Vloerplan van die Pantheon, Rome

Vloerplan van die Pantheon, Rome


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Vloerplan van die Pantheon, Rome - Geskiedenis

Die Pantheon, wat tussen 118-128 nC gebou is, beskik oor argitektoniese kenmerke wat gewild was tydens die konstruksie, maar behou ook sy eie uniekheid. Die stoep en die tussenblok het 'n Griekse styl, met 'n instabiliteit wat op sestien kolomme rus. Nadat u deur die portiek gegaan het, kom u die groot rotonde teë wat 'n Romeinse styl volg, omdat die groot koepel ondersteun word deur spanning op die wande van die silinder waarop dit rus. Die besondere ontwerp van die Pantheon, insluitend die vereniging van Griekse en Romeinse styl, het tot bespiegelings gelei oor wie die argitek van die Pantheon was. Alhoewel daar nog afdoende bewyse van die identiteit van die argitek gevind moet word, meen sommige dat Hadrianus die hele gebou sou ontwerp het. Hadrianus het 'n groot belangstelling in argitektuur en 'n liefde vir sowel die Griekse as die Romeinse kultuur. Die Pantheon simboliseer dus sy poging om beide kulture en argitektuurstyle in een gebou te kombineer.

Die bou van die Pantheon sou 'n groot onderneming gewees het. In totaal is vyfduisend ton beton gebruik om die rotonde te bou deur opeenvolgende ringe beton in 'n voorheen geboude houtraamwerk te gooi. Die mure van die silinder was ses meter breed om die spanning van die hele koepel op die fondament te ondersteun. Die hoogte en deursnee van die binneste rotonde meet beide 43,3 m. Die implikasie hiervan is dat 'n perfekte bol met dieselfde deursnee perfek in die rotonde pas. Die oculus, of opening aan die bokant van die koepel, is 8,8 m breed en verlig die las op die fondament van die struktuur aansienlik. Dit is ook in ooreenstemming met die oortuiging dat daar nie 'n dak op 'n Romeinse tempel moet wees nie. Die oculus dien as die belangrikste ligbron in die Pantheon, en laat ook reën en sneeu toe, wat 'n ander atmosfeer skep gedurende die seisoene. Die vloer skuins na dreine wat teenwoordig is om reën op te vang. Blinde vensters langs die rotonde, waarskynlik bedoel om lig in die uitgebreide netwerk van deurgange wat deur instandhoudingspersoneel gebruik word, in te laat. William MacDonald, 'n Pantheon -kenner, is van mening dat die vensters die gebou ook laat asemhaal deur lug te sirkuleer om te verhoed dat vog versamel wat krake in die gietsement kan veroorsaak. Die marmerwerk op die vloer met patrone van sirkels en vierkante is 'n akkurate weergawe van die oorspronklike vloer uit die 19de eeu.

By die waarneming van die Pantheon van buite speel die kolomme 'n belangrike rol in die toevoeging tot die grootsheid. Die sestien monolitiese kolomme is gemaak van rooi en grys graniet en die skagte staan ​​40 voet hoog. Die vervoer van die kolomme na die bouperseel, wat in die ooste van Egipte gesny is, het vereis dat hulle op 'n skuit langs die Nyl moes dryf, deur die Middellandse See en teen die Tiberrivier op. Toe hulle Rome bereik, is hulle deur die strate van die stad gedra en dan opgerig. Drie van die kolomme aan die oostekant van die gebou het geval en is vervang deur die pous Urbanus VIII en Alexander VII. Die kolomme van die Pantheon het baie bespreking ontlok omdat geleerdes meen dat as die kolomme slegs 10 voet hoog was, hulle kon toelaat dat daar kontinuïteit is tussen die stoep en die middelste blok wat nie in die huidige struktuur ontbreek nie. Dit was beslis aansienlik moeiliker om 50 monolitiese kolomme van Romeinse voet te bekom, maar die groter kolomme is eerder gebruik vir die Tempel van Trajanus, wat rondom dieselfde tyd deur Hadrianus vir sy aanneemvader gebou is. Probleme met die verkryging van groter kolomme kan die argitek van die Pantheon dus daartoe gelei het om 'n kompromie aan te gaan en kleiner kolomme te gebruik. Polities sou dit vir Hadrianus belangrik gewees het om die groter kolomme aan die Tempel van Trajanus te wy om respek vir Trajanus te betoon, veral omdat die grootte van die kolomme baie belangrik was vir die Tempel van Trajanus, aangesien dit die grootte van die hele gebou bepaal het, terwyl dit nie so belangrik was vir die struktuur van die Pantheon nie.

Toe dit eers gebou is, sou die hele buitekant van die koepel, sowel as die binnekant van die plafon, met brons bedek gewees het. Van die brons is egter verwyder om die 80 kanonne by Castel Sant पngelo, Hadrianus se mausoleum te maak, maar is uiteindelik teruggegee toe dit gesmelt is vir die graf van Vittorio Emanuele II, wat nou by die Pantheon rus. Nog 'n paar brons is deur die Gote gestoof, maar die meeste daarvan is geneem deur die Barberini -pous Urban VIII, wat die uitdrukking laat ontstaan ​​het wat die barbare nie gedoen het nie, die Barberini. ”

Baie aspekte van die buitekant soos dit vandag duidelik was, sou baie anders gewees het toe die Pantheon die eerste keer gebou is. Die metselwerk wat die buitemuur van die rotonde bedek, sou bedek wees met pleisterwerk, marmerpanele of selfs travertyn. Tans sit die Pantheon effens versonke in die vloer omdat die straatvlak rondom die gebou gestyg het. Oorspronklik sou die Pantheon hoog bo straatvlak gesit het, met vyf steil trappe om dit te bereik.

Die UW KnowledgeWorks -sagteware wat gebruik is om hierdie webwerf te skep, is ontwikkel deur die The Program for Educational Transformation Through Technology by die Universiteit van Washington.


Afmetings van die Pantheon

Die reuse koepel wat die binnekant oorheers, is 43,30 meter in deursnee (ter vergelyking is die koepel van die Withuis 96 voet in deursnee). Die Pantheon was die grootste koepel ooit tot Brunelleschi se koepel by die katedraal van Florence van 1420-36. Dit is steeds die grootste messelwerk koepel in die wêreld. Die Pantheon word perfek harmonieus gemaak deur die feit dat die afstand van die vloer tot die bokant van die koepel presies gelyk is aan die deursnee daarvan. Adytons (heiligdomme wat in die muur ingeduik is) en koffers (versonke panele) verminder die gewig van die koepel slim, net soos 'n ligte sement van puimsteen wat op die boonste verdiepings gebruik is. Die koepel word dunner namate dit die oculus nader, die gat aan die bokant van die koepel wat as ligbron vir die binnekant gebruik word. Die dikte van die koepel op daardie stadium is slegs 1,2 meter.

Die oculus is 7,8 meter in deursnee. Ja, reën en sneeu val af en toe daardeur, maar die vloer is skuins en dreineer slim om die water te verwyder as dit die vloer kan tref. In die praktyk val reën selde binne die koepel.

Die massiewe kolomme wat die portiek ondersteun, weeg 60 ton. Elkeen was 11,8 m lank, 1,5 meter in deursnee en gemaak van klip wat in Egipte ontgin is. Die kolomme is met houtslede na die Nyl vervoer, na Alexandrië aangery en op vaartuie gesit vir 'n rit oor die Middellandse See na die hawe van Ostia. Van daar af kom die kolomme per skip op die Tiber.


Buite

Voorkant, buitekant van die Pantheon. Toon argitektuur wat beïnvloed word deur tradisionele Griekse tempels, insluitend kolonnade wat die driehoekige voorkant hou.

Aan die voorkant van die Pantheon vorm sestien monolitiese kolomme die bekende portiek van die monument. Die skagte (silindriese deel van die kolom) is gemaak van Egiptiese graniet, terwyl die hoofstede (dekoratiewe bokant van die kolom) en voetstukke uit wit Griekse marmer gesny is. Die Korintiese hoofstad gee die struktuur 'n ingewikkelde, dekoratiewe kwaliteit wat sterk kontrasteer met die gladde, swaar as hieronder.

