geometria = geo-metria = terra-misura = misurare la terra.
Il nome dice il suo scopo.
Come scrive Erodoto i primi geometri furono gli agrimensori dell'antico Egitto, che misuravano le superfici dei campi per dividerli equamente tra i contadini; coi paletti conficcati nel suolo tra i quali tendevano delle corde annodate. Percio' i Greci chiamarono questi antichi geometri “arpedonapti” (annodatori / tenditore di corde).
Un'operazione di cui resta una traccia in molte lingue moderne, nell'espressione "tirare una retta".
L'uso delle corde per operazioni sul terreno e' anche odierno
es nell'orto per seminare in fila, tiro una corda.
wp/Matematica_egizia#Geometria
aton-ra/strumenti-di-misura-dellantico-egitto
La geometria di Euclide inizia con la formalizzazione delle operazioni degli agrimensori: tirare una retta, descrivere un cerchio. Riga e compasso, tramutati in oggetti mentali, regolati da un sistema di definizioni e assiomi.
Having evolved from antiquity from often-used methods for measurement of figures drawn mainly on plain surfaces, the methods and principles became distilled, for ready reference and use, as mathematical propositions, particularly in Greece in the peace and prosperity of the few centuries following the rule of Pericles. Then Euclid, in around 300 B.C., gathered, improved, and systematically wrote down all that was known in Geometry to his day. The work - called The Elements - attempted to develop Geometry from the firm foundation of axioms and succeeded in great measure to provide rigorous demonstrations - proof - of the mathematical results loosely proved by his predecesors.
While most of the proofs in Euclid's work were correct, blemishes were discovered in some proofs one of which being the very first proposition in the Elements. However, these blemishes were not due to erroneous deduction but tacit assumptions or "intuitively obvious" facts that were not justified by the axioms.
Considerations of these blemishes culminated in 1899 A.D. with David Hilbert's proposal of a revised axiom system that would not only preserve the validity of the proofs in the Elements but which was in conformity with the modern notion of the axiomatic method as proceeding from a set of undefined terms, definitions, and the axiom statements on the undefined terms. The Euclidean Geometry of today is the Geometry based on this revised axiom system or other equivalent systems since proposed.
The geometry taught today in school is a confused mixture of Euclid's and Descartes'.
credits: mathpath.org/concepts/geometries.htm
non pour dénigrer le génial mathématicien grec, mais pour fustiger l'enseignement excessif de la géométrie du triangle au collège et au lycée. Il est ainsi à l'origine de l'avènement de l'enseignement des mathématiques dites modernes des années 1970, dont l'efficacité fut cependant très contesté et source de nombreuses polémiques. Les excès du "modernisme" furent d'ailleurs regrettés par Dieudonné lui-même. Il publia également de nombreux livres et articles sur les mathématiques, leur enseignement et leur histoire.
credits: serge.mehl.free.fr/Dieudonne.html
Geometry Revisited 1967 H. S. M. Coxeter and S. L. Greitzer.
review parziale the-foundations-of-euclidean-geometry-by-h-g-forder-1927 credits: >>>
