THE PLAN-NET AS A GEOMETRY FOR ANALYSIS OF PRE-MODERN ARCHITECTURAL DESIGN AND LAYOUT Arthur John Lawton submitted to the faculty of the University Graduate School in partial fulfillment of the requirements for the degree Doctor of Philosophy in the Department of Folklore and Ethnomusicology December 2013 Accepted by the Graduate Faculty, Indiana University, in partial fulfillment for the degree of Doctor of Philosophy Doctoral Committee Henry Glassie, Ph.D. Jason Jackson, Ph.D Pravina Shukla, Ph. D. Eric Sandweiss, Ph. D. November 12, 2013 ii Copyright © 2013 Arthur J. Lawton iii Arthur Lawton PLAN-NET GEOMETRY AND ANALYSIS OF PRE-MODERN ARCHITECTURAL DESIGN AND LAYOUT Limited Pre-Modern calculating skills favored geometry for design and layout. Technical limitations precluding durable, detailed measured drawings favored sequentially proportional steps transmitting information from design to construction. The Ancient Egyptian phrase “Casting the plan-net on the ground” implies a rectilinear network of geometrical lines serving to locate plan elements on the ground. Reconstruction of Polykleitos’ Kanon demonstrates design parameters based on sequential proportionality that extracts a “correctly” proportioned human figure from an original square base figure. Fifteenth century booklets describe extraction of a completed architectural form from the base figure. Iconographic sources trace these Ancient World methods from their use in practical implementation to symbolization as eighteenth century remembrances in Free Mason paraphernalia. To associate floor plan elements with a rectilinear network, plan-net geometry manipulates proportional relationships of squares and rectangles in sequentially proportional steps. Geometrical design steps by divider and straightedge are identical to ground-lines steps by cord and peg, eliminating calculation from scale change. Marking plan features by plan-net analysis reveals an inherent geometrical unity that appears to cross diachronic and synchronic borders. Varied plan-net patterns offer a new perspective for classifying vernacular floor plans. Conformance to plan-net lines by iv indeterminate architectural elements validates elements in question and suggests other elements missing from the architectural or archeological record. Seeking to understand how a house is thought as Henry Glassie said, and if culture is pattern in the mind, then plan-net analysis renders such pattern visible, to be understood as a unity crossing boundaries of culture and time but whose products can be differentiated as artifacts localized within cultural and temporal boundaries. To understand what has disappeared from the record, we must be willing to imagine what was, and then test what is imagined to ascertain how it fits to what is. v Table of Contents Abstract - - - - - - - - - p. Table of Contents - - - - - - - - p. Table of Illustrations - - - - - - - - p. Chapter 1. Introduction - - - - - - - - p. 1 2. Previous Works - - - - - - - p. 9 Jay Hambidge - - - - - - - p. 16 Kenneth Conant - - - - - - p. 17 Rudolf Helm - - - - - - - p. 23 Paul Frankl - - - - - - - p. 28 J. J. Coulton - - - - - - - p. 35 Lothar Haselberger - - - - - - p. 38 Laurie Smith - - - - - - - p. 39 Robert Bork - - - - - - - p. 41 Tons Brunés - - - - - - - p. 41 Lon Shelby - - - - - - - p. 49 J. Marshall Jenkins - - - - - - p. 50 Summary - - - - - - - p. 52 3. Root Rectangles and Sequential Proportionality - - - p. 58 Socrates and the Meno Problem - - - - p. 58 Tons Brunés and the Development of Geometric Thought - p. 61 vi Richard Tobin’s reconstruction of the Kanon of polykleitos - p. 71 Lon Shelby, Matthes Roriczer and “Constructive Geometry” p. 77 The Sulva Sutras and lay-out by Cord and Peg - - p. 90 4. The plan-Net narrative over Time - - - - - p. 98 Plan-Net Method - - - - - - p. 99 The plan-Net in Egyptian Foundation Texts - - - p. 70 Gudea of Lagash with a Building Plan - - - p. 107 Gunzo’s Dream of a Plan for Cluny III - - - p. 109 Norbert’s Vision, Weissenau Chapel and symbolization - p. 116 Plan-net instruments in the Symbols of Free Masonry - p. 119 Chapter summary - - - - - -- p. 121 5. The Application of Plan-Net Analysis - - - - p. 122 Quadrilateral Rectilinear Plans - - - - p. 137 Analysis - Bertolet Log House, Pennsylvania, ca. 1745 p. 122 Analysis - Henrich Antes House, Pennsylvania, 1736 p. 128 Analysis - Palladio’s Villa La Rotunda, Italy, 1570 - p. 134 Analysis – Herr House, Pennsylvania, 1719 - - p. 138 Analysis – Schultheiss House, Germany, 1799 - p, 139 Analysis – Church Farm, England, 1670 - - p. 140 Analysis – Wittenschlager Stable, Germany, 15-16th C. p. 141 Trilateral Rectilinear Plans - - - - - p. 142 Analysis – Eckstein House, Germany, 1766 - p. 143 Analysis – Sperber House, Germany, 1799 - - p. 144 vii Analysis – Hupfer House, Germany, 1745 - - p. 145 Analysis – Ottörfer House, Germany, 1766 - - p. 146 Analysis – Buchner house, Germany, 1725 - - p. 147 Analysis – Heberlein House, Germany, 1745 - p. 148 Analysis – Kofer Distillery, Germany, 1702 - p. 149 Bilateral Rectilinear Plans - - - - - p. 150 Analysis – Mangohick Church, Virginia, ca. 1731 - p. 152 Analysis – Middle Church, Virginia, begun in 1712 - p. 153 Analysis – St. Peter, Church, Virginia, 1701-1703 - p. 154 Analysis – St. Luke’s Church, Virginia, ca. 1683 - p. 156 Analysis – Ellen Cutler’s house, Ireland, Undated - p. 158 Analysis – Clloney Townland, Ireland, ca. 1780 - p. 160 Analysis – lunniagh, Townland, Ireland, Undated - p. 161 Analysis - Nant-y-ffin, Carmarthenshire, Wales, - p. 162 Analysis – Ystradamen, Carmarthenshire, Wales, - p. 163 Plan-net Analysis and Indeterminate Architectural Fabric - p. 165 Plan-net and implicit architectural message - - - p. 173 Plan-net and the Strasbourg Cathedral facade - - p. 175 6. Conclusions - - - - - - - p. 178 viii List of Illustrations Chapter one. Fig. 1. - Matthes Roriczers’ base figure p. 9 Fig. 2. - Lorentz Suckows’ symmetrical facade formula p. 10 Chapter two. Fig. 3. - Babylonian number array p. 21 Fig. 4 - Helm’s analytical drawing p. 25 Fig. 5 - Stornalocco, Milan Cathedral drawing p. 32 Fig. 6 - Construction lines, temple at Didyma p. 39 Fig. 7 - five circle module at Old Impton Porch p. 40 Fig. 8 - Strasbourg Cathedral, Klotz drawing p. 42 Fig. 9. - Bork’s generating octagon p. 43 Fig. 10 - Full set of generating octagons p. 45 Fig. 11 - Nested squares in cathedral floor plan p. 46 Fig. 12 - Jenkin’s Root rectangle analysis, Welsh houses p. 51 Chapter three Fig. 13 - Plato’s Meno problem p. 59 Fig. 14 - Parthenon facade analysis by Brunés p. 61 Fig. 15 - Brunés, circle and cross p. 62 Fig. 16 - Brunés, formation of a square p. 63 Fig. 17 - Brunés, circle with squares p. 63 Fig. 18 - Brunés, division of circle and