Interessant genoeg het studies getoon dat die kolomme se hoogtes en breedtes van kolom tot kolom verskil. Navorsing het bewys dat die verskil in metings heel waarskynlik was omdat hulle materiaal en arbeid van verskillende plekke uitgekontrakteer het. Die kolomme, wat na die buiteland gestuur moes word, het 10 meter korter geword en moes op 'n onderste stoep gehuisves word. 1 Aangesien die projekte aan verskillende konstrukteurs versprei is, het die bouers verwag dat hulle teenstrydighede sou hanteer. Vir die Pantheon het sulke verstellings verskillende ashoogtes en breedtes van die as ingesluit. 2 Nadat die trommel gebou is, is die reghoekige tussenblok gemaak om die sirkelvormige deel van die struktuur met die tempelagtige stoep te verbind. 3 In die oudheid het konstruksie verfyning en vergoeding behels, veral by die skep van 'n monumentale struktuur soos die Pantheon.

Tekening wat die buitekant en deursnit van die Pantheon toon.

Die Pantheon -trommel is 'n massiewe, silindriese struktuur wat die grootste deel van die monument vorm. Alhoewel dit van beton gemaak is, is dit bedrieglik lig - die dikker dele van die muur bied leë, halfsirkelvormige ruimtes. 4 Die drom se soliede voorkoms verberg sy hol binnekant en behou sy sterkte. Die Romeine het 'n stelsel uitgevind en gebruik om bakstene, gewelwe en piere met mekaar ineen te steek om die drom se ewe gewigverdeling en -ondersteuning moontlik te maak. Van buite lyk die monument dig, maar laat dit 'n hol binnekant toe: hierdie Romeinse tegniek kan gesien word in Trajan's Column, wat 'n wenteltrap in sy skag huisves. Sommige historici het hierdie parallel met Trajanskolom gebruik as steun vir die Pantheon se sterker verbintenis met Trajanus, eerder as Hadrianus. 5

Die koepel self word gemaak deur oorvleuelende vatkluise oor die kamers met die derde verdieping, wat hierdie tegniek verband hou met die voormelde agthoekige plan van Nero se paleis. Die trommel en trapringe (die gestapelde, vlak silinders aan die onderkant van die koepel) dra ongeveer 65 persent van die gewig van die koepel. 6 Die koepel se noukeurige gewigsverdeling het die hoeveelheid nie -ondersteunde gewig tot 'n minimum beperk, wat die algehele struktuur versterk en stabiliseer. Die koepel is steeds bedek met gips, maar die buitekant, wat oorspronklik met bronsplate beskerm is, is uiteindelik met lood vervang. 7 Die enigste oorblywende brons funksioneer as 'n beskermende steun rondom die okulus.

1 Mark Jones, "Bou op teëspoed," in Die Pantheon, red. Marder en Jones, (New York, NY: Cambridge UP), 220.

2 Lothar Haselberger. "Die menslike oog en 3D -laserskandering: die gevel van die Pantheon en sy hoofstede," in Tydskrif vir Romeinse Argeologie, (Rhode Island: Journal of Roman Archaeology, 2015), 54.

4 Giangiacomo Martines, "Die konsepsie en konstruksie van die trommel en koepel," in Die Pantheon, red. Marder en Jones, (New York, NY: Cambridge UP), 106.


Die Pantheon

Hierdie beroemde gebou staan ​​in die sakegebied van Rome-net soos dit ongeveer 18 eeue gelede gebou is. Verbasend genoeg het dit die verwoesting van beide die elemente en die oorlog weerstaan, wat 'n eerstehandse blik op 'n unieke produk van Romeinse hande moontlik gemaak het. Nou word dit blootgestel aan suurreën en dampe uit verbygaande motors en word dit oorskadu deur geboue met minderwaardige smaak, maar met vertroue in die toekoms sal die Pantheon oorleef.

Die ontwerp van hierdie antieke betongebou onthul ongeëwenaarde kenmerke wat nie in moderne ontwerpstandaarde voorkom nie. Onlangse studies toon verskeie groot krake in die koepel, maar dit funksioneer steeds ongedeerd. Hierdie toestand sal die nuuskierigheid van ons konstruksie -ingenieurs beslis opwek. Die gebou is geheel en al sonder staalversterkingsstawe gebou om trekkrake te weerstaan, wat so nodig is in betonelemente, en hierdie betonkoepel met 'n lang span tot laaste eeue is ongelooflik. Vandag sou geen ingenieur dit waag om hierdie struktuur te bou sonder staalstawe nie! Moderne kodes van ingenieurswese sal sulke onheil nie toelaat nie. Geen belegger met kennis van betonontwerp sou die geld verskaf nie. Bykomende beperkings by die bou van 'n struktuur so groot soos die Pantheon sal later bespreek word, maar dit bevat kortliks die gebruik van onvoldoende handgereedskap en onveilige hefapparate. Ek glo dat ons uit hierdie aktiwiteit kan leer. Werkers kan uit 'n plan bou en slegs hul beproefde praktyke suksesvol gebruik as die kwaliteitskontrole van die konstruksie gehandhaaf word.

Die geskiedenis vertel ons dat die Pantheon 'n Griekse woord is wat alle gode (veral die Olimpiese goddelikhede) eer. Dit is ironies dat ons gebou in baie oorloë bestaan ​​het, terwyl dit aan alle gode toegewy is, en dit kan maklik as 'n tempel vir ons enigste God beskou word. En die Kerk het hierdie heilige struktuur as 'n rusplek vir sy beroemdste pouse opgeëis, daarom gaan ons voort om die wonderlike godheid te eer.

Die eerste inkarnasie van hierdie ou tempel is gebou deur Agrippa, die skoonseun van die Romeinse keiser Augustus, ongeveer 27 v.C. Vandag, bo die ingang wat in klip gekap is, is die woorde "M. AGRIPPA L. F. COS. TERTIUM FECIT" wat vertaal word, "Marcus Agrippa, seun van Lucius, in sy derde konsulaat, het dit gemaak." Dit is inderdaad die moeite werd om te noem dat Agrippa se ingenieurs -talente gebruik is vir die bou van die beroemde Pont de Gard -akwaduk in Frankryk.

Soos met baie stede, het tragedie in die vorm van groot vuur, soos dié van 60, 64, 79, 100 en 110 nC, Rome gelyk. Oorspronklik bevat baie Romeinse geboue travertyn (kalksteen) wat maklik in brande kan kraak. Die eerste Pantheon is erg beskadig en moes vervang word, behalwe vir sommige dele van die onderste stoepgedeelte en fondament.

Die Pantheon is herbou deur die keiser Hadrianus gedurende die tydperk 118 tot 128 nC ('n tyd wat deur Ward-Perkins gegee is). 2 Maar die tydperk van die Ward-Perkins word betwis deur Lugli wat gesê het dat die gebou iewers na 123 nC begin is en deur keiser Pius ongeveer 140 nC voltooi is. Die meeste stene is egter gemaak en in 123 nC in die Pantheon geplaas datum waarop die vervaardiger op sy stene gestempel het. Dit is in 1892 deur die Franse argeoloog, George Chedanne, ontdek. Dit lyk asof die bou van die rotonde mure 'n tydperk van 4 tot 5 jaar geneem het, en die koepel het 'n soortgelyke tydperk nodig vanweë die hoogte en die geringe gereedskap wat die Romeine gebruik het. Hierdie lang konstruksietydperk was gelukkig, aangesien dit aan hierdie pozzolan -beton genoeg tyd gegee het om te genees en krag te kry.

Was die tweede tempel soos die eerste? Ja, die fundamentele beginsel van die ou Romeinse godsdiens het vereis dat die tempels herbou moes word sonder om die oorspronklike vorm te verander. Tradisie vereis dat die hoofingang noordwaarts wys, en dus is die hele gebou op die noord-suid-as van die gebou gerig.

