Tools for understanding the geometric thought of the twentieth century and the new concepts of "space". The new needs of representation.
teacher profile teaching materials
INTRODUCTION TO TOPOLOGY AND NON EUCLIDEAN GEOMETRIES: SPHERIC GEOMETRIC (geodesics, difference with euclidean geometry) .
plus two TOPICS AMONG THE FOLLOWING:
1) INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS: SOLUTION BY SEPARATION OF VARIABLES. EQUATIONS OF HARMONIC OSCILLATOR AND OF VIBRATING STRING. FIELD AND LAB: SOUNDWALKS, PROBLEMS OF REVIEW AND DOCUMENTATION OF SOUND IN PUBLIC SPACES
OR:
2) PARAMETRIC SURFACES, POINTS WITH NEGATIVE, POSITIVE OR ZERO GAUSSIAN CURVATURE. MEAN CURVATURE. INTRODUCTION TO MINIMAL SURFACES.
3) PLATONIC SOLIDS, EULER CHARACTERISTIC. FULLERENES AND GEODETIC DOMES.
GROUPS OF PLANE ISOMETRIES, GROUPS OF TRIANGULATION ON THE SPHERE, COXETER TRIANGULATIONS.
4) 2d locally euclidean geometries. groups of isometries of the plane. generators, fundamental domain. distances and geodetics. discussion of problems arising whane applying this theory to actula acrchitecture.
-H.S.M. COXETER INTRODUCTION TO GEOMETRY, JOHN WILEY&SONS
-COURANT, ROBBINS What is mathematics?
-V. NIKULIN I.R.SHAFAREVICH GEOMETRIES AND GROUPS, SPRINGER VERLAG 1994
-L. RUSSO FLUSSI E RIFLUSSI; INDAGINE SULL’ORIGINE DI UNA TEORIA SCIENTIFICA. FELTRINELLI 2003
-G.GIURIATI L.TEDESCHINI LALLI SPAZI SONORI DELLA MUSICA, L’EPOS 2010
-A.CARLINI L.TEDESCHINI LALLI INTERROGARE LO SPAZIO, GANGEMI 2012
Programme
INTRODUCTION TO TOPOLOGY AND NON EUCLIDEAN GEOMETRIES: SPHERIC GEOMETRIC (geodesics, difference with euclidean geometry) .
plus two TOPICS AMONG THE FOLLOWING:
1) INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS: SOLUTION BY SEPARATION OF VARIABLES. EQUATIONS OF HARMONIC OSCILLATOR AND OF VIBRATING STRING. FIELD AND LAB: SOUNDWALKS, PROBLEMS OF REVIEW AND DOCUMENTATION OF SOUND IN PUBLIC SPACES
OR:
2) PARAMETRIC SURFACES, POINTS WITH NEGATIVE, POSITIVE OR ZERO GAUSSIAN CURVATURE. MEAN CURVATURE. INTRODUCTION TO MINIMAL SURFACES.
3) PLATONIC SOLIDS, EULER CHARACTERISTIC. FULLERENES AND GEODETIC DOMES.
GROUPS OF PLANE ISOMETRIES, GROUPS OF TRIANGULATION ON THE SPHERE, COXETER TRIANGULATIONS.
4) 2d locally euclidean geometries. groups of isometries of the plane. generators, fundamental domain. distances and geodetics. discussion of problems arising whane applying this theory to actula acrchitecture.
Core Documentation
-H.S.M. COXETER INTRODUCTION TO GEOMETRY, JOHN WILEY&SONS
-COURANT, ROBBINS What is mathematics?
