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.
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
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.
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.
Core Documentation
-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
Reference Bibliography
same as textbooks. more info and suggestions at www.formulas.itType of delivery of the course
frontal lessons and recitations in case of perduring emergency due to COVID-19 we will follow all provisions geared at ruling the educational and evaluation activities.Attendance
Students must attend at the least the 75% of lessons to be admitted to the final examType of evaluation
written exam followed by oral exam. In case of perduring emergency due to COVID-19 we will follow all provisions geared at ruling the educational and evaluation activities. Specifically, there will be oral examinations on the programme