the geometry of architecture by Lawrence Kasparowitz

the geometry of architecture

compiled and illustrated by

Lawrence Kasparowitz

INTRODUCTION Do architects use geometrical relationships when designing floor plans? Maybe. Does the study of the process of a design morphing from a basic fundamental generic form to a clear diagram help architects visualize a process for design generation? Definitely. I created two previous books which led to this. The first was Spatial Composition (an enlargement of a set of notes from my professor at Oregon). The second book was a collection of architectural plans through 2,000 years of history simply called Plan. It seemed that this volume was predestined to occur. I began collecting the plans with the strongest geometrical references. Bramante’s plan for the Basilica of St. Peter’s in Rome is a classic. It’s obvious this plan starts with a square - the four quarters are mirror images. The central vertical and horizontal aisles are wider than the others. There are two additional smaller aisles on each side of the central aisle. The center of the plan has a circular form (indicating a dome above).

Shaded areas show the additions through the evolution of the plan. For each plan I have attempted to show the pattern of thought from the generic form to the final plan. Adjacent to each set of diagrams are statements that explain the compositional role the revisions are playing. Finally, an exterior and an interior photo follows on the next page. A connection between the diagrams, plan and completed building is obvious.

TABLE OF CONTENTS San Vitale Church (548) Julius Argentarius, architect

Chartres Cathedral (1194) Architect unknown

Coucy Castle (1245) Eugene Viollet-le-Duc, architect

Chenonceau Castle (1524) Philbert l’ Orme, architect

St. Peters Basilica (1506) Donato Bramante, architect

Palace of Charles V (1527) Pedro Muchaca, architect Villa Capra (1571) Andrea Palladio, architect

Selimiye Mosque (1575)

Mimar Sinan, architect

TABLE OF CONTENTS

Taj Mahal (1648) Ustad Ahmad Lahouri, architect

Luton Hoo House (1774) Robert Adam, architect

Unity Temple (1910) Frank Lloyd Wright, architect

Guggenheim Museum (1959) Frank Lloyd Wright, architect

Vanna Venturi House (1964) Robert Adam, architect

Condominum 1 (1965) MLTW, architects

Mt. Angel Library (1970) Alvar Aalto, architect

Philips Exeter Library (1971) Louis Kahn, architect

17 19 21 23 25 27 29 31

TABLE OF CONTENTS

Winton Guest House (1982) Frank Gehry, architect

Kidosaki House (1986) Tadao Ando architect

Friesen House (2000) Richard Meier, architect

Sherger-Kolberg House (2005) Bart Prince, architect

Santo Volto Church (2006) Mario Botta, architect

Ziedler Residence (2011) Steven Ehrlich, architect

case

studies

San Vitale Church Ravenna, Italy Julius Argentarius, architect

Octagon and tube shape align at center Octagon rotated Center (dome) marked Nave on tilted axis flanked by circular chapels Stairs at bottom of octagon Apse of nave added Enclosure of stairs and entry Subdivision of dome area

Chartres Cathedral Chartres, France architect unknown

Vertical and horizontal rectangles Central axis in both directions Half circle at apse Widened rectangles at ends Subdivisions provide aisles and location of columns Rectangle reinforces center location Circles indicate sub-spaces at apse

Coucy Castle Coucy-le-Château-Auffrique, France Eugene Viollet-le-Duc, restoration architect

Basic forms Diagonal location of main hall Towers at each corner “markers” Primary tower Interior of towers hexagonal (as opposed to circular)

7Â

Chenonceau Castle Val d’ Loire, France

Philibert L’ Orme, architect

Rectangle with courtyard at center Central axis in both directions Corner “anchors” Circulation corridors Entry and room at rear Indentations at sides

9Â

St. Peter's Basilica Rome, Italy Donato Bramante, architect

Basic square plan with subdivisions Addition of bays, Central focus (rotunda) Corner anchors Repeat of circular elements at intersections

Palace of Charles V Granada, Spain Pedro Machuca, architect

Exterior rectangle Circular interior court Hexagon corner Rooms areas within square Interior circle defines colonnade Rooms at vertical and horizontal axis

Basic square with subdivisions Additional subdivision within square Extensions around square form Central rotunda Circulation areas in both directions Stairs at four corners

