 171.85pt; position: absolute; visibility: visible; width: 77.5pt; z-index: 251666432;" type="#_x0000_t75"><br /></v:shape><v:shape alt="tengericsillag_11.jpg" id="Kép_x0020_14" o:spid="_x0000_s1043" style="height: 77.45pt; left: 0px; margin-left: 354.4pt; margin-top: 171.85pt; position: absolute; visibility: visible; width: 77.5pt; z-index: 251666432;" type="#_x0000_t75"><br /></v:shape><v:shape alt="tengericsillag_11.jpg" id="Kép_x0020_14" o:spid="_x0000_s1043" style="height: 77.45pt; left: 0px; margin-left: 354.4pt; margin-top: 171.85pt; position: absolute; visibility: visible; width: 77.5pt; z-index: 251666432;" type="#_x0000_t75"><br /></v:shape></v:oval></div>
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<span style="line-height: 150%;">A szimmetrikus és aszimmetrikus</span><span style="line-height: 150%;"> áramvonalas formák legjellemzőbb vetületeinek szerkezeti felépítésében</span><span style="line-height: 150%;"> spirális elrendeződések </span><span style="line-height: 150%;">fedezhetők fel.</span></div>
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<span lang="EN-GB" style="font-family: "times new roman" , serif;">In the most typical
projections of symmetrical and unsymmetrical streamline shapes spiral
arrangements can be found.<o:p></o:p></span></div>
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<span style="line-height: 150%;"><br /></span></div>
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<span style="line-height: 150%;">A derékszögű háromszögekből és a hozzájuk rendelt körívekből logaritmikusan felépülő fraktál spirál geometriai összefüggéseivel megközelítő pontossággal modellezhető számtalan természeti forma befoglaló alakzata.</span></div>
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<span style="font-family: "times new roman" , serif;"><span style="line-height: 24px;">The overall shapes of many natural shapes can be described precisely with the geometric correlations of logarithmically from right-angled triangles built up fractal spiral arrangements </span></span></div>
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<span style="line-height: 150%;">Logaritmikusan felépülő fraktál spirál / </span><span style="font-family: "times new roman" , serif; line-height: 150%;">Logarithmically built up fractal spiral</span><span style="font-family: "times new roman" , serif; line-height: 150%;"> </span><span style="line-height: 150%;">:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE2Kz_NWqx70TfaM-IN_hotsOEKfnZJRQ4x62T5wUPvDvNwOT3-ZufE60XU6Vp9yM5pG7sD_c5pQ8ToC8IipXZanqxV3pY7tGeP_JDOwqG9FlPly7uUSGdbie9sdwamfy2QJP6kpxYp-k/s1600/45+fok.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="208" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE2Kz_NWqx70TfaM-IN_hotsOEKfnZJRQ4x62T5wUPvDvNwOT3-ZufE60XU6Vp9yM5pG7sD_c5pQ8ToC8IipXZanqxV3pY7tGeP_JDOwqG9FlPly7uUSGdbie9sdwamfy2QJP6kpxYp-k/s320/45+fok.jpg" width="320" /></a></div>
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<span style="font-size: 12.0pt; line-height: 115%;"><b>TERMÉSZETI ANALÓGIÁK</b></span><br />
<span style="line-height: 115%;"><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;"> NATURAL
ANALOGIES<br />
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Központi szög / <span style="font-family: "times new roman" , serif; line-height: 115%;">Central
angle</span><span style="line-height: 150%;">: 12⁰</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicBaM3fIA4vLeYDXT-hpiSFL3GExIZK-pQn_G2OpNXzl2UaTycOZ6bIrD2YRk4AAG-jiR7SrI1-FedwJEQ8FwRj9Qk9LqMilaLKgWYJm9DLDm_VDs_9b0xiwFQiXpPuYbgD_cN6BOisvw/s1600/amonitasorszerk_blog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="111" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicBaM3fIA4vLeYDXT-hpiSFL3GExIZK-pQn_G2OpNXzl2UaTycOZ6bIrD2YRk4AAG-jiR7SrI1-FedwJEQ8FwRj9Qk9LqMilaLKgWYJm9DLDm_VDs_9b0xiwFQiXpPuYbgD_cN6BOisvw/s1600/amonitasorszerk_blog.jpg" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU5120X0JLBh47RGgbQ-KHwDzJZDzoG13aTUWTHmNl7IX5UJzxyb5P4Drr-uWKZoOdovUB3E87RRoYS8lPqQeGFR04sk6HKQD0P8Y-nDTF-JH7Mra2VWudw2KoC1UWNsT6nfxiYefiDqg/s1600/amcsik_blog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="177" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU5120X0JLBh47RGgbQ-KHwDzJZDzoG13aTUWTHmNl7IX5UJzxyb5P4Drr-uWKZoOdovUB3E87RRoYS8lPqQeGFR04sk6HKQD0P8Y-nDTF-JH7Mra2VWudw2KoC1UWNsT6nfxiYefiDqg/s640/amcsik_blog.jpg" width="640" /></a></div>
