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History of Geometry

The document outlines the history and development of geometry, tracing its origins from Babylonian civilization to the axiomatic framework established by Euclid. It discusses the practical applications of geometry in various fields such as astronomy, cartography, and design, as well as the evolution of different types of geometries, including Euclidean and non-Euclidean geometries. Additionally, it highlights the importance of geometric figures and their properties in understanding spatial relationships.

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18 views3 pages

History of Geometry

The document outlines the history and development of geometry, tracing its origins from Babylonian civilization to the axiomatic framework established by Euclid. It discusses the practical applications of geometry in various fields such as astronomy, cartography, and design, as well as the evolution of different types of geometries, including Euclidean and non-Euclidean geometries. Additionally, it highlights the importance of geometric figures and their properties in understanding spatial relationships.

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© © All Rights Reserved
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History of Geometry

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TheGeometryas one of theLiberal ArtsyEuclid.
Geometry is one of thesciencesolder. Initially, it constituted a
body of knowledge practical in relationship with
thelongitudes, areasyvolumes.
The Babylonian civilization was one of the first cultures to incorporate the
study of geometry. The invention of the wheel paved the way for the study of
the circumference and subsequently to the discovery of thenumber π(pi); Also
developed thesexagesimal system, upon knowing that each year has 365
days, they also implemented a formula to calculate the area
oftrapezoidrectangle.1
In theancient Egypt it was very developed, according to the texts
ofHerodotus, StraboyDiodorus Siculus. Euclidin the 3rd century B.C. configured
geometry in axiomatic form andconstructive,2treatment that established a
norm to follow for many centuries: theEuclidean geometrydescribed inThe
Elements.
The study of theastronomyand thecartographytrying to determine the
positions of stars and planets in the celestial sphere served as important
source of geometric problem solving for more than a
millennium.René Descartessimultaneously developed the algebra ofequationsy
theanalytic geometrymarking a new stage, where the figures
geometric shapes, such as planar curves, could be represented
analytically, that is, with functions and equations. Geometry is
enriches with the study of the intrinsic structure of geometric entities
what they analyzeEuleryGaussthat led to the creation of thetopologyy
thedifferential geometry.

Geometry is a part of mathematics that deals with studying some


idealizations of the space we live in, which are points, lines and
plans, and other conceptual elements derived from them, such as polygons or
polyhedra.

In practice, geometry is used to solve concrete problems in the


world of the visible. Among its utilities is the theoretical justification of
many instruments: compass, theodolite, pantograph, system of
global positioning. It also allows us to measure areas and
volumes, it is useful in the preparation of designs, and even in manufacturing
crafts.

Classical or axiomatic geometry is a mathematics in which the objects, in


instead of being numbers, they are points, lines, planes, and other figures defined in
function of these.

GEOMETRIC FIGURES
The progress of geometry heavily depends on advances in definitions.
the properties of triangles can be stated without reference
to these, but it would be a long, tedious, and useless process.

Fundamental figures: Point, Line, and Plane.


In the lecture, you can see: Segments, semi-rectangles, and vectors
In the plane, a line determines two half-planes, their intersection.
determine the figures convex
belt, Angle, Triangle, quadrangle and Polygon.
Using the concept of distance: the circle is defined
the sphere.
Using the concept of half-spaces, the dihedral angle is defined:
prismatic space, the triedron, the polyhedral angle, and the polyhedra.
Among the last we find as particular cases: the
tetrahedron, the prism, the pyramid, and the parallelepiped.
The concept of circle in space gives rise to: the cone
the cylinder

RELATIONS AND PROPERTIES

Between two or more figures there can be different relationships, two straight lines can
parallel, perpendicular or oblique (intersecting at a point forming
angles no rectos).
In space, they can also be warped (or crossed). One of the
the most important concepts within geometry is that of congruence or
equality.

CLASSES OF GEOMETRIES

Considering more axioms, other geometries are obtained (in which


everything said so far is valid). If we take the axiom of
Euclidean parallelism, we obtain Euclidean Geometry also known as
as planar geometry.

Adding to these the axioms related to space, we obtain geometry.


spatial (the latter are nothing more than extensions of the axioms related to
plan). Descriptive Geometry is responsible for addressing the problems
enabling the resolution of space geometry problems through
of operations carried out on a plane.

If we add other axioms, whether different postulates of parallelism or of


existence of sets of points greater than the plane (and smaller than the
non-Euclidean geometries are obtained in space

Utilizing the knowledge from other areas (and therefore their axioms
respective), are obtained: Geometry
analytics, the methods of algebra and mathematical analysis.

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