'N Beskrywing van die strukturele kenmerke daarvan word geskei in die konfigurasie, fondamentring, sirkelvormige mure en koepel om die verskillende komponente duideliker te definieer. Hoe hierdie stukke uniek is in die lig van die huidige ontwerpvereistes, sal binnekort bespreek word.

Michelangelo, die groot skilder van die Sixtynse kapel, het die ontwerp van die Pantheon eens beskryf as 'n "Engelse en nie menslike ontwerp nie." 4 Met reg, want dit is inderdaad een van die mees ongewone strukture wat ooit deur mensehande gebou is. Die vermoë van die antieke Romein om die ingewikkelde planne te maak en slegs die mees suksesvolle, beproefde konstruksietegnieke te kies, het hierdie komplekse gebou moontlik gemaak. Weereens, dit is werklik 'n eer aan hul geestelike bekwaamheid en organisatoriese vaardighede. Die volgende foto's toon die pragtige interieur.

Die bou -ontwerp is een van 'n groot ronde vorm, baie soos 'n groot vat met 'n koepel wat die bokant bedek. Daar is 'n ligput in die middel van die koepel. Lae van pragtige dun metselwerk bedek die buitekant, ronde mure. Af en toe kom daar klein toegangsgate in die muur, wat tydens die konstruksie gebruik is om binneluise te raam. Die hoofingang is indrukwekkend: dubbele bronsdeure van 21 voet hoog (6,4 meter), 'n blywende en gepaste bydrae van hul metaalsmede. Hierdie deure word beskerm deur 'n hoë, breë stoep met 16 goed gerangskikte granietkolomme wat 'n gewildak ondersteun. Die balke in die dakstruktuur van die stoep is van hout. Hulle is vervang met bronslede wat ontneem is deur diegene wat later jare metaal nodig gehad het vir hul kanonne. Professionele Romeinse landmeters het die ingelegde marmervloer gevind om aan te pas by 'n konvekse kontoer wat die reën vir die honderde jare van die oculus af weggevoer het.

In die volgende beskrywings word enkele algemene afmetings gegee om die omvang van hierdie onderneming deur die Romeine aan te dui. Die rotonde het 'n buitengewone binnediameter van 43,4 m, meestal gemaak van beton. Vergelykend gesproke verteenwoordig hierdie afstand ongeveer die helfte van die lengte van ons voetbalveld. En van die vloer tot die bokant van die opening in die koepel is dieselfde afstand. In werklikheid kan ons die ontwerp van hierdie gebou aanskou as 'n teoretiese bal van ongeveer 143 voet in deursnee. Die ontwerp is nie heeltemal ongewoon nie, want daar is ander Romeinse geboue met 'n soortgelyke opset, maar die grootte is ongewoon. Ander geboue soos die Tempel van Mercurius (71 voet/21,5 m deursnee) by Baiae en Domitian Nympheaum in Albano (51 voet/15,6 m deursnee) het koepels van hierdie tipe. Die Pantheon het nog steeds die langste span wat voor die 19de eeu gebou is.

Om besonderhede oor hierdie komplekse opset te gee, toon die volgende figure die gebou met sy twee-ring fondament, leemtes in die mure en die trap-ring en koffer rangskikking in die koepel.

Pantheon -afdelings (linker foto: Ward-Perkins 6, regs prent: MacDonald 7)

Die Pantheon is gebou op moerasagtige, onstabiele aarde, wat die bouers 'n ernstige ondersteunende probleem gegee het. Die Jutland Argeologiese Genootskap het verskeie aspekte van die ringfondasie breedvoerig beskryf en gevind dat dit op 'n bedding van bloukleurige rivierklei rus. 8 Hierdie toestand het 'n ramp veroorsaak, en in die laaste boufase het die fondament aan die twee ente van die Noord-Suid-as gebars. 9

Soos u kan dink, as 'n gedeelte van 'n gebou effens vinniger en laer as 'n aangrensende gedeelte gaan lê, word baie groot buigingspannings begin op 'n punt tussen hierdie twee dele wat die beton kan kraak. En die bouers het die probleem met 'n ongelyke vestiging gekry. Die huidige ingenieursoplossing vir hierdie tipe fondamentprobleem is om stapels deur die klei tot in die grond te dryf, sodat die gebou stewig ondersteun kan word. Die Romeinse bouers het 'n ander benadering gekies. Hulle het 'n tweede ring gebou om die eerste ring verder te laat kraak en om die klei meer ruimte te gee om die struktuur te ondersteun. Dit het gewerk omdat die gebou meer as 1800 jaar lank bestaan ​​het.

Behalwe dat die spleet nie uitrek nie, het die bouers steunmure aan die suidekant teenoor die massiewe stoep geplaas. Dit het as 'n klemapparaat gedien, en hoewel die strukturele uitsteeksel 'n ekstra kamer blyk te wees, dien dit slegs as deel van die klem.

Aanvanklik was die breedte van hierdie ringfundament 7,2 m breed, slegs ongeveer 0,9 m groter as die mure wat dit ondersteun het. Die tweede ring wat die oorspronklike saambind, is 3,0 m. wyd, wat die totale breedte van die fondament ongeveer 34 voet maak. Van die vloer tot by die onderkant van die fondasie is 4,7 m (15'-4 "). 10

Hierdie ringe is gemaak van pozzolanbeton wat bestaan ​​uit travertynstukke in lae wat deur 'n kalkmortel en pozzolan aanmekaar gehou word. Dit sal later in hierdie werk bespreek word. Interessant genoeg het die ondersoek van die Jutland Society getoon dat die grondmateriaal 'kliphard' geword het, 'n geval wat ons kan verwag as ons die chemie van pozzolaniese reaksie onder hierdie omstandighede bestudeer.

Die ronde muur kan die beste beskryf word as een met baie holtes en kamers op verskillende vlakke. Daar is geen bewyse dat daar 'n trapstelsel tussen hierdie boonste kamers bestaan ​​nie, en ons kan aanvaar dat hulle funksie saam met ander nisse was om konstruksiemateriaal saam met die gewig te verminder. Hierdie muur kan struktureel beskou word as 'n reeks betonpiere wat op vloervlak geskei is deur 8 baie groot nisse wat ewe ver langs die binneste omtrek is. Die dik muur werk baie soos 'n steunpilaar om 'n stoot uit die koepel te ondersteun.

Om hierdie nisse op te spoor, kyk na die sirkelvormige plan van die rotonde met 'n stel asse by die belangrikste kompaspunte; een van hierdie nisse is aan elke kant van 'n hoofas (4 in getal). Hulle is halfsirkelvormig, behalwe die een by die hoofdeur wat effens vierkantig is. Die ander 4 nisse is aan die ente van die diagonale assestelsel geleë. Dit is 'n groot reghoekige vorm met die lang kant wat die kromming van die muur volg. Twee kolomme van graniet help om die plafon in die nisse te ondersteun. Dit is interessant om op te let dat binne hierdie nisse groot konings van Italië lê, belangrike pouse, en op 'n tyd die beroemde skilder Raphael.

Die nisse, sowel as alle ander muuropeninge, het 'n boog van bakstene, bekend as 'n aflosboog, om die boonste muur oor die openinge te ondersteun. Die aflosboog is 'n halfsirkel van dun stene wat radiaal aan die einde van die betonmuur gestrek het. Hierdie boog versprei boonste vragte aan die piere gedurende die lang tyd wat die pozzolan -beton uithard, maar na uitharding word dit 'n integrale deel van die muur. Hierdie boog van stene was slegs 'n deel van die muur en strek nie tot in die koepel nie. Hierdie tipe boog is gebruiklik met die Romeinse konstruksie vir daardie tydperk. Dit word saam met die nisse en hul kolomme in die volgende figuur getoon:

Om die muur te dimensioneer is nie 'n maklike taak nie. Eerstens is die standaard algehele breedte by die piere ongeveer 6,2 m, maar die gordynmuur aan die kant van die groot nisse word verminder tot 2,2 m dik. Binne die piere is daar klein holtes wat halfsirkelvormig is met 'n radius van 7'-8 "(2,3 m). Die logika agter hierdie vorm is onbekend, maar geboë oppervlaktes verminder die konsentrasie van spannings wat in strukture aanstootlik is. Die ingang na die holtes is deur 'n 1,1 m lange gang van buite.

