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Square!
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fifi
La geometria coincide fino all'inizio
del XIX secolo con la geometria euclidea.
Questa definisce come concetti primitivi
il punto, la retta e il piano, e assume
la veridicità di alcuni assiomi, gli Assiomi
di Euclide, il più noto dei quali è che la
somma degli angoli interni di un triangolo
corrisponde sempre a 180°. Da questi
assiomi vengono quindi dedotti dei teoremi
anche complessi, come il Teorema di
Pitagora ed i teoremi della geometria
proiettiva.
La geometria coincide fino all'inizio del XIX secolo
con la geometria euclidea. Questa definisce come
concetti primitivi il punto, la retta e il piano,
e assume la veridicità di alcuni assiomi, gli Assiomi
di Euclide, il più noto dei quali è che la somma
degli angoli interni di un triangolo corrisponde
sempre a 180°. Da questi assiomi vengono quindi
dedotti dei teoremi anche complessi, come il
Teorema di Pitagora ed i teoremi della geometria
proiettiva.
La geometria coincide fino all'inizio del XIX secolo
con la geometria euclidea. Questa definisce come
concetti primitivi il punto, la retta e il piano,
e assume la veridicità di alcuni assiomi, gli Assiomi
di Euclide, il più noto dei quali è che la somma
degli angoli interni di un triangolo corrisponde
sempre a 180°. Da questi assiomi vengono quindi
dedotti dei teoremi anche complessi, come il
Teorema di Pitagora ed i teoremi della geometria
proiettiva.
The introduction of coordinates by René Descartes
and the concurrent developments of algebra
marked a new stage for geometry, since geometric
figures such as plane curves could now be
represented analytically in the form of functions
and equations. This played a key role in the
emergence of infinitesimal calculus in the 17th
century. Furthermore, the theory of perspective
showed that there is more to geometry than just
the metric properties of figures: perspective is the
origin of projective geometry. The subject of
geometry was further enriched by the study of the
intrinsic structure of geometric objects that
originated with Euler and Gauss and led to the
creation of topology and differential geometry.
The introduction of coordinates by René Descartes
and the concurrent developments of algebra
marked a new stage for geometry, since geometric
figures such as plane curves could now be
represented analytically in the form of functions
and equations. This played a key role in the
emergence of infinitesimal calculus in the 17th
century. Furthermore, the theory of perspective
showed that there is more to geometry than just the
metric properties of figures: perspective is the
origin of projective geometry. The subject of
geometry was further enriched by the study of the
intrinsic structure of geometric objects that
originated with Euler and Gauss and led to the
creation of topology and differential geometry.
SS01
SS02
SS03
SS04
SS05
SS06
Osf
Circle
Geometric
Was, was
Algebra
Infinite
Theory
(a×b), 10%
12.380
Circle
Geometric
Was, was
Algebra
Infinite
Theory
(a×b), 10%
12.380
KŸW/G
(2×4), 3%
00
Polygons
Solids
CC
Geometry is a branch of mathematics
concerned with questions of shape, size,
relative position of figures, and the
properties of space. A mathematician
who works in the field of geometry is
called a geometer. Geometry arose
independently in a number of early
cultures as a body of practical knowledge
concerning lengths, areas, and volumes,
with elements of formal mathematical
science emerging in the West as early
as Thales (6th century BC).
Synthetic
Geometry
Some examples are given by inscribed
and circumscribed circles of polygons,
lines intersecting and tangent to conic
sections, the Pappus and Menelaus
configurations of points and lines.
In the Middle Ages, new and more
complicated questions of this type
were considered: What is the maximum
number of spheres simultaneously
touching a given sphere of the same
radius (kissing number problem)?
Nikolai
Ivanovich Lobachevsky
(1792–1856)
Carl Friedrich Gauss
(1777–1855)