Geometry is the branch of mathematics that deals with flat shapes, solid geometry, dimensional space, and properties of flat shapes and solid shapes.
This science began with a foundation of practical knowledge about areas, lengths, and volumes. Then, in ancient Greece, the first hypotheses that included Euclid's postulates began to be formulated.
The axioms allowed for a mathematical definition of different basic geometric figures: curves, planes, lines, and points.
Plane geometry deals with representing three-dimensional elements in a plane with different techniques such as projective geometry.
What are the essential components of geometric shapes?
The most essential elements are flat shapes which can be represented in a piece of paper because they are bi-dimensional objects. They are composed of points, lines, angles, and surfaces.
Depending on the type of shape, line segments can be straight lines in the case of polygons or curved.
Examples of geometry in everyday life
Geometric figures appear in many aspects of everyday life. Here are some examples:
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In the kitchen, geometric shapes appear among kitchen utensils such as cups, plates, and pans. Chefs need to measure and weigh ingredients to adjust the quantities and volumes of ingredients to use.
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Video games use geometry to give the sensation of depth and movement of the scenes where the game takes place.
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Other recreational activities, such as scooter ramps, kite building, bicycles, etc.
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Machines and motors are made up of parts with various geometric shapes. The properties of these shapes are what determine their stiffness and physical behavior.
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Musical instruments are geometric elements whose sounds depend on their shape. Therefore, the perfection, size, and volume of these bodies are vital to obtaining the desired sound of the instrument.
Uses and applications of geometry
The study of this branch of mathematics has multiple applications. Here are some examples:
Astronomy and solar energy
In astronomy, geometry has been widely used to describe the trajectory of the planets of the solar system.
In the field of solar energy, geometry and astronomy play a fundamental role in calculating solar hours, the angle of incidence of solar radiation on the earth's surface, etc.
Art
Mathematics, forms, and art have always been closely related.
The concepts of proportions have been the inspiration for many artists over time.
The particular golden ratio, for example, has played an important role in artistic works. Another example has been the construction of mosaics that have been carried out in different historical periods.
Architecture
Architecture works with this branch of science in many uses. They include:
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the use of projective geometry
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the calculation of spherical and conical sections in the construction of domes
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the use of symmetry and mosaics.
Some figures, such as triangles and rectangles, are vital in structural design.
Physics
It is used to calculate lengths, areas of flat geometric figures, and volumes in physics. In many applications, trigonometric ratios, the Pythagorean theorem, etc., are used.
Evolution of geometry in history
The ancient Greeks who were particularly interested in constructing geometric elements of space were already known. The compass and a ruler without a scale were the classic instruments to study geometric figures.
In this way, the lengths and areas of the figures could be represented with numerical values. However, these means do not solve all the problems presented due to their difficulty.
Algebraic geometry
René Descartes reintroduced numbers in the form of coordinates. He realized that their algebraic representation could make the study of geometric shapes could be easier by their algebraic representation.
Analytic geometry is the branch of geometry that applies algebraic methods to geometric questions, typically relating geometric curves and algebraic equations.
Differential geometry is the study of geometry using the tools of mathematical analysis and multilinear algebra. The objects of study in this field are the manifolds, which generalize the notion of surface in Euclidean space and the diverse uses between them.
Non-Euclidean geometry
In the more than two thousand years since the Greek mathematician Euclid, the basic understanding of spatial problems has remained essentially unchanged.
Gauss, Bolyai, and Lobachevsky showed that ordinary Euclidean space is only one of the possible bases for the development of the study of forms. Subsequently, Bernhard Riemann expressed a broad view of this new geometry type.
Riemann's new ideas about space proved crucial in developing Einstein's general theory of relativity and Riemann's geometry.