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<span style="font-family: "calibri" , sans-serif; line-height: 115%;"><span style="font-size: x-small;">Ammonita
/ <i>Ammonoidea</i></span></span></div>
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<span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 115%;"><i><br /></i></span>
<span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 115%;"><i><br /></i></span></div>
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<b>SPIRÁLIS RENDSZEREK KÖZVETETT MEGJELENÉSE</b><br />
<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;"> THE INDIRECT APPEARANCE OF SPIRAL SYSTEMS </span><span lang="EN-GB" style="font-family: "times new roman" , "serif"; font-size: 13.5pt; line-height: 115%;"><br />
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<b style="line-height: 24px;"><span style="font-weight: normal; text-align: justify;">A</span><span style="font-weight: normal; text-align: justify;">z áramvonalas formák legjellemzőbb vetületeiben </span><span style="font-weight: normal; text-align: justify;">megfigyelhető spirális elrendeződések</span></b><br />
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<b style="line-height: 24px; text-align: center;"><span style="font-weight: normal; text-align: justify;"><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">Spiral arrangements in the
most typical projections of streamline shapes</span></span></b></div>
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<span style="font-size: small; line-height: 24px;">Központi szög / </span><span style="font-size: small; line-height: 24px; text-align: justify;"> </span><span style="font-family: "times new roman" , serif; font-size: small; line-height: 18.4px; text-align: justify;">Central angle</span><span style="font-size: small; line-height: 24px;">: 45</span><span style="font-size: small; line-height: 24px; text-align: justify;">⁰</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-1N4wl0JCVdlsPoyjwBFvWacrn2IvO-uxpdkMwMmm0BMFTJ2dY6GbaFp4Qa8wLblaI3uaw1vqKMeEpS6mjEhiheaRMCfXt6bb7dQq_SSyIUFw1Yl-3TUgr6E8M3sfkuseSEqsknRNKUc/s1600/45FOKSZERKSOR.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="91" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-1N4wl0JCVdlsPoyjwBFvWacrn2IvO-uxpdkMwMmm0BMFTJ2dY6GbaFp4Qa8wLblaI3uaw1vqKMeEpS6mjEhiheaRMCfXt6bb7dQq_SSyIUFw1Yl-3TUgr6E8M3sfkuseSEqsknRNKUc/s1600/45FOKSZERKSOR.jpg" width="400" /></a></div>
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<b><span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 115%;"><br /></span></b>
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<a href="http://4.bp.blogspot.com/-s7y_c184wnQ/VDFA4RJJPEI/AAAAAAAACNE/XYibLbF-JkM/s1600/levelek.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="188" src="https://4.bp.blogspot.com/-s7y_c184wnQ/VDFA4RJJPEI/AAAAAAAACNE/XYibLbF-JkM/s1600/levelek.jpg" width="640" /></a></div>
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<b style="line-height: 24px; text-align: center;"><span style="font-weight: normal; text-align: justify;"><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 18.4px;"><span style="font-family: "times new roman"; font-size: small; line-height: 24px; text-align: left;">Központi szög / </span><span style="font-family: "times new roman"; font-size: small; line-height: 24px;"> </span><span style="font-family: "times new roman" , serif; font-size: small; line-height: 18.4px;">Central angle</span><span style="font-family: "times new roman"; font-size: small; line-height: 24px; text-align: left;">: 60</span><span style="font-family: "times new roman"; font-size: small; line-height: 24px;">⁰</span></span></span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhowBQgxNfFN6RKHFhls9tcbR3gwFBx4ilUGsL6UxOrv8e-99vtohVzZgpwPmvEAVezsZtbyPaA33iq__vbEG-xfK33mjwXtjLp52T7qIH7nbTd4UddGcbDfC9jt3AOJSUTASq5jWVyWRM/s1600/tulip+60+fok.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="235" data-original-width="993" height="151" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhowBQgxNfFN6RKHFhls9tcbR3gwFBx4ilUGsL6UxOrv8e-99vtohVzZgpwPmvEAVezsZtbyPaA33iq__vbEG-xfK33mjwXtjLp52T7qIH7nbTd4UddGcbDfC9jt3AOJSUTASq5jWVyWRM/s640/tulip+60+fok.jpg" width="640" /></a></div>
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<div style="text-align: left;">
