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Cosmological Motifs of Peruvian Huacas JOHN MCKIM MALVILLE, MICHAEL ZAWASKI , AND STEVEN GULLBERG SEDDON, M. T. and BAUER, B.S., 2004. Excavations at Tikani. In: C. STANISH and B.S.BAUER, eds. Archaeological Research on the Islands of the Sun and Moon, Lake Titicaca, Bolivia. Los Angeles: Cotsen Institute of Archaeology, 83-93. URTON, G., 1981. At the Crossroad of Earth and Sky: An Andean Cosmology. Austin: University of Texas Press. ZUIDEMA, R. T., 1982. Catachillay: The Role of the Pleiades and of the Southern Cross and α and β Centauri in the Calendar of the Incas. Annals of the New York Academy of Sciences, vol 385, 203-229. ZAWASKI, M., 2007. Archaeoastronomical Survey of Inca Sites in Peru, M.A. Thesis, Greeley, Colorado. Received: 2 November 2007; Revised: 5 May 2008 KOSMOLOGINIAI PERUJIETIŠKŲ HUAKŲ MOTYVAI susiję su kūrimo mitais. Urubamba kolonos ir Huayna Capac rūmai Urubambos mieste yra orientuoti saulėtekio kryptimi vasaros saulėgrįžos metu. Maču Pikču Šventoji aikštė, Intiwatana upė ir Llactapata Saulės šventykla yra išsidėsčiusios beveik tiksliai pagal saulėtekio vasaros saulėgrįžos metu ir saulėlydžio žiemos saulėgrįžos metu ašį. Urubambos Intiwatana upė yra archetipinė šventykla (huaka), kuriai priklauso olos, versmės, laiptai ir platformos. Ypač senas šaknis turinčią solsticinę orientaciją, būdingą Andų civilizacijai, gyvavusiai 1700 metų, atskleidžia Chankillo vietovė. Pagrindinė geometrinė Chankillo ašis atitinka saulėtekį per žiemos ir vasaros saulėgrįžas. Tikėtina, jog kalendorinė bokštų paskirtis galėjo būti suderinta su šamaniškais ritualais, panaudojant laiptus, platformas ir eitynių tarp huakų vietas. Vertė Vykintas Vaitkevičius John Mckim Malville, Michael Zawaski, Steven Gullberg Santrauka Tiriant Peru šventyklas huakas (huacas) išryškėja trys pagrindinės tarpusavyje glaudžiai susijusios temos: protėvių garbinimas, šamanizmas ir kūrimo mitai. Saulė inkų buvo suprantama kaip pati svarbiausia iš protėvių, o šamanizmas greičiausiai yra pati seniausia pasaulio religija. Nagrinėdami daugiau kaip pusantro tūkstančio metų laikotarpį apimančių archeologinių vietų astronominius ypatumus, aptikome, kad visose jose atsižvelgiama į solsticijas. Kiti bendri bruožai yra kilimo aukštyn simbolika ir ritualams skirti paaukštinimai. Vanduo, akmenys ir olos inkų kosmologijoje yra 182
A GEOMETRICAL ANALYSIS OF MESOAMERICAN PRE-HISPANIC ARCHITECTURE: SQUARING TRIADS, NUMBERS, LENGTH UNITS AND THE CALENDAR MARCELLO RANIERI Abstract This work extends to Mesoamerica researches on archaic geometry previously performed on architectures of the “Old World”. CAD (Computer Aided Design ) tools are used to fit theoretical forms to spatial segments on archaeological plans. The analyses provide quantitative information on the forms, on the numbers involved and on the units of length used. Everywhere, numbers appear mainly to be multiples of 9, 10 and 13, rather than pertaining to Squaring Triads, although these are nonetheless attested in all regions. Three units of length are found: a “Teotihuacán unit” t ≈ 0.58 m, a “Monte Albán unit” ma ≈ 0.50 m and a “Chichen Itza unit” ci ≈ 0.66 m. Units t and ma clearly appear to be linked to the distances between the main monuments, associated with the Tzolkin calendrical numbers 13-20 at Teotihuacán and with the Haab calendrical numbers 18-20 at Monte Albán. Key words: geometry, Squaring Triads, length-units, calendar, Mesoamerica, Teotihuacán, Monte Alban, Chichen Itza. ARCHAEOLOGIA BALTICA 10 Introduction The repertory of distinct geometrical forms identifiable on archaeological plans consists mainly of right-angled shapes and circles. In the vast majority of cases, right-angled shapes prevail and show a remarkable perfection. Among the supposed methodologies that the ancients may have used to achieve the squaring, the most interesting is the one in which three appropriate integer numbers (a Squaring Triad or Triple) define the lengths of the sides and diagonals in terms of given units of length. This approach has proved successful in decoding geometric arrangements of relevant structures in the “Old World” (Ranieri 1997, 2002, 2005, 2006, 2007, 2008; Malgora 2000; Patanè 2006). A suitable repertory of Squaring Triads can be found in Table 2. Circular forms can be predominant in certain contexts (as for the Nuraghic culture) but are also present in rectangle-dominated contexts. Of importance for the present work is the “Circle-Square-Circle” (CQC) composition: two concentric circles, the smaller of which is inscribed within, and the larger circumscribed to, a square. In CQCs the dimensions of the diameters are those of the sides and diagonal of the square (Fig.1a) so that the circular dimensions can be deduced in their turn from the squaring numbers of the square (first four entries in Table 2). A study of the occurrence of CQC patterns in the geometry of ancient structures is under way and will be presented elsewhere. Methodological Approach Even for a single monument – in my experience - a through analysis would require about one year on average. Given that there are hundreds of Mesoamerican sites and monuments, analyses of even only a hundred of them would therefore take a century. Therefore I opted for a more practicable (3-4 years’ work) “largenumber” approach with less detailed analyses (only providing “good-fits” rather than best-fits) on about 150 monuments in the hope that statistics would eventually help to explain major geometric features (if any existed) common to all Mesoamerican architecture. As we shall see, the results have been more than encouraging with unexpected discoveries of undeniable importance. With few exceptions, plans were taken from Marquina (1951), starting with plans of more than 200 monuments altogether. About 75% were considered eligible for CAD analysis. “Good-fits” For the Squaring Triads in the repertory, the differences between two nearby proportion values (r = B/A) can be small. For this reason, “triadic” interpretations may be of low reliability with uncertainties on average greater than 3%. On the other hand (and unlike what had been experienced with “Old World” artefacts), Triads, although clearly present, do not appear to be the principal characters in the numerical repertory of Mesoamerican architecture. It appears rather that the V V. REFLECTIONS OF ASTRO- NOMICAL AND COSMOLOGICAL KNOWLEDGE IN MONUMENTS, LANDSCAPES AND ARCHITECTURE 183