Die buitekant van die sirkelvormige muur is 31,7 m, wat fantasties lyk as dit van die deur af gesien word. Dit is die hoogte van ongeveer 'n kantoorgebou van 7 verdiepings. Die boonste kroonlys op die muur het 'n oorhang van ongeveer 1,1 m wat dien as 'n effektiewe reënskerm vir die baksteen. Die kroonlys is van marmer en het goed verweer. Hierdie ronde muur word gedeel deur twee onderste kroonlyste. Die een is 12,8 m bo die vloer en die ander 21,8 m van die vloer af. Laasgenoemde dien as die springlyn vir die koepel. Die muur Die gedeelte word baie dikker bo die tweede kroonlys namate die koepel van die muurlyn afwyk.

Kenmerkend vir alle Romeinse mure van daardie tyd, is die muur vasgemaak met 'n spesiale horisontale laag metselwerk elke 3'-11 "(1,2 m). Hierdie bindingsbane is gemaak van teëlagtige stene wat bipedale genoem word (ongeveer 0,6 m) m vierkant) wat heeltemal deur die muur strek. Steenwerk aan beide kante van die muur is na vore gebring met die plasing van die beton. Dit sal in latere gedeeltes verduidelik word.

Die samestelling van die muur is deur die Jutland Archaeological Society 13 gedokumenteer en deur Lugli 14 stem dit redelik ooreen. Die onderste gedeelte naby vloervlak bestaan ​​uit afwisselende lae travertynfragmente en fragmente van tufa (die caementae) in 'n mortier van kalk en pozzolana. Die middelste plasing van die muur was alternatiewe lae stukke tufa en gebreekte teëls of bakstene ook in dieselfde mortier. Die boonste vlak van die muur bestaan ​​uit beton, hoofsaaklik uit gebreekte bakstene in mortel. Die muur is ligter gemaak namate dit hoër was, 'n merkwaardige voorbeeld van gradering in hul ingenieursbeplanning.

Die koepel is 'n interessante en moeilike kenmerk om te beskryf omdat die opset aan beide kante so ongewoon is. Die radius van die koepel is 21,7 m, wat as basis dien vir die oorspronklike ontwerp. 15 Dit word daarop gewys om aan te toon dat daar konflikte is tussen die spesialiste wat die Pantheon bestudeer. In hierdie geval lyk die vorige figuur voldoende. Die relatiewe dikte van die koepel word verminder van 19'-8 "(5,9 m ) aan die voet tot byna 1,5 m bo. 16

Aan die buitekant is daar 'n reeks van sewe trappe halfpad teen die koepel, en dan verander die koepellyn in 'n sirkelvormige lyn. Aan die binnekant bevat die koepel 'n reeks van 5 bande wat bestaan ​​uit wafelagtige verdiepings wat koffers genoem word. Daar is 140 koffers wat spesiale vorming benodig vir die wafelvorm. In die middelpunt verander die koepelkontoer van hierdie kas na 'n sirkelvormige lyn. In die middel van die koepel is 'n groot opening, die oculus.

Die buiteringe is nie eenvormig nie, daar is 7 ringe, en die afmetings van die koepels is slegs beskrywend. Die eerste ring het sy buitekant in die middel van die hoofmuur. Dit blyk ongeveer 2,3 m dik te wees met 'n horisontale afstand tot die volgende ring omtrent dieselfde afstand. Die oorblywende 6 trapringe word na binne getrap, net soos om 'n reeks wasmasjiene te plaas, die een bo die ander met hul diameters wat afneem namate hulle gestapel word. Die hoogte van hierdie 6 ringe wissel, en dit word na raming gemiddeld 0,8 m (2'- 6 "). Die horisontale afstand na die volgende van hierdie kleiner ringe word na raming 1,2 m. 'n buitentrap wat deur hierdie ringe na die oculus lei.

Vir 'n oomblik kan ek die antieke konstruksiepraktyke waarneem om hierdie koepel te bou, sien. Dit is bekend dat die baie ou Mykene -grafte in Griekeland gemaak is deur klipblaaie oor mekaar te bedek. Na aanleiding van hierdie voorbeeld in die geskiedenis, is dit waarskynlik dat die Romeine hierdie beginsel gebruik het om die een ring op die ander te plaas in die bou van hierdie gedeelte van die koepel. Hierdie werk het lank geneem. Die sementmateriaal het behoorlik genees en sterk geword om die volgende boonste ring te ondersteun. Die kleiner trapringe word gekonfronteer met semilateres (bakstene) 16, wat geloofwaardigheid verleen aan die afstrykingsmetode. Elke ring is gebou soos 'n lae Romeinse muur. Die sirkelvormige deel van die boonste koepel is waarskynlik met behulp van houtsteigers geplaas.

Die drukring (oculus) in die middel van die koepel is 5,9 m in deursnee en 1,4 m dik. Die ring bestaan ​​uit 3 horisontale teëls, regop, die een bo die ander is die ring 2 stene dik. 16/17 Hierdie ring is effektief om die kompressiekragte op hierdie punt behoorlik te versprei. Daar is 'n bronsring wat die lip bedek wat dateer uit die oorspronklike konstruksie, maar ander bronsplate bo -op die dak is verwyder en later vervang met loodplate.

Volgens die Jutland Archaeological Society-ondersoeke, is die onderste gedeelte van die koepel van beton met afwisselende lae stene en tufa het 'n goeie affiniteit met die kalk-pozzolan-mortier wat die leemtes gevul het. Die boonste koepel bokant die trapringe (die boonste 9,1 m) is van beton en bestaan ​​uit ongeveer 9 duim ligte tufa en poreuse vulkaniese slakke in afwisselende lae wat met mortel vasgemaak is. 18 Dit was gebruiklik dat die Romeine groter klippe in die koepelbeton gebruik het as in die mure. Die keuse van ligte klippe vir die totaal is nog 'n geval van gradering om ligte beton te kry, 'n proses wat blykbaar in die middel van die eerste eeu v.C.

Die volgende figure toon die verskillende kenmerke soos die trapringe, koepeltrap, koffers, loodplate.

MAAR HOE STAAN DIT?

Die uitdaging om spanning in verskillende dele van die Pantheon te bepaal, het argitekte sowel as ingenieurs wat in die gebou belangstel, altyd opgewonde gemaak. Tegniese ontwerpers het besef dat die lang 143 voet van die ou koepel kritieke spanningskonsentrasies kan hê wat tot 'n katastrofiese mislukking van die struktuur kan lei, maar dit het nie gebeur nie.

Niks in die lewe lyk perfek nie, en dit is die geval met die Pantheon. Die koepel en mure het gebars. Betonskeure onder oormatige trekspanning soos gesien in 'n hoepel toestand. A. Terenzio, 'n Italiaanse opsigter van monumente, het krake in die mure en koepel gedokumenteer tydens sy inspeksie van die Pantheon in 1930. In 'n ontwerpstudie van die Pantheon deur Mark en Hutchinson is soos volg verwys:

Terenzio identifiseer ook breuke 'wat van die rotonde af tot by die top van die koepel' kom, wat volgens hom ontstaan ​​het deur differensiële vestiging deur ongelyke laai van die muur, veral naby die ingang van die rotonde in die hoofnis. In plaas van om 'n vertikale differensiële nedersetting te vind, het ons slegs spore van laterale opening oor die skeure waargeneem- wat ooreenstem met die effek van hoepelspanning. 21

Terenzio het geglo dat die krake kort na die konstruksie plaasgevind het as gevolg van herstelwerk van stene. Sy sketse van die krake word getoon:

Pantheon kraak (Terenzio 22)

Die Mark en Hutchinson -studie het getoon dat meridionale krake in die koepel in die onderste helfte tot ongeveer 57 grade van die horisontaal op die veerlyn strek.22 'n Vorige stresontleding van hierdie koepel deur Cowan het hierdie punt teoreties op 37 grade 36 'geplaas. .23

Dit is die punt waar hoepelspanning in die koepel verander van spanning na kompressie, wat 'n punt van swakheid in die onwapende betonkoepel bied. Hierdie teoretiese punt stem redelik ooreen met die werklike einde van meridionale krake. Die Mark en Hutchinson -studie het die krake gevind wat algemeen voorkom by die openinge binne die boonste silindriese muur, wat die plaaslike trekstrookspanne verhoog het. Benewens die koepel, het Terenzio genoem dat skeure in die mure opwaarts strek vanaf 24,6 voet (7,5 m) bo die vloer.