Központi szög / <span style="font-family: "times new roman" , serif; line-height: 18.4px; text-align: justify;">Central angle</span><span style="line-height: 150%;">: 72</span><span style="line-height: 150%; text-align: justify;">⁰</span></div>
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<a href="https://2.bp.blogspot.com/-jG6pkzeKfpo/Vw6kCms6DZI/AAAAAAAACh8/7YEX-jtKpCEsXTiy2hGbUOMJtLymnwi8wCKgB/s1600/SZITASOR.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://2.bp.blogspot.com/-jG6pkzeKfpo/Vw6kCms6DZI/AAAAAAAACh8/7YEX-jtKpCEsXTiy2hGbUOMJtLymnwi8wCKgB/s640/SZITASOR.jpg" width="425" /></a></div>
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Tengelyesen szimmetrikus elrendeződések nézőponttól függően<br />
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<a href="http://1.bp.blogspot.com/-dzGWNMB4Nt8/VCCiwAF3_zI/AAAAAAAACJc/ptjgLH4mOcM/s1600/cseppcs%C3%ADk.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="146" src="https://1.bp.blogspot.com/-dzGWNMB4Nt8/VCCiwAF3_zI/AAAAAAAACJc/ptjgLH4mOcM/s1600/cseppcs%C3%ADk.jpg" width="640" /></a></div>
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<b>DINAMIKUS FORMAI KÖLCSÖNHATÁSOK</b></div>
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;"> DYNAMIC SHAPE INTERACTIONS </span></div>
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<span style="color: #ffd966;"><br /></span></div>
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<span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 115%;">Az áramvonalas alakzatok, a
rész-egész -viszonyrendszer tükrében, meghatározó szerepet játszanak a pozitív
és negatív formák között fennálló, dinamikusan változó formai kölcsönhatásokban.</span></div>
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<span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 115%;"></span></div>
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;">The streamline shapes have
major roles in the dynamically changing shape interactions between positive and
negative shapes</span><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;"> in the mirror of part-total
relationship system</span><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;">.</span><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;"><o:p></o:p></span></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-HeztDfpnZYI/VcxuR0KqmDI/AAAAAAAACao/jmjvBekfpx4/s1600/k%25C5%2591%2Bkisebb%2Bm%25C3%25A1solat.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://3.bp.blogspot.com/-HeztDfpnZYI/VcxuR0KqmDI/AAAAAAAACao/jmjvBekfpx4/s320/k%25C5%2591%2Bkisebb%2Bm%25C3%25A1solat.jpg" width="216" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Adriai-tenger hullámai és a fúrókagylók által formálódott kavics<br />
<span style="font-family: "times new roman" , serif; line-height: 115%;"><span style="font-size: x-small;">The waves
of the Adriatic sea and the pebble formed by scallop shells </span></span></td></tr>
</tbody></table>
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<b>KÖZÉPPONTOSAN SZIMMETRIKUS ELRENDEZŐDÉSEK</b><br />
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;">CENTRALLY SYMMETRICAL
ARRANGEMENTS </span></div>
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<b>Szabályos sokszögek, poliéderek / </b><b style="line-height: 150%;"><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;">Regular polygons, polyhedrons</span></b><br />
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<b><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;"><o:p></o:p></span></b></div>
<b><span style="color: #f6b26b;"><br /></span></b>A körből közvetlenül eredeztethető nevezetes szögek és szabályos sokszögek<br />
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">Significant
angles and polygons drawn from circles directly<span style="background-attachment: initial; background-clip: initial; background-color: yellow; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial;"><o:p></o:p></span></span></div>
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<span style="text-align: justify;">A természetben számtalan esetben figyelhetők meg a középpontosan szimmetrikus, <br />szabályos sokszögű formációk </span></div>