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ARCHAEOLOGIA BALTICA10 Astronomy an
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UDK 902/904 Ar 46 Volume 10 Editori
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Vytautas Tumėnas. The visual and t
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PREFACE Jonas VaiškūnaS Preface T
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Jonas VaiškūnaS Preface cists, ma
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LIST OF CONTRIBUTORS List of Contri
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List of Contributors Dimitar Kolev
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List of Contributors 16 Dainius Raz
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Second Parts can always be better!
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Conference Summary: A Historian’s
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THE MILKY WAY AND ITS STRUCTURING F
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THE MILKY WAY AND ITS STRUCTURING F
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CECILIA PAULA GÓMEZ Venus And The
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CECILIA PAULA GÓMEZ Venus And The
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Astronyms in Belarussian Folk Belie
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Traditional Astronomical Knowledge
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Traditional Astronomical Knowledge
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A Solar Calendar from Latvian Daina
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A Solar Calendar from Latvian Daina
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SAULĖS KALENDORIUS PAGAL LATVIŲ D
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Mesopotamian Influences on Persian
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THE BIRTHDAY OF ASAKKU ARKADIUSZ SO
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ARKADIUSZ SOŁTYSIAK The Birthday o
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ARKADIUSZ SOŁTYSIAK The Birthday o
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NOEMI MIRANDA, JUAN A. BELMONTE, MI
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NOEMI MIRANDA, JUAN A. BELMONTE, MI
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Tracing the Celestial Deer - an Anc
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Tracing the Celestial Deer - an Anc
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Calendrical Deer, Time-Reckoning an
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The Mythological Moon Horse as Refl
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The Visual and the Mythical- Poetic
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VYTAUTAS TUMĖNAS The Visual and th
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Some Peripheral Forms of the Medite
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JONAS VAIŠKŪNAS Some Peripheral F
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Were the 185 A.D. and 369 A.D. “G
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Indigenous Astronomical Traditions
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A new attempt to date the Xia, Shan
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GÖRAN HENRIKSSON A new attempt to
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Eleventh-Century Supernovae: Anothe
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Eleventh-Century Supernovae: Anothe
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The Date of Purim and Calendars in
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L’abbé Jean Lebeuf, (1687- 1760)
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Orientations at the Minoan Peak San
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Page 156 and 157: The Nuraghic Well of Santa Cristina
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Page 164 and 165: ANDREI PROKHOROV Images on the Ston
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Page 176 and 177: JOHN MCKIM MALVILLE, MICHAEL ZAWASK
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Page 184 and 185: MARCELLO RANIERI A Geometrical Anal
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Page 204 and 205: RIMVYDAS LAUŽIKAS Some Cosmologica
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From Umm Al Qab to Biban Al Muluk:
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The Orientations of Central Alentej
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Cardinal and Lunisolar Alignments a
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Cardinal and Lunisolar Alignments a
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Searching for the Astronomy of Abor
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Alternative Archaeoastronomies - An
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Alternative Archaeoastronomies - An
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THE CASE STUDY OF THE BOORONG The C
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The Case Study of the Boorong JOHN
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The Case Study of the Boorong JOHN
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Nationalism and Politics in the Rec
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Nationalism and Politics in the Rec
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Cosmic Catastrophes and Cultural Di
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In Memoriam Izold’s interests wer
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Klaipėdos universiteto leidykla AR
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Plates 1 11 Plate VI. VI Antonio C
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