Mark en Hutchinson het professioneel die uitdaging aangegaan om die spanning in die Pantheon te definieer. Hul rekenaaranalise het 'n driedimensionele, eindige element-modelleringskode gebruik om agt toestande van die koepel te hersien, twee hiervan sluit krake in. Enkele ontwerpparameters op een van die gekraakte modelle was: 1) 'n Soliede muur van 5,5 m breed is gebruik in plaas van die oorspronklike muur met baaie. voet (1,5 m) is gebruik sonder trapringe en 4) die gewigte was 99,8 lb/ft 3 (1600 kg/m 3) vir die onderste koepel, 84,2 lb/ft 3 (1350 kg/m 3) vir die boonste koepel, en 109,2 lb/ft 3 (1750 kg/m 3) vir mure. Die Romeine het die gewig van die aggregaat verminder namate die hoogte verhoog is. Interessant genoeg het die analise getoon dat as die beton 2200 kg m 3 gebruik is, die spanning 80 persent hoër sou gewees het, sodat die Romeine kundig en versigtig was. 24

Die kraakpatroon van die beton in die Pantheon bied 'n unieke spanningskonfigurasie wat in die koepel en mure werk. Mark en Hutchinson beskryf hierdie prentjie as een waarin die belangrikste interne kragte in die gebarste koepel slegs in die meridionale rigting is, en hierdie gebied dien as 'n reeks boë wat 'n algemene druksteen in die vorm van die ongekraakte boonste koepel dra. Die gebarste mure dien as 'n reeks onafhanklike piere om hierdie boë te ondersteun.

By die modellering van hierdie konfigurasie het 'n maksimum buigspanning van 1,3 kg/cm2 by die pont plaasgevind waar die koepel by die verhoogde buitemuur aansluit. 25 Geen trektoetsresultate is op die Pantheon beskikbaar nie. However, Cowan discussed tests on ancient concrete from Roman ruins in Libya which gave a compressive strength of 2.8 ksi (200 kg/cm 2 ). An empirical relationship gives a tensile strength of 213 psi (15 kg/cm 2 ) for this specimen. 26 I conclude that the outstanding design work of Mark and Hutchinson places the stresses in the Pantheon within a safe design limit.

Perhaps as insurance against some future dislocation, should we add a steel band around a step-ring? Although the building has survived centuries, this valuable, cracked landmark of Roman history should be protected against future earthquakes at a small cost.


Pantheon (Rome): Plan

Description of work: Commissioned by Hadrian the building has captivated Western architects for generations. In 608 it was one of the first Roman temples to be converted into a church, Santa Maria Rotonda, and it has never been a ruin. "It compromises two elements: the first a conventional but deep porch supported by unfluted granite columns, its plinth originally approached via a flight of steps. This crudely abuts and provides the entrance to the second: the highly unconventional circular temple with its hemispherical dome. The dome springs from a drum whose height is exactly that of the radius of the dome (43.2 meters, 142 feet). " (Woodward, Christopher. The Buildings of Europe: Rome. Manchester University Press, 1995. p 40.)

Work type: Architecture and Landscape

Style of work: Ancient: Roman

Source: Blomfield, Reginald. A history of French Architecture: From the death of Mazarin till the death of Louis XV, 1661-1774. 2 vols. London: G. Bell and sons, ltd, 1921. (Vol. 2 plate CVII)


Floor Plan of the Pantheon, Rome - History

Kim Williams, Architect
Via Mazzini 7
50054 Fucecchio (Firenze) Italy
e-mail: [email protected]

W hat does the seventeenth-century Rundetarn (Round Tower) of Copenhagen have in common with the thirteenth-century Leaning Tower of Pisa? Or Houston's Astrodome, the first indoor baseball stadium built in the United States, with the vast dome of the Pantheon in Rome? Or a Chinese pagoda (fig. 1) with the Sydney Opera house (fig. 2) ? A first response might be "shape" but a more accurate answer would be "symmetry". Each of these strange couples of buildings share a different kind of symmetry that links them, in spite of their temporal and cultural differences. As Magdolna and István Hargittai have noted, symmetry, in architecture as in other arts, is "a unifying concept".[1]

Architecture, as any compositional art, makes extensive use of symmetry. Across all cultures and in all time periods, architectural compositions are symmetrically arranged. There are so many kinds of symmetry, so many kinds of architecture, and so many ways of viewing architecture, that the argument threatens to become so generalized that it loses all meaning. The general exposition of symmetry types found in architecture has been admirably presented in recent work.[2] While I wish to review symmetry types in architecture briefly in order to provide as wide an overview as possible within the limits of this paper, my ultimate object is to explore why an architect might choose a given symmetry type, and thus to provide insight into the design process from the point of view of symmetry.


The special case of architecture


A rchitecture differs fundamentally from other arts because of its spatiality. Identifying a type of symmetry in a two-dimensional composition is relatively straightforward the identification of symmetry types in a three-dimensional object such as a sculpture is somewhat more complicated because our perception of the object changes as we move around it. In the case of architecture, we not only move around it, but we move through it as well. This means that architecture provides us with a special opportunity to experience symmetry as well as to see it. This is possible because architecture consists of two distinct components: solid and void. Architecture is most frequently characterized by the nature of its elements: we recognize a Greek temple by its portico and pediments a Gothic cathedral is characterized by its pointed arches and flying buttresses. These are the elements that make up the solid component of architecture, and it is likely that it is with this solid component the lay person has the most experience. Naturally in the composition of these elements that one would expect to find various kinds of symmetry relations, and this, the symmetry that we see, is what I will be examining in the first part of this paper.
On the other hand, all these solid elements constitute an envelope around what we experience when we move through a building, that is, the void, or architectural space. In a very real way, the true work of the architect is to shape the void, which becomes the theater of the actions that take place in the building. This architectural space is most likely characterized by symmetry as well, though it is perhaps less familiar, and it is a symmetry which we experience. This is what I will examine in the second part of this paper.

An Overview of Symmetry types in Architecture

S ymmetry types are divided into two categories: point groups and space groups. Point groups are characterized by their relationship to at least one important reference point space groups lack such a specific reference point. Both point groups and space groups are found in architecture.