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<span style="text-align: justify;"> Natural analogias</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9-gTbUXrREcKk6F3zmHQMAPAajjPVpK2hVT9By4_qOjCwvq-DmaWiygPXUFsRP1hq7nWmBG8qEIgDxNcTK44NyUBuVbdWuUxaz5JLsc0gclE3BlXDqRn7B8pYF01AtdZAVGjbUg8eADc/s1600/kp_szimmetria.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9-gTbUXrREcKk6F3zmHQMAPAajjPVpK2hVT9By4_qOjCwvq-DmaWiygPXUFsRP1hq7nWmBG8qEIgDxNcTK44NyUBuVbdWuUxaz5JLsc0gclE3BlXDqRn7B8pYF01AtdZAVGjbUg8eADc/s1600/kp_szimmetria.jpg" width="640" /></a></div>
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<span style="line-height: 150%;">Forgásszimmetrikus elrendeződések</span><br />
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 150%;">Axially symmetrical
arrangements</span><span lang="EN-GB" style="font-family: "times new roman" , "serif"; font-size: 13.5pt; line-height: 150%;"><o:p></o:p></span></div>
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<br />
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<span style="line-height: 150%;">A kör és a
hozzá tartozó ortogonális rendszer közötti geometriai összefüggés magában foglalja a természetben is gyakran előforduló </span><span style="line-height: 150%;">nevezetes szögek rendszerét, valamint </span><span style="line-height: 150%;"> az </span><span style="line-height: 24px;">aranymetszés</span><span style="line-height: 24px;"> </span><span style="line-height: 24px;">(ф) </span><span style="line-height: 24px;">arányrendszerét.</span></div>
<span style="line-height: 24px;"></span><br />
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">The geometric
connection between the circle and the relevant orthogonal system includes the
system of mostly appearing significant angles as well as the classic relation
system of golden section </span><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">(ф)</span><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">.<span style="font-size: 13.5pt;"><o:p></o:p></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdU_EoPlRSnbuJlHjV95tH98GclFLgbpBDvhY7CGFMFIZaaG8SqOWsv8zKoW9sQoWqgBiCA1qlxPzvbxqAV5duyHKALZV2DSQMJnl85uBfUXd-FuEBlaIA-1xhSpM9PQzDDaIoC_JtfK4/s1600/kereszt_csik.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="378" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdU_EoPlRSnbuJlHjV95tH98GclFLgbpBDvhY7CGFMFIZaaG8SqOWsv8zKoW9sQoWqgBiCA1qlxPzvbxqAV5duyHKALZV2DSQMJnl85uBfUXd-FuEBlaIA-1xhSpM9PQzDDaIoC_JtfK4/s1600/kereszt_csik.jpg" width="640" /></a></div>
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<b>KÜLÖNLEGES SZÖGEK A TERMÉSZETBEN</b><br />
<span lang="EN-GB" style="font-family: "calibri" , "sans-serif"; font-size: 13.5pt; line-height: 115%;"> SPECIAL ANGLES IN THE NATURE </span><span lang="EN-GB" style="font-family: "calibri" , "sans-serif"; font-size: 13.5pt; line-height: 115%;"><br /></span><br />
<span lang="EN-GB" style="font-family: "calibri" , "sans-serif"; font-size: 13.5pt; line-height: 115%;"><br /></span>
<span style="line-height: 150%;"><span style="line-height: 150%;">Különleges szögek a körből </span><span style="line-height: 150%;"> </span><span style="line-height: 150%;">közvetett módon, </span></span><br />
<span style="line-height: 150%;">szögharmadolással szerkeszthetők, mint </span><span style="line-height: 150%;">pl. </span><span style="line-height: 150%;">a kilencszög és a tizennyolcszög,</span><br />
<span style="line-height: 150%;"> melyek központi szöge </span><span style="line-height: 150%; text-align: justify;">20⁰ ill. 40⁰ .</span><br />
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<span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">The special
polygons can be drafted form the circles by trisection indirectly, such as
polygons of 9, 18, the central angles of which are 20</span><span lang="EN-GB" style="line-height: 115%;">⁰</span><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">, 40</span><span lang="EN-GB" style="line-height: 115%;">⁰</span><span lang="EN-GB" style="font-family: "times new roman" , serif; line-height: 115%;">.<o:p></o:p></span></div>
<span style="line-height: 150%;"><br /></span>KÜLÖNLEGES SZÖGŰ FORMÁCIÓK<br />
<span lang="EN-GB" style="font-family: "calibri" , "sans-serif"; font-size: 13.5pt; line-height: 115%;">- FORMATIONS OF SPECIAL ANGLES -</span><br />
