Università Roma Tre

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.
4) sound as bodily orientation factor, Soundscape
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.

-T. BANCHOFF OLTRE LA TERZA DIMENSIONE ZANICHELLI 1993
-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
-B. RIEMANN SULLE IPOTESI CHE STANNO ALLA BASE DELLA GEOMETRIA BORINGHIERI 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

COVID19: bibliography available at www.formulas.itcorsi geometrie e modelli