B ilateral symmetry is by far the most common form of symmetry in architecture, and is found in all cultures and in all epochs. In bilateral symmetry, the halves of a composition mirror each other. It is found in the facade of the Pantheon in Rome some 1700 years later on a continent undreamed of when the Pantheon was built, we find the same symmetry in the mission-style architecture of the Alamo in San Antonio, Texas. Bilateral symmetry is present also not only on the scale of a single building, but on an urban scale. An example of this is found in the design of the PraHo do Comercio in Lisbon, Portugal, where three urban elements (a major public square, a monumental gate and the wide commercial street beyond the gate) are symmetrical with respect to a long horizontal axis that governs our visual perspective.
The popular of bilateral symmetry is probably an expression of our experience of nature, and in particular with our experience of our own bodies. As many cultures believe that God created man in His own image, architecture has in turn probably been created in the image of man. Not all bilateral symmetry is of equal value in architecture, however. Two schemes for facades are shown in fig. 3. In one, there are an unequal number of bays in the other, there are an equal number of bays. The first is an example of "orthodox" bilateral symmetry, where the facade is divided into two equal halves but in the second, the axis of symmetry that divides the facade into two equal and independent halves creates a dualism. If it is true, as Dagobert Frey maintains, that bilateral symmetry represents "rest and binding"[3], then dualism represents divisibility. Traditionally, dualism in architecture has been considered something to be avoided. The temples of ancient Greece, for example, always had an even number of columns so that there was never a column on the central axis of the facade. The avoidance of the dual by classical architects probably stems from the ambiguity frequently attributed to the number 2, regarding with suspicion from the time of Pythagoras. The number 2 was considered untrustworthy (a female number) because it could be divided into halves, in contrast to the number 3 (a male number) which was not divisible into two parts. Even in modern architectural theory, dualism in architecture is considered a "classical and elementary blunder" and identified with the "amorphous or ambiguous".[4] These reservations not withstanding, dualism does exist in architecture. The fourteenth-century Oratory of Orsanmichele in Florence is an example (fig.4). It has a dual function: an oratory on the ground floor and a granary above. It has an unusual two-aisled plan. It has two altars. The difficulty of the dual on the level of architectural experience is best exemplified by the problem of the two altars. Where does one stand in the church? One is forced to make a decision whether to stand in front of one altar or the other. It is comparable to a house with two front doors. Where is the entrance? Usually this kind of decision is made for the spectator by the architect, who places one altar in a central position, or one prominent front door on the facade of a house. Thus, dualism in architecture presents a kind of a challenge to both the spectator and the architect.

R otation and reflection provide a sense of movement and rhythm in architectural elements and an emphasis on the central point of the architectural space. The Sacristy of the basilica of S. Spirito in Florence, designed by Giuliano da San Gallo in the last years of the fifteenth century, is octagonal in plan and both the architecture and the distinctive pavement design exhibit rotational and reflection (fig. 5). Domes, whether hemispherical such as that of the Pantheon or octagonal such as the great cupola of the Cathedral of Florence designed by Filippo Brunelleschi, also exhibit both rotation and reflection.

C ylindrical symmetry is that found in towers and columns Verticality in towers represents a defiance of gravity. Rare examples of spherical symmetry may also be found in architecture, though the sphere is a difficult form for the architect because human beings move about on a horizontal plane. The project for a cenotaph for Isaac Newton, designed by Etienne-Louis Boulée in 1784, demonstrates spherical symmetry.

C hiral symmetry is perhaps less well-known than other types of symmetry but frequently effectively used in architecture. Chiral symmetry is found in two objects which are each other's mirror image and which cannot be superimposed, such as our hands. The two opposing colonnades designed by Gianlorenzo Bernini that surround the elliptical piazza in front of St. Peter's in Rome exhibit chiral symmetry (fig.6). In Budapest, the two Klotid Palaces that tower above Felszabadul<s Square, each with asymmetrically placed towers and facade embellishments, are examples of chiral symmetry. A very subtle form of chiral symmetry is presented by the two leaning towers of the newly-completed Puerta de Europa in Madrid, designed by architect John Burgee in collaboration with Philip Johnson. Chiral symmetry in architecture is another way to place visual emphasis on the central element of a composition. In the case of the Puerta de Europa, for example, the two inclined towers emphasize the broad boulevard that passes between them, aptly forming a "gateway to Europe".

S imilarity symmetry is currently receiving a great deal of attention and is best known for its identification with fractals. Similarity symmetry is found where repeated elements change in scale but retain a similar shape, such as in the layered roofs on a pagoda (see fig. 1 above), the forms of which diminish in size but retain their form as they get closer to the top of the building. Another example of similarity symmetry is found in the nestled shells of the Sydney Opera House, designed by Joern Utzon in 1959 (see fig. 2 above). The shells are all segments of a sphere, thus similar in shape while differing in size and inclination. Another example of similarity symmetry is found in the Castel del Monte in Apulia in Italy, built by Friedrich II at the end of the first millennium. The basic form of the octagonal outer walls of the fort is repeated at a smaller scale in the interior courtyard, and again in the smaller towers which are added to each apex of the main octagon.[5] Similarity symmetry is also often used where it is least obvious, as in the relationships between room sizes. Frank Lloyd Wright used a kind of similarity symmetry in his design for the Palmer House in Ann Arbor, Michigan, in 1950-51.[6] In this case, Wright chose an equilateral triangle as a planning module, repeated at a number of levels and sizes to organize the design of the house. Similarity symmetry, whether visually apparent or not, results in a high degree of order within an architectural design, and lends unity to a composition.

S piral or helical symmetry may be thought of as a special kind of similarity symmetry. Helixes and spirals in architecture often represent continuity. In spiral staircases, the unbroken form expresses the continuity of space from level to level throughout the building. In the fantastic twisted spires of Copenhagen or of Borromini's S. Ivo alla Sapienza in Rome, the theme of continuity is expressed by the unbroken upward progression of the form. Frank Lloyd Wright used the helix in his 1946 design of the Guggenheim Museum of New York. In this case, the exterior of the building reflects the form of the giant helical ramp on the interior. The gallery spaces are arranged along one side of the ramp. The museum visitor takes the elevator to the top floor of the space, then spirals his way down the ramp to the bottom, admiring the art on display along the way. Criticism of the building focused on the fact that the downward spiral forced the visitors to hurry through the museum, unconsciously rushed by the pull of gravity. Legend has it that Wright, who placed greater value on architecture than on art, deliberately designed the building in order to get the visitor out as quickly as possible! In reality, however, the helical ramp once again expresses spatial continuity.

T ranslational symmetry falls in the category of space group symmetry, and is, after bilateral symmetry, the most common kind of symmetry found in architecture. Translation of elements in one direction is found in solemn rows of soldier-like columns, or in the springing succession of arches in an aqueduct. Translation of elements in two directions is present in the wallpaper-like patterns of the curtainwall facades of many modern buildings. Translation may also involve the repetition of entire pieces of buildings, especially in our own century, and may be one reason by modern architecture is so often referred to as boring or monotonous. Translational symmetry seems to carry with it an emphasis on a superlative quality in architecture: the longest, the broadest, the tallest.


This concludes my survey of types of symmetry found in arrangements of architectural elements. For the architect, the knowledge of symmetry types is a powerful tool, for it provides him not with a means for precisely describing a building, but with a range of expressive possibilities. We will learn more about the expressive possibilities of symmetry when we look at the use of symmetry in architectural space. However, before turning to this, I should emphasize another aspect of symmetry in architecture that makes it a special case in the study of symmetry.