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<a href="http://1.bp.blogspot.com/-Ey9v9n3ApHg/VEjWBrjHI0I/AAAAAAAACOA/q9VD0Mgqh5E/s1600/ricinus_maszk.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="195" src="https://1.bp.blogspot.com/-Ey9v9n3ApHg/VEjWBrjHI0I/AAAAAAAACOA/q9VD0Mgqh5E/s1600/ricinus_maszk.jpg" width="200" /></a></div>
<b>Ricinus / </b><i>Ricinus communis</i><br />
<i><br /></i>
<span style="line-height: 150%;">A természeti formák aritmetikai tulajdonságai utalnak a belső szerkezet</span><br />
<span style="line-height: 150%;">geometriai sajátosságaira.</span><br />
Az összefüggés megfigyelhető pl. a Ricinus 18 részre osztható levelénél.<br />
A szabályos tizennyolcszögből szerkesztett, logaritmikusan felépülő fraktál spirál körvonala megközelítő pontossággal illeszkedik a levél legjellemzőbb nézetére.<br />
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<span lang="EN-GB">The
numbers appearing in the natural shapes can refer to the attributes of geometric<br /> defining their structure.<br />
<!--[endif]--><o:p></o:p></span></div>
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<span lang="EN-GB">For
instance this relationship can be seen on the leaf of Ricinus/Castor-oil with 18
divisions. <o:p></o:p></span></div>
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<span lang="EN-GB">The
overall shape of fractal spiral arrangement drawn from of logarithmically structured
regular 18-polygon fits precisely to the most typical view of the leaf.<span style="font-size: 13.5pt;"><o:p></o:p></span></span></div>
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<span style="font-family: "calibri" , sans-serif; font-size: 15px; line-height: 16.8666667938232px; text-align: left;">Központi szög / </span><span style="font-family: "times new roman" , serif; line-height: 18.4px;">Central angle</span><span style="font-family: "calibri" , sans-serif; font-size: 15px; line-height: 16.8667px; text-align: left;">: 20⁰</span></div>
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<b>KÜLÖNLEGES SZÖGEK SZERKESZTÉSE</b><br />
<span lang="EN-GB" style="font-family: "calibri" , sans-serif; line-height: 115%;"> DRAWING
OF SPECIAL ANGLES </span><br />
<b><span style="color: #ffd966;"><br /></span>SZÖGHARMADOLÁS / TRISECTION</b><br />
<b><br /></b>
<span style="color: #ffd966;"><br /></span>
Egy híres ókori probléma újszerű megközelítése és megoldása<br />
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<b>A kör </b><b style="line-height: 150%;">és a hozzátartozó</b><b style="line-height: 150%;"> </b><b style="line-height: 150%;">ortogonális rendszer </b><b style="line-height: 150%;"> </b><b style="line-height: 150%;">szerkezeti
kapcsolata által </b><b style="line-height: 150%;"> </b><b style="line-height: 150%;"> különleges szögeket is kaphatunk, mint pl. 20⁰ 40 ⁰... stb., valamint nem-euklideszi szerkesztéssel a szögharmadolás is megoldható.</b><br />
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<div style="text-align: center;">
<span lang="EN-GB" style="font-size: 13.5pt; mso-ansi-language: EN-GB;">The new approach
and solution of a famous ancient problem<o:p></o:p></span></div>
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<b style="line-height: 150%;">
</b><br />
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<span lang="EN-GB" style="font-family: "times new roman" , "serif"; font-size: 13.5pt; line-height: 150%;">With the structural
connection of the circle and the relevant orthogonal system we can get special
angles, such as 20</span><span lang="EN-GB" style="font-family: "cambria math" , "serif"; font-size: 13.5pt; line-height: 150%;">⁰</span><span lang="EN-GB" style="font-family: "times new roman" , "serif"; font-size: 13.5pt; line-height: 150%;">, 40 </span><span lang="EN-GB" style="font-family: "cambria math" , "serif"; font-size: 13.5pt; line-height: 150%;">⁰</span><span lang="EN-GB" style="font-family: "times new roman" , "serif"; font-size: 13.5pt; line-height: 150%;">... etc., and the trisection can also be solved by non Euclidean drawing.</span><span lang="EN-GB" style="font-family: "times new roman" , "serif"; font-size: 13.5pt; line-height: 150%;"><o:p></o:p></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">copyright </span><span style="line-height: 150%;">© 2014. 07.10. </span></div>
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<span style="line-height: 150%;">Lektorálta / Lector: Ruff Feremc </span></div>