-V. NIKULIN I.R.SHAFAREVICH GEOMETRIES AND GROUPS, SPRINGER VERLAG 1994
-L. RUSSO FLUSSI E RIFLUSSI; INDAGINE SULL’ORIGINE DI UNA TEORIA SCIENTIFICA. FELTRINELLI 2003
-G.GIURIATI L.TEDESCHINI LALLI SPAZI SONORI DELLA MUSICA, L’EPOS 2010
-A.CARLINI L.TEDESCHINI LALLI INTERROGARE LO SPAZIO, GANGEMI 2012
Reference Bibliography
Nikulin, I. R. Shafarevich, Geometries and groups, Springer 1994. Cap 1 (sfera) H. Pottmann, A. Asperl, M.Hofer, A. Kilian Architectural Geometry Bentley Institute Press 2007 Courant, Robbins Che cos’è la matematica? Bollati Boringhieri, Cap 5 §1,2. Cap 7§7. T. Banchoff Oltre la terza dimensione Zanichelli 1993 A. Kostovskii Geometrical Constructions with compasses only Little Maths Library MIR Publishers Moscow, 1982 R. Osserman Poesia dell’ universo: l’ esplorazione matematica del cosmo Longanesi 1995 B. Riemann Sulle ipotesi che stanno alla base della geometria Boringhieri 1994 L.A. Lyusternik The Shortest Lines Little Mathematics Library MIR Publishers Moscow 1983 E.A. Abbott Flatland: a Romance of Many Dimensions, Princeton University Science Library 1991 (Dover 1953); trad. italiana: Flatlandia, Adelphi 1996 L. Russo: L’America dimenticata. I rapporti tra le civiltà e un errore di Tolomeo, Mondadori Università, 2013 L.Russo: Ingegni minuti. Una storia della scienza in Italia, Feltrinelli 2010 L.Russo: Flussi e riflussi. Indagine sull’origine di una teoria scientifica, Feltrinelli 2003 Murray Schafer: Educazione al suono: 100 esercizi per ascoltare e produrre il suono, Milano : Ricordi, 1998 Benade “Fundamentals of Musical Acoustics” Dover 1990. Cap 1 §1, Cap 12 Room acoustics II: §12.2(effetto precedenza), §12.3 localization by ears. B. Blesser L.R. Salter “Spaces Speak, Are You Listening? Experiencing Aural Architecture” MIT Press 2007 (Roma Tre possiede la versione E-bbok, accessibile tramite Discovery) Frova: “Fisica nella musica“ Zanichelli, 1999. Cap 2 §1,2,3. Cap 15 § 1,2,…. G.Giuriati e L. Tedeschini Lalli (a cura di) “Spazi sonori della musica“ L’Epos 2010,(lo trovate in biblioteca) in particolare i saggi: “La localizzazione uditiva dei suoni nello spazio“, di G.Canévet, pp53-78; “Acustica delle sale. Fondamenti di fisica, metodi di progettazione, valutazioni soggettive” , di G. Müller, pp79-98; “Spazi fisici e spazi virtuali nella musica d’oggi“, di Alvise Vidolin, pp 117-134; “Mappatura sonica di un’area romana“, di Laura Tedeschini Lalli, pp135-148. Murray Schafer: “The Soundscape” , 1977 Murray Schafer: “Il paesaggio sonoro” BMG Ricordi Publications, 1985 Murray Schafer: “The Tuning of the World“, 1977 Radicchi: “Sull’immagine sonora della città” Firenze University Press 2012 Voci dell’Enciclopedia Treccani sul suono: http://www.treccani.it/enciclopedia/udito_%28Enciclopedia-dei-ragazzi%29/ http://www.treccani.it/enciclopedia/udito_%28Enciclopedia-del-Novecento%29/ Carlini, E. Conversano, L. Tedeschini Lalli: Matematica per l’ archeologia in Dialoghi di archeologia e architettura, edizioni Quasar, Roma, 2009, pp.168-181 Moran, K. Williams: I pavimenti dei Cosmati (Lettera Matematica Pristem)Type of delivery of the course
classes, recitations, hands on workshops, fieldworkAttendance
Attendance is required for at least 75% of the lessonsType of evaluation
Covid19: exams will only be oral exams. the oral exams evaluates noth the technical aspect and the ability to apply it, and (hopefully) the ability to manage recent scholarly literature using such language a written exam, followed by an oral arguing conversation the written is geared toward assessing the competence in a newly acquired technical language, and the abilty to apply it. The oral examination is geared toward assessing the ability to tackle and manage recent scholarly literature, in relation to stimuli spurred by the newly acquired language.