Multiple Symmetries in Architecture

I n choosing the examples of various symmetry types for the previous section of this paper, I purposely focused on one aspect or part of a building that exhibits a single kind of symmetry. However, in most buildings we find more than one kind of symmetry. For example, in the Chinese pagoda, we can see at the same time both the cylindrical symmetry inherent in the building's organization about the vertical axis, and the similarity symmetry of the diminishing sizes of the layered roofs. A colonnaded temple facade may demonstrate bilateral symmetry, but it also demonstrates translation. These are examples of multiple symmetries that can be observed without requiring us to change our viewpoint of the building. We also perceive multiple symmetries when we change our position relative to the building, as for example, when we move from outside to inside. Domes are a very good example of this. From the outside, domes appear to be organized about a vertical axis (as they indeed are). When viewed from the inside, however, they appear to be organized about a central point.
Multiple symmetries also arise when a building is composed of multiple elements, some or all of which having its own symmetry. The symmetry type that we identify at any given moment, then, is a result of our physical position in relation to the building. It is important to make this point about multiple symmetries, because most architecture of any complexity at all is designed as a series of spaces that are meant to be experienced sequentially, as though the architect is telling us a story. Changing symmetries can be as important to the unfolding of the story as any of the other devices an architect has at his service. A closer examination of the Pantheon will illustrate the experience of an architectural "story".
The Pantheon in Rome is an excellent example of the experience of multiple symmetries that is common in architecture. When we stand in the piazza in front of the Pantheon, we notice right away the bilateral symmetry of the principle facade. Moving around the building, we discover that the Pantheon is composed of three easily-identified elements: the columned porch, a small intermediate block, and the great rotunda (fig. 7). The three are arranged in sequence: here is the beginning of the "plot" of the story. As we enter the Pantheon, we see that the three elements are arranged with respect to a common horizontal axis it is this axis that gives rise to the bilateral symmetry. However, once inside, the horizontal axis that we have followed to gain entrance into the rotunda disappears. It is replaced by a vertical axis that runs from the center of the pavement up to and through the oculus of the dome above. Thus the dominant symmetry is no longer bilateral. The lower zone exhibits cylindrical symmetry, while the hemispherical dome above exhibits rotation and reflection . The reason for the change in symmetries is that, when we enter into the rotunda we leave behind the zone of the terrestrial, represented by the horizontal axis, and experience the zone of the celestial, symbolized by the vertical axis. The Pantheon is a temple dedicated to all the gods the universe itself is represented in the rotunda by the form of the sphere, half of which is actually present in the coffered cupola which crowns the space, while the other half is only made implicit in the proportions of the space (as mentioned before, the sphere is problematic in architecture because human beings require a horizontal plane). The sphere contains an infinite number of planes of reflection and rotation its infinity symmetry makes it an apt symbol for the cosmos.

Symmetry in Architectural Space

H aving examined how symmetry is found in the parts of a building that we see, we may take a look at how symmetry relates to the part of the building we don't see, which is the void that is the architectural space. Two concepts are fundamental in describing architectural space: center and path. Center relates to a single important place within the larger architectural space, such as the altar in a church. Path relates to the spectator's movement through the space. Christian Norberg-Schulz writes that ". centre and path are present in any church, but their relationship differs."[7] This relationship actually determines how we perceive the architectural space of any given time period. In terms of symmetry, center may be thought of as "point" and path, as "axis." The following, very brief, examination of some 1500 years of architectural history hopes to demonstrate that as architectural space evolved through the centuries, so did the dominant symmetries.
In Roman architecture, strictly observed axial symmetry gives rise to spaces that are monumental and static, that is, generally embodying a sense of equilibrium rather than expressing a sense of dynamic movement.[8]

Consider the symmetry relations of the plan of a Roman basilica, a secular building type used as a court of law (fig.8). It is rectangular, with an apse on each end of the major axis and a doorways on each end of the minor axis. The architectural elements are always arranged so that like elements are always opposite: apse to apse, column to column, doorway to doorway. Excavations have brought to light the remains of the pavements used in basilicas they underline the sense of balance and equilibrium that characterize the architecture, as frequently they are based on patterns described by translational symmetry in two directions, rather than by any other kind of more dynamic symmetry type such as rotation. This same static arrangement of architectural elements is found in the rotunda of the Pantheon, Rome. Here the plan is a circle, with eight reflection planes and one four-fold axis of rotation (to be precise, the symmetry is approximate because the entrance is opposite a large round apse). Again we find oppositions: apse to apse, aedicule (a canopied niche flanked by colonnettes) to aedicule, niche to niche, column to column. The strict axial symmetry establishes the sense of equilibrium within the space that is characteristic of Roman architecture. It is interesting to note, however, that neither the axes nor the center point is made explicit through the pavement design of the rotunda, which is like that of the basilica based upon translation in two directions. Thus the symmetry was an organizing device for the architecture, but does not determine the movement of the spectator within the space. This is one characteristic that distinguishes Roman architecture from that of later periods, in which we will see how axes and centers are used to provide a specific dynamic emphasis and encourage movement.
After the legalization of Christianity in the fourth century, Christian architects chose to adapt the Roman basilica to their own ecclesiastical needs. To do so, they removed the entrances from the minor axis and placed a principal entrance on one end of the major axis, placing the altar in the remaining apse (fig. 9).[9]

Thus the symmetry was radically altered, there remaining only a single plane of reflection and no planes of rotation: the plan of the Christian basilica is bilaterally symmetrical. The axis of symmetry takes on an all-important symbolic role: it becomes a path, symbolizing the earthly pilgrimage of the Christian making his way towards the Kingdom of God. The pavement designs of many of these churches make explicit the axis that governs the architecture. Bilateral symmetry is favored over all other symmetry types during the Early Christian, Romanesque and Gothic periods, spanning from 300 to 1300 AD, because it best expressed the Christian ideal. It is the necessity of expressing the concept of pilgrimage, and not only that of expressing order as suggested by Hermann Weyl, that gave rise to the bilateral symmetry that dominated Christian architecture up until the Renaissance.[10] In addition to bilateral symmetry in plan, the sense of movement along a path is underlined by the translation of elements in a horizontal direction parallel to the dominant longitudinal axis. It is this kind of dynamic indication of direction that is lacking in Roman architecture.
As architectural and philosophical ideals changed in the Renaissance, so did the type of symmetry most frequently used. Sacred architecture was intended as a model of the cosmos created by God. To this notion, Humanism added the concept that, because man is God's most important creation in the cosmos, his place is in its center. The centrally-planned building was favored as best reflecting the perfection of the cosmos, thus rotational and reflectional symmetries were particularly favored during this period. The center point is usually made explicit in the pavement design: this particular emphasis on the center point induces the spectator to place himself there.
Pavement designs from the fifteenth, sixteenth and seventeenth centuries use rotation, reflection and similarity symmetry to emphasize the center. The rosette is a motif that often appears in pavement designs of this time, as for example, in the octagonal Sacristy of the basilica of S. Spirito in Florence (see fig.5 above). Here the rosette is formed from sections of a logarithmic spiral. To create the curvilinear checkerboard motif, a logarithmic segment is rotated a given number of times about the center in one direction, forming a fan pattern, then the direction of the segment is reversed and rotated about the center the same number of times in the opposite direction. The resulting rosette pattern has modules that increase in size but maintain their proportional similarity as they move farther from the center, and is therefore characterized by similarity symmetry as well as rotation and reflection. Another example of paving patterns from this period may be seen in the Cathedral of Florence, S. Maria del Fiore, in which trapezoid-shaped modules increase in size as they move away from the pattern's center, again demonstrating reflection, rotation and similarity symmetry. These patterns were no doubt favored because the perspective illusion they create is an excellent means of emphasizing the central point of the design, and through this, the central point of the architectural space.
Thus we see that in this arc of architectural history, the dominant symmetry evolved from a generalized axial symmetry in the Roman age, to bilateral symmetry in the Paleo-Christian, Romanesque and Gothic ages, to rotational and reflectional symmetry in the Renaissance. Our recognition of the symmetry in an architectural space is one step towards our understanding of the architecture, a means we are given to interpret the architectural "story" we are experiencing.

Gevolgtrekkings
At this point I draw to a close this discussion of architecture and symmetry. I hope that the wide variety of symmetry types and their various combinations as well as the use of symmetry to define space has been made clear. However, the topic of symmetry in architecture is far from exhausted. There are some further aspects of the subject that I am now studying but about which I am not yet in a position to draw conclusions, and for which this present paper forms a background.
One of these aspects has to do with "broken symmetries". The Pantheon in Rome provides one example of a symmetry break: the cylindrical lower zone of the rotunda is characterized by four planes of reflection and fourfold rotation, while the hemispherical dome above is characterized by twenty-seven-fold rotation. Four and twenty-seven have no common divisors, thus the symmetry "break." Another example of broken symmetries is found between horizontal tiers of the Baptistery of Pisa, which are alternately based on rotations of twelve and twenty.[11] These of course, are historical examples. Many other examples are present in modern architecture.
A second, very important question concerning the architecture today is this, "Why have contemporary architects deliberately chosen to disregard traditional types of symmetry in their architecture? The designs of Richard Meyer and Frank Gehry in the United States come to mind. The advantage of examining contemporary architecture lies in the fact that the architects are most often still living, and while we can never ask the architect of the Pantheon why he broke the symmetry of the rotunda, we can ask Frank Gehry why the design of Guggenheim Museum in Bilbao apparently throws a consideration of symmetry to the wind. I say apparently, because I would want to ask the architect for an explanation before hazarding any judgement of my own. So I hope in a future paper to be able to present the fruits of this current research, and shed even more light on the uses of symmetry, both apparent and otherwise, in architecture.