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<span style="line-height: 150%;"> matematika - fizika szakos egyetemi tanár / matematics and physics university professor /</span></div>
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<b>Fotók, szerkesztések
szerzői adatai / photos, edits, copyright informations:<o:p></o:p></b></div>
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Műholdfelvétel / Satelite images: ELTE Űrkutató
Központ<span style="background: #000077; color: cyan; font-family: "verdana" , "sans-serif";"><o:p></o:p></span></div>
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Űrfelvétel / Satelite images: Gemini Obszervatory-t és a GMOS Team, NASA<o:p></o:p></div>
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APOD:
2003 May 24 – M 74: The Perfect Spiral<o:p></o:p></div>
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Természetfotók szerkesztések / <span style="line-height: 150%;"> Natural photos, </span><span style="line-height: 150%;">edits</span><span style="line-height: 150%;">: Ádám Anita</span><br />
<span style="line-height: 150%;">Fordította / Translated by Rezsnyák Tímea</span><br />
<span style="line-height: 150%;"><br /></span>
<o:p></o:p><br />
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<span style="line-height: 150%;">MUNKÁIM / MY WORKS:</span></div>
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<br /></div>
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A <b>Természeti alapformák c. </b>tanulmány az alkotások szellemi háttere<br />
<div style="line-height: 18pt; margin: 0cm 0cm 0.0001pt; text-align: center;">
<span lang="EN-GB">The
study on <b>Natural basic shapes</b> is a theoretical background for the works of art exhibited.<span style="font-size: 13.5pt;"><o:p></o:p></span></span></div>
<b><br /></b></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: medium;">"ÖSSZHANG A SOKSZÍNŰSÉGBEN"</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: medium;">"HARMONY IN VARIEGATION"</span></div>
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<span style="font-size: large;">Sacra Geometria</span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;">grafika / graphic 28 x 45 cm</span></div>
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márvány / marble 25 x 25 2 cm<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOfR6to3GckafBqt9O_s3G-AJzq6ptbthD0M2lkJlJSVNMcMhXozfS5F2p2x_nNdXV96AXrAKwqVfxq43Qbb6jooBvu-GaoYrRVIdzx8Ofo78qbaf_A5-77DG2pjg0xb-DcHgvZdbzqUg/s1600/04_.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="316" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOfR6to3GckafBqt9O_s3G-AJzq6ptbthD0M2lkJlJSVNMcMhXozfS5F2p2x_nNdXV96AXrAKwqVfxq43Qbb6jooBvu-GaoYrRVIdzx8Ofo78qbaf_A5-77DG2pjg0xb-DcHgvZdbzqUg/s320/04_.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Fundamentum</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw8N_Cd8F_DkP12_cjN5ck-vNBcV5NsOoAHjd0LZVzmwLk1Fd4UT2vFQVMR0v2oC71kvECAVokc2W9xNYOJQDtJMoKF4NwPuTcRI2fcLf9wC3-eEZOtqd41jNNDooPAGl-HRYp30WmALo/s1600/05_.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="314" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw8N_Cd8F_DkP12_cjN5ck-vNBcV5NsOoAHjd0LZVzmwLk1Fd4UT2vFQVMR0v2oC71kvECAVokc2W9xNYOJQDtJMoKF4NwPuTcRI2fcLf9wC3-eEZOtqd41jNNDooPAGl-HRYp30WmALo/s320/05_.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Dinamikus egyensúly 08 / Dynamic equlibrium 08</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzRY7uSTyY71kZSFAGsMZIGAL1RobAhjqR9tZT9T_vcouvGUntWgM_rIfwETgpEiMCdpDaXPV_MLDwBQyDl2ugF5JzrKCvAC6Rnx7EUjyECxIO0jSpiijMxH9ieuB0ep4bBcFLFM8u6II/s1600/06_.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzRY7uSTyY71kZSFAGsMZIGAL1RobAhjqR9tZT9T_vcouvGUntWgM_rIfwETgpEiMCdpDaXPV_MLDwBQyDl2ugF5JzrKCvAC6Rnx7EUjyECxIO0jSpiijMxH9ieuB0ep4bBcFLFM8u6II/s320/06_.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Dinamikus egyensúly 05 / Dynamic equlibrium 05</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-0iqzyt5DkUI/Vw6Yo0s9adI/AAAAAAAACfc/ThCCwXiVhn4KjC-4Pur9rGzZ1RijgXkEwCLcB/s1600/07_.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://1.bp.blogspot.com/-0iqzyt5DkUI/Vw6Yo0s9adI/AAAAAAAACfc/ThCCwXiVhn4KjC-4Pur9rGzZ1RijgXkEwCLcB/s320/07_.jpg" width="308" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Dinamikus egyensúly 06 / Dynamic equlibrium 06</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoV6ltDorXuzc21P_6MOUHcmPI5JGweaJJZCN-wLezDg25HsQ4NXtSz4ZXUbiHqGC2cbLBMmF1qqNeURi_MY4ntOUbh3gMC8s6_MwJq0QKHLwTg0GG4mtlwjl4ADRF_y1IN3pDRWdqUSU/s1600/01+poligon.