squares p. 64 Fig. 19 - Brunés, squares in parallel p. 65 Fig. 20 - Brunés, square with Sacred Cut p. 66 Fig. 21 - Brunés, Square, with eight-pointed star p. 68 Fig. 22 - finding intervals of 3, 4 and 5 p. 69 Fig. 23 - Polykleitos, Doryphoros statue p. 72 Fig. 24 - Tobin, Polykleitos canon applied to the forearm p. 73 Fig. 25 - Tobin, canon applied to the whole body p. 74 ix Fig. 26 - Villard de Honnecourt , Sketchbook, fol. 18v p. 76 Fig. 27 - Divide a line segment into equal parts p. 80 Fig. 28 - Roriczer, straight line equal to circle circumference p. 81 Fig. 29- Plimpton 322, solution by constructional geometry p. 82 Fig. 30 - Roriczers’ first three steps p. 84 Fig. 31 - How to draw nested parallel squares p. 85 Fig. 32 - Roriczer, the completed base figure p. 86 Fig. 33 - Roriczer, the extraction device p. 87 Fig. 34- Roriczer, extracting pinnacle from base figure p. 88 Fig. 35 - Roriczer, extracting gablet from base figure p. 89 Fig. 36 - Thibaut, Vedic Indian cord and peg solution p. 93 Fig. 37 - Thibaut, Sulvasutra altar layout diagram p. 95 Chapter four Fig. 38 - Rotating the square’s diagonal p. 99 Fig. 39 - Any diagonal may be used to increase nodes p. 100 Fig. 40 - Hieroglyphic inscription, Thutmosis III p. 103 Fig. 41 - Hieroglyphic inscription from Dendera p. 103 Fig. 42 - Ostrakon from Valley of the Kings p. 105 Fig. 43 - Gudea, king of Lagesh, with floor plan p. 107 Fig. 44 - Gunzo’s Dream illumination p. 111 Fig. 45 - Norbert’s vision of the crucifixion p. 116 Fig. 46 - Weissenau monks build a chapel p. 116 Fig. 47 - Cord detail, Weissenau monks p. 117 Fig. 48 - The initial plan-net square p. 119 Fig. 49 - masonic apron, constellation of symbols p. 119 Fig. 50 - French Masonic handbook, symbol constellation p. 120 Chapter five Fig. 51 - The Bertolet log house, ca. 1745 p. 122 Fig. 52 - Bertolet log house floor plan p. 123 x Fig. 53 - Bertolet house plan-net analysis, step one p. 124 Fig. 54 - Bertolet log house, steps two and three p. 125 Fig. 55 - Bertolet log house, steps four and five p. 126 Fig. 56 - Completed Bertolet log house plan-net analysis p. 127 Fig. 57 - Henry Antes house, 1736, first floor plan p. 128 Fig. 58- Henry Antes house, initial base figure p. 129 Fig. 59- Antes, First two expansions of the plan-net p. 130 Fig. 60 - Longer diagonals lay out larger kitchen space p. 131 Fig. 61 - Henry Antes house, full expansion of plan-net p. 132 Fig. 62- Henry Antes house, 1736, exterior view p. 133 Fig. 63 - Palladio, Villa La Rotunda , floor plan, 1570 p. 134 Fig. 64 - Villa La Rotunda, initial square base figure p. 135 Fig. 65 - Villa La Rotunda, first set of extractions p. 135 Fig. 66 - Villa La Rotunda, second set of extractions p. 136 Fig. 67 - Villa La Rotunda, third set of extractions p. 136 Fig. 68 - Christian and Anna Herr, house, 1719 p. 138 Fig. 69 - Eltersdorf,, Schultheiss house, demolished 1799 p. 139 Fig. 70 - Church Farm, Great Waldingfield, 1670 p. 140 Fig. 71- Kalchreuth, Wittenschlager stable, undated p. 141 Fig. 72 - Weissenbrunn, Eckstein house, derelict in 1766 p. 143 Fig. 73 - Haimendorf, Sperber house, derelict in 1799 p. 144 Fig. 74 - Weissenbrunn, Hupfer house, demolished in 1745 p. 145 Fig. 75 - Weinhof, Ottörfer house, derelict in 1766 p. 146 Fig. 76 - Unterhaidelbach, Buchner house, derelict in 1725 p. 147 Fig. 77 - Entenberg, Heberlein house, derelict in 1745 p. 148 Fig.