Erkennings
This paper developed from a lecture I gave in April 1998 at the Department of Mathematics of the University of Milan. I wish to thank Simonetta di Sieno and Liliana Curcio for the invitation to undertake this study.

1.Cf. István Hargittai and Magdolna Hargittai, Symmetry: A Unifying Concept (Bolinas, California: Shelter Publications, 1994). return to text

2.Cf. "The Universality of the Symmetry Concept", Nexus: Architecture and Mathematics, Kim Williams, ed. (Fucecchio, Florence: Edizioni dell'Erba, 1996), 81-95. return to text

3.Cf. Dagobert Frey, "On the Problem of Symmetry in Art" quoted in Hermann Weyl, Symmetry (Princeton: Princeton University Press, 1989), 16. return to text

4.Cf. Sinclair Gauldie, Architecture (London, 1969), 16. Gauldie considers the unresolved dual a "classic and elementary" error. return to text

5.Cf. Heinz Gotze, "Friedrich II and the Love of Geometry", Nexus: Architecture and Mathematics, 67-79. return to text

6.Cf. Leonard K. Eaton, "Fractal Geometry in the Late Work of Frank Lloyd Wright: The Palmer House", Nexus II: Architecture and Mathematics , Kim Williams, ed. (Fucecchio, Florence: Edizioni dell'Erba, 1998), 23-38. return to text

7.Christian Norberg-Schulz, Meaning in Western Architecture (New York: Praeger Publishers, 1975), 145. return to text

8.Cf. Bruno Zevi, Saper vedere l'architettura (Turin: Einaudi Editori, 1948) 57. "Impera negli ambienti circolari e rettangolari la simmetria. una grandiosità duplicement assiale. " ("Symmetry reigns in circular and rectangular environments, based on dual axes. " --translation by Kim Williams). return to text

9.Ibid., 59. " La basilica romana è simmetrica rispetto ai due assi: colonnati contro colonnati, abside di fronte ad abside. Essa crea quindi uno spazio che ha un centro preciso ed unico, funzione dell'edificio, non del cammino umano. Che cosa fa l'architetto cristiano? Praticamente due cose: 1) sopprime un'abside, 2) sposta l'entrata sul lato minore. In questo modo, spezza la doppia simmetria del rettangolo, lascia il solo asse longitudianle e fa di esso la direttrice del cammino dell'uomo. " (The Roman basilica is symmetric with respect to the two axes: colonnade opposite colonnade, apse opposite apse. This creates a space which has a precise and unique center, a function of the building, not of man's movement. What did the Christian architect do? Essentially two things: !) suppressed an apse, 2) moves the entrance to the shorter side. Thus he breaks the dual symmetry of the rectangle, leaving only the longitudinal axis, which he makes the directrix of man's movement.--translated by Kim Williams.) return to text

10.Cf. Hermann Weyl, Symmetry , 16. return to text

11.Cf. David Speiser, "The Symmetries of the Baptistery and the Leaning Tower of Pisa", Nexus: Architecture and Mathematics , 135-146. return to text

Nexus Network Journal: Architecture and Mathematics Online

Symmetry: Symmetry online featuring Symmetry: A Unifying Concept by Magdolna and Istvan Hargittai


Construction Technique

Figure 10. Pantheon interior, light from the oculus illuminating the hole left by the cutting of Brunelleschi’s sample

The Pantheon is a marvel of construction ingenuity- the result of a century of experimentation with the use of advanced building elements such as the relieving arch, vaulting rib, lightweight caementa, and step rings. What is particularly unique to the Pantheon however is the method by which these elements were incorporated into a structural system that has allowed the largest unreinforced concrete dome ever built to stand for almost two millennia.

Until the 20th century, the Pantheon was the largest concrete structure in the world. And it remains the world’s largest unreinforced concrete dome. [17] An engineering marvel, the dome’s components are a tribute to the creativity of the design. For example, the oculus (otherwise known as the “open eye”) serves to reduce loading at the top.

Otherwise, the dome still stands at 142 feet high and wide under a circular rotunda for additional reasons. According to the analysis of Filippo Brunelleschi, an engineer and architect of 1377, a material sample taken from the Pantheon’s dome, to the right of the entrance, shows that the concrete composition of the structure was non-homogenous. (Figure 10.) The construction technique applied to the dome involved applying thinner and lighter concrete at greater heights- the highest part incorporating volcanic pumice as aggregate.


What's the Difference Between the Pantheon and the Parthenon?

If a friend who was about to go off on a European adventure told you they were going to visit the Pantheon, would you immediately picture ruins of ancient white marble columns? What if that same friend told you they would also be stopping by the Parthenon. Would you also picture a similar scene in your head?

The point is, the Parthenon and the Pantheon are often confused as being the same thing. And that's no surprise because the names are super similar. But the two are very different they're not even located in the same country. The Parthenon, for instance, is in Athens, Greece, and the Pantheon is in Rome, Italy. And aside from both being made of marble and sharing a similar etymology — both names are derived from the Greek word parthenos, which is an epithet of the Greek goddess Athena, meaning "virgin" — these two famous buildings of the ancient world actually have very little in common.

We spoke with Christopher Ratté, a classical archaeologist and professor at the University of Michigan and Dr. C. Brian Rose, the curator-in-charge of the Mediterranean Section at the Penn Museum and archaeologist who's been digging in the field for more than 40 years, to find out exactly what makes these two ancient ruins so different.

1. They Were Built in Different Centuries

The Parthenon and the Pantheon are two of the most famous temples ever built in ancient Athens and ancient Rome. The Pantheon was constructed in the second century A.D., while the Parthenon we know today was built much earlier around 447 B.C.E. However, neither, as they say, was built in a day.

The Pantheon is one of today's best-preserved ruins from ancient Rome. It was built sometime between 126 and 128 A.D. during the reign of Emperor Hadrian, who was emperor from 117 to 138 A.D. "It was a reign largely marked by peace . there was plenty of money throughout the empire," Rose says. "Economically it was a very prosperous time and you see that reflected in the building program. [The Pantheon] is primarily made of concrete, but the inside is lined with marble imported from Egypt, Greece, Asia Minor and North Africa these international materials bolster the Pantheon as a symbol of the extent of the Roman Empire."

The Parthenon, on the other hand, took 15 years to build, Rose says. It was built between 447 and 432 B.C.E. during the aftermath of the Persian Wars to highlight the victory of the Greeks over the Persians. At the time, the Greeks were led by (or controlled by, depending on who you talk to) Athens, which was being controlled by a commander named Pericles. Athens had access to a treasury that could pay for additional arms conflict if the Persians came back. This treasury helped to fund the construction of the Parthenon. The goddess Athena was credited with steering the Greeks toward victory, which is why, had you visited the site at the time, you would've found a statue of her in the temple's main room (more on that next).

2. They Honor Different Gods

While both were built to honor gods, the Parthenon was built to honor Athena and the Pantheon was built to honor all of the Greek gods.


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Kommentaar:

  1. Gok

    but another variant is?

  2. Ayub

    Hulle is goed vertroud hierin. Hulle kan help om die probleem op te los. Saam kan ons by 'n korrekte antwoord vorendag kom.

  3. Gene

    Ek dink jy is verkeerd. Ek is seker. Kom ons bespreek dit. E -pos my by PM, ons sal praat.

  4. Ceneward

    Jy het dit reg gesê :)

  5. Holcomb

    The double understood as something

  6. Voshura

    Bloot die glans



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