Villa Capra Vicenza, Italy Andrea Palladio, architect

Selimiye Mosque Edirne, Turkey Mimar Sinan, architect

Attached rectangles with rectangular interiors (right: courtyard, left: mosque) Courtyard - central focus (fountain) with subdivisions in covered area Mosque - octagonal shape defines column locations Courtyard - “mini-domes” over each bay Mosque - alcoves at four corners, larger alcove provides focus

Taj Mahal Mausoleum Agra, India Ustad Ahmad Lahauri, architect

Octagon centered in square locates site of tomb Interior circulation to connect subspaces Subspace shape repeats central space Indentations give undulation to facade Chamfered corners soften mass of building Interior passages connect tomb area to sub spaces through interior ring

19Â

Luton Hoo Manor Bedfordshire, England Robert Adam, architect

Rectangular central space with horizontal aisle in middle Vertical rectangles for flanking wings Central entry room Bays at each end of wings Primary rooms at center of wings Rotunda at entry Bay at rear continues theme Bays at front entry

Unity Temple Oak Park, IL Frank Lloyd Wright, architect

Served space - link - servant spaces Vertical and horizontal axis Square “anchors” at corners Subdivision of major and minor spaces Addition of outdoor “rooms”

Guggenheim Museum New York, NY Frank Lloyd Wright, architect

Two rectangles with central axis Variation in orientation Main area (large circle) at intersection Circular end of street area Diagonal orientation Balcony at upper floor Diamond shape denotes elevator Circular shape enlivens street volumes

Vanna Venturi House Philadelphia, PA Robert Venturi, architect

Rectangular form with uneven subdivisions Carve-outs and mass locations Addition of curves Entry definition Accentuation of diagonals

Condominium 1 Sea Ranch, CA MLTW, architects

Rectangle area for cars Rectangle centered for interior court Condominium units located around court Varied pattern suggesting individuation Sub areas for covered parking located Walkways indicated for pedestrian circulation

Mt. Angel Library Mt. Angel, Oregon Alvar Aalto, architect

Rectangle support area Fan shape for reading and stacks Variation in shapes for functional requirements Lecture area trapezoidal Trapezoidal shape at entry repeats lecture shape Circular area for desk and reading

Philips Library Exeter, NH Louis Kahn, architect

Nine part square Subdivision of square, Chamfer of corners Location of central space Circular stairs and anchor components

Winton Guest House Lake Minnetonka, Minnesota Frank Gehry, architect

Rectangular pinwheel arrangement of varying sizes Angular tilt of all but one element Transformation of central element Addition of curvilinear edge condition

Kidosaki House Tokyo, Japan Tadao Ando, architect

Square and circle located on parallelogram site Circle offset from square axis Additional rectangular spaces Interior circle defines path Trapezoid shapes complete interior spaces Circles shrunk to arcs for entry

Rectangular wings in both directions Circle centers organization Circles indicate vertical circulation Rooms extend off main rectangle Outdoor area added at rear Rooms added

Friesen house Los Angeles, CA Richard Meier, architect

Sherger-Kolberg House Aspen, CO Bart Prince, architect

Circular center Radial “arms” Variation in “arm” length Circular circulation around center Rooms created between arms Circles mark service areas

41Â

Santo Volto Church Torino, Italy Mario Botta, architect

Rectangle with vertical and horizontal axis Circle on axis barely overlapping Circle axis tilted Ancillary wings at edge s Rectangle tessellation Circle outlining seating area Radial “spokes” Two foci added at plaza

Squares indicate separation of uses Rectangle defines courtyard in middle Squares divided at half points Entry “carved out” of squares Fireplace and elevator located as mass

Ziedler Residence Rio del Mar, CA Steven Ehrlich, architect

colophon

This book was produced on a Toshiba Chromebook 2. Google applications such as Docs, Drive, Draw, etc. were used to layout the pages, insert the images and format the text. There are three fonts that were used; Macando Swash Caps for the book title Balthazar for the project titles Acme for the notations. Printing is done by Createspace. Fulfillment and shipping are through Amazon.

images All images were obtained through internet sources. Most came from Pinterest boards about architecture, some came from online design blogs, and some were obtained through architect’s web sites. There was an attempt to get the best quality images available, however the printing process has it’s limitations.

Planimetric diagrams of the architectural elements inserted into G. B. Piranesi’s Campo Marzio, from Manfredo Tafuri, The Sphere and the Labyrinth, 1987 (via: quondam.com)