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="314" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoV6ltDorXuzc21P_6MOUHcmPI5JGweaJJZCN-wLezDg25HsQ4NXtSz4ZXUbiHqGC2cbLBMmF1qqNeURi_MY4ntOUbh3gMC8s6_MwJq0QKHLwTg0GG4mtlwjl4ADRF_y1IN3pDRWdqUSU/s320/01+poligon.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Nonagon / Nonagon</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOuo-sZpWo5q_tqn0VidTB4uyTnT_IgbH1Go8-5d0BS8XqWl72E0_9dFB9BE0Xb789amGhlSBZHRBoNes_RcOX-UD-kbt8qmTXiPQvhFnaYd-pgrFe9E3u3Aa2QYDHUeGiDv8AN_Mrlp8/s1600/03.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOuo-sZpWo5q_tqn0VidTB4uyTnT_IgbH1Go8-5d0BS8XqWl72E0_9dFB9BE0Xb789amGhlSBZHRBoNes_RcOX-UD-kbt8qmTXiPQvhFnaYd-pgrFe9E3u3Aa2QYDHUeGiDv8AN_Mrlp8/s320/03.jpg" width="316" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Dinamikus egyensúly 09 / Dynamic equlibrium 09</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCwoOQ7Vl5CI-nWuInzY1Y90CIRVHPCeEGtieXE9Cu7HGaXYhIGkxuXmeIF5Jh__kc3bflyy1eWMUZoWq3vGzukHpSOmsZkrQpWwKCk8xjG-YNYmlZVrERncw0TOyEbKNcQQ0DtgqUSDA/s1600/02+trisectio.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="316" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCwoOQ7Vl5CI-nWuInzY1Y90CIRVHPCeEGtieXE9Cu7HGaXYhIGkxuXmeIF5Jh__kc3bflyy1eWMUZoWq3vGzukHpSOmsZkrQpWwKCk8xjG-YNYmlZVrERncw0TOyEbKNcQQ0DtgqUSDA/s320/02+trisectio.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Trisectio</span></td></tr>
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<span style="font-size: large;">Forma Viva</span></div>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-MAC3hY_0mLg/Vw6b449QsjI/AAAAAAAACgI/F4c34wyrGP0RmhJ1XfBmeljVf5cOmVhkw/s1600/forma_viva%2B04.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="640" src="https://3.bp.blogspot.com/-MAC3hY_0mLg/Vw6b449QsjI/AAAAAAAACgI/F4c34wyrGP0RmhJ1XfBmeljVf5cOmVhkw/s640/forma_viva%2B04.jpg" width="339" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">60 x 30 x 15 cm</span></td></tr>
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<span style="font-size: large;">Spirálből áramló formák / Froms flowing from a spiral</span></div>
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<span style="font-size: x-small;">print 50 x 70 cm</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5ZxgeTzyjnmjaoiljEASrShS21zA9NsCnvsb0s4UmfPje0O5PhZiQ_2dfZlLUuJy7V7S97w4B4rJJ4tcV665sNxGHvXKWo-GF9TAcc2D24W9ME36tovk5j9MrwxZ_DSxRhZJvwVW0A8k/s1600/inverz+04.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5ZxgeTzyjnmjaoiljEASrShS21zA9NsCnvsb0s4UmfPje0O5PhZiQ_2dfZlLUuJy7V7S97w4B4rJJ4tcV665sNxGHvXKWo-GF9TAcc2D24W9ME36tovk5j9MrwxZ_DSxRhZJvwVW0A8k/s400/inverz+04.jpg" width="285" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Inverzió 01 / Inversion 01</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJnWjVKVmXfP1yxvs7no0AJLZ5YYZUOTGPdTnrNhFkJkOr1ZMdn8jZjqspcbECvHl9vcULfSYpvMztMAWRK_mVQV_HzECtPK1XsyxF-q_yJJVVBGDZ4FgY_cQzBR6t2sAIgi5w6uJPG8s/s1600/inverz+03.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJnWjVKVmXfP1yxvs7no0AJLZ5YYZUOTGPdTnrNhFkJkOr1ZMdn8jZjqspcbECvHl9vcULfSYpvMztMAWRK_mVQV_HzECtPK1XsyxF-q_yJJVVBGDZ4FgY_cQzBR6t2sAIgi5w6uJPG8s/s400/inverz+03.jpg" width="286" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Inverzió 02 / Inversion 02</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvoFgc9X52LW3yLWBHcBhFwQazpaTEhHekh1CboBn983Gb_peqXOq-bG3gEi7FpZxO9C0TYi0-t63R1rFa-0sAR3L634Jlj2Qce23LH2MvP036Hbs1CN-OKqmPlCPnFAxxHAIxpjukZi0/s1600/ph+fotongrafia+01.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvoFgc9X52LW3yLWBHcBhFwQazpaTEhHekh1CboBn983Gb_peqXOq-bG3gEi7FpZxO9C0TYi0-t63R1rFa-0sAR3L634Jlj2Qce23LH2MvP036Hbs1CN-OKqmPlCPnFAxxHAIxpjukZi0/s400/ph+fotongrafia+01.jpg" width="285" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Foto(n)gráfia 01 / Photo(n)graphy 01</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh01jLMof6aW6fzdYljHtU7dycbwCFeDxh8EOWYMfPMbtx6aN4RP9kHVTHNqO4dZ_o3f0x7F5gdh5-jDUwt886ilUvhXFgYxRjIt0eVq1Tt9iVbZ3pJfFpYPbANGrR-EsyMF4osP9ro76c/s1600/ph+fotongrafia+02.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh01jLMof6aW6fzdYljHtU7dycbwCFeDxh8EOWYMfPMbtx6aN4RP9kHVTHNqO4dZ_o3f0x7F5gdh5-jDUwt886ilUvhXFgYxRjIt0eVq1Tt9iVbZ3pJfFpYPbANGrR-EsyMF4osP9ro76c/s400/ph+fotongrafia+02.jpg" width="307" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Foto(n)gráfia 02 / Photo(n)graphy 02</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-mEjx_Gg9p_M/Vw6hcxXIAlI/AAAAAAAAChY/vH9OmrGXqds9gOaVgj4C0AJfMTUN3GmmgCLcB/s1600/ph%2Bfotongrafia%2B03.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://3.bp.blogspot.com/-mEjx_Gg9p_M/Vw6hcxXIAlI/AAAAAAAAChY/vH9OmrGXqds9gOaVgj4C0AJfMTUN3GmmgCLcB/s400/ph%2Bfotongrafia%2B03.jpg" width="285" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Foto(n)gráfia 03 / Photo(n)graphy 03</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-e86KPsJSzUk/Vw6h1kw5TyI/AAAAAAAAChc/NFrAQnO7JDodXm4qYMezZcR4ESYw1Ke7QCKgB/s1600/ph%2Bfotongrafia%2B04.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://3.bp.blogspot.com/-e86KPsJSzUk/Vw6h1kw5TyI/AAAAAAAAChc/NFrAQnO7JDodXm4qYMezZcR4ESYw1Ke7QCKgB/s400/ph%2Bfotongrafia%2B04.jpg" width="280" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;">Foto(n)gráfia 04 / Photo(n)graphy 04</span></td></tr>
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<span style="font-size: large;">Trisectio</span><br />
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<span style="font-size: x-small;">animáció</span><br />
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Ádám Anitahttp://www.blogger.com/profile/11736367907214966643noreply@blogger.com0tag:blogger.com,1999:blog-8384654599673951610.post-80699260388564984692013-12-24T09:47:00.000-08:002013-12-24T09:47:07.502-08:00<div class="separator" style="clear: both; text-align: center;">
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Ádám Anitahttp://www.blogger.com/profile/11736367907214966643noreply@blogger.com0tag:blogger.com,1999:blog-8384654599673951610.post-22786269908120238492013-10-09T11:14:00.000-07:002013-10-09T11:14:18.259-07:00<div class="separator" style="clear: both; text-align: center;">
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<br />Ádám Anitahttp://www.blogger.com/profile/11736367907214966643noreply@blogger.com0tag:blogger.com,1999:blog-8384654599673951610.post-28942041635670825162013-04-27T00:57:00.002-07:002013-10-09T12:51:07.228-07:00<div class="separator" style="clear: both; text-align: center;">
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Ádám Anitahttp://www.blogger.com/profile/11736367907214966643noreply@blogger.com0tag:blogger.com,1999:blog-8384654599673951610.post-88263541822487553692013-04-22T08:53:00.001-07:002013-10-09T13:36:21.285-07:00Szögharmadolás / Trisection<div class="separator" style="clear: both; text-align: center;">
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<span style="color: #ffd966; font-family: Arial, Helvetica, sans-serif; font-size: large; text-align: left;">SZÖGHARMADOLÁS</span><b style="color: #ffd966; font-family: Arial, Helvetica, sans-serif; font-size: x-large; text-align: left;"> </b><span style="color: #ffd966; font-family: Arial, Helvetica, sans-serif; font-size: large; text-align: left;">/ Trisection</span></div>
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<span style="color: orange; font-family: Arial, Helvetica, sans-serif;">/ Egy híres, ókori, geometriai feladvány /</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-family: Arial, Helvetica, sans-serif;">Euklideszi szerkesztéssel a </span><span style="color: orange; font-family: Arial, Helvetica, sans-serif;">szögharmadolás</span><span style="color: #ffd966; font-family: Arial, Helvetica, sans-serif;"> </span><span style="font-family: Arial, Helvetica, sans-serif;">problémáját nem lehet megoldani, <br />viszont </span>lehetséges, ha körzőn és vonalzón kívül más eszköz használata is megengedhető.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Szerkesztéseim során egy érdekes megoldást találtam ...</span></div>
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<span style="color: #ffd966; font-family: Arial, Helvetica, sans-serif;">Szerkesztés:</span></div>
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Ádám Anitahttp://www.blogger.com/profile/11736367907214966643noreply@blogger.com0tag:blogger.com,1999:blog-8384654599673951610.post-42252879006998739992013-03-24T22:07:00.001-07:002019-11-14T09:19:38.584-08:00<h3>
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<br />Ádám Anitahttp://www.blogger.com/profile/11736367907214966643noreply@blogger.com0