The definition of geometry establishes that it is the part of mathematics that deals with the properties and measurement of space or plane, fundamentally concerned with metric problems (calculation of the area and diameter of figures or volume of solid bodies). It deals with the shape of a body independently of its other properties. For example, the volume of a sphere is 4/3 πr3, even if the sphere is made of glass, iron, or a drop of water.
What is geometry
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When we talk about what geometry is, we talk about the branch of mathematics that is responsible for studying the measurements, shapes and spatial proportions of figures, which are defined by a limited number of points, lines and planes. These shapes are known as geometric bodies. The concept of geometry is very useful for architecture, engineering, astronomy, physics, cartography, mechanics, ballistics, among other disciplines.
The geometric body is a real body considered only from the point of view of its spatial extension. The idea of figure is even more general, since it also abstracts from its spatial extension and a shape can have many figures when representing “cuts” of them.
The etymology of the term comes from the Greek үɛωμɛτρία, which means "measurement of the earth", in turn composed of ge, which means "earth"; métron, which means "measures" or "measure"; and the suffix ía, which means "quality".
What does geometry study
When it is said that it is geometry, it is talking about the study of location, shape, composition, dimensions, proportions, angulation, inclination, the equations that determine objects in space. The teaching of what geometry is allows to develop visual and spatial skills, thinking logically about the theorems and axioms that are taught in the discipline.
Specifically, it allows you to determine the area of a surface; the volume of a solid or other object; calculate perimeters; determine from an equation, the shape of an object, and vice versa; calculate and determine angles from other data provided; With the same principle, lengths can be determined; among other aspects that it studies.
In medicine there is a term that is molecular geometry, which refers to the structure and arrangement of the atoms that make up the molecules, and various properties depend on it. This can be determined by the spatial arrangement of the atoms in the molecules.
In its application in the academic area, the figures and forms can be projected with the help of a geometry game, which consists of several elements that help to project representations of geometric figures on paper.
It is based on theorems, corollaries, and axioms. Theorems are propositions of an assumption or hypothesis that asserts a reason or thesis and that can (and should) be proved, since it is not proven by itself. A corollary is a rational affirmative statement that is the logical result of a previously proven theorem, which can also be proved with the same principles as the theorem to which it belongs. The axioms, on the other hand, are statements that are accepted as true, and based on these theories will be demonstrated as other theorems.
The origin of geometry
The history of geometry dates back to ancient times, when the first civilizations built their structures, such as houses, temples and other complexes, in which the knowledge in this discipline was basic for its application. Even earlier, this had part in the first inventions, for example, in the wheel, a fundamental geometric figure for all human inventions, which brought with it the concepts of circumference and the discovery of the number π (pi), among other findings.
Ancient peoples used it to develop their knowledge in astronomy with the position of the celestial bodies and their angles, and thus determine the seasons of the year, the construction of buildings and other ways of guiding themselves in their daily activities. In the same way, it was very useful in the area of cartography, to determine distances and locations of geographical sites in the world.
It was the Greek Euclid (325-265 BC) who, in the 3rd century BC, gave mathematical expression to all man's experiences with this discipline, in his work "Elements", which did not undergo any modification until more than two thousand years later. In it, the study of the properties of lines and planes, circles and spheres, triangles and cones, among others, is formally presented. The theorems or postulates (axioms) that Euclid presents are those that are taught today in school. Euclid's has been very useful in mathematics as well as in other sciences such as physics, astronomy, chemistry and various engineering.
Among the most outstanding minds in the history of geometry, whose contributions are decisive for this field as it is known today, were, in addition to Euclides, the mathematician and geometrist Thales de Mileto (624-546 BC), considered one of the seven sages of Greece, who used deductive thinking in this field and achieved, through the use of shadows, measure heights and other proportions of triangles.
The mathematician Archimedes (288-212 BC) managed to calculate the centers of gravity of geometric shapes and their areas. In the same way, he developed the so-called Archimedean spiral, which is defined as the geometric place or the path that a point makes moving along a line that rotates about a fixed point. On the other hand, the mathematician Pythagoras (569-475 BC) developed several famous theorems, such as the postulate that says that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the legs.
Relationship between geometry and trigonometry
Geometry and trigonometry are closely linked. While the first studies the properties of all shapes and figures in space and on a plane, taking into account all the elements that make them up (points, lines, segments, planes); Trigonometry studies the properties, proportions, the relationships between the sides and angles of triangles, taking plane trigonometry (the triangles contained in a plane) and spherical trigonometry (the triangles that the surface of a sphere contains).
The triangle is a three-sided polygon that gives rise to three vertices and three interior angles. It is the simplest figure, after the line in this area. As a general rule, a triangle is represented by three capital letters of the vertices (ABC). Triangles are the most important geometric figures, since any polygon with a greater number of sides can be reduced to a succession of triangles, by drawing all the diagonals from a vertex, or by joining all their vertices with an interior point of the polygon.
This is responsible for the study of trigonometric ratios, such as the sine, cosine, tangent, cotangent, secant and cosecant. This is applicable in the fields of astronomy, in architecture, in navigation, in geography, in various areas of engineering, in games such as billiards, in physics and in medicine. From this it is possible to establish that the relationship between geometry and trigonometry is that the second is included in the first.
Geometry classes
You cannot talk about a concept of geometry without describing the classes that exist. The definition of geometry includes plane geometry, spatial geometry, analytic geometry, algebraic geometry, projective geometry, and descriptive geometry.
Plane geometry
Plane or Euclidean geometry is the one that studies the points, angles, areas, lines and perimeters of geometric figures, for which the so-called Euclidean plane is used.
This seeks to know the aforementioned system to know the plane, the line, the equations that define them, locate points, the elements of figures such as the triangle, recognize the equations of the forms and use formulas that allow knowing properties of the forms, such as your area, for example.
Spatial geometry
Spatial geometry studies the volume of shapes, their occupation and their dimensions in space. In this area there are two types of solids: polyhedra, whose faces are all made up of planes (for example, the cube); and round bodies, in which at least one of their faces is a curve (like the cone). Its properties are its volume (or if gaps are found, its capacity) and its area.
Spatial geometry is an extension of the projections of plane geometry, being the foundation for analytical and descriptive, engineering and other disciplines. In this case, a third axis is added to the system (formed by the X and Y axes), which is Z or depth, which is a vector product of X and Y.
Analytic geometry
Analytical geometry studies geometric shapes in a coordinate system from an analytical point of view in mathematics and algebra. When it is said that it is analytical geometry, it is said that it allows a geometric figure to be represented in a formula, in the form of functions or another type. In it, each point that makes up said shape has two values on the plane (one value along the X axis and one value along the Y axis).
In analytic geometry, the plane consists of two Cartesian or coordinate axes, which are the X or horizontal axis and the Y or vertical axis, named for the mathematician René Descartes (1596-1650), considered the father of analytics, since he used them formally for the first time, and it serves to determine coordinates of the points that define a figure in space, fundamental for what is analytical geometry.
Algebraic geometry
Algebraic geometry is made up of abstract and analytical geometry, which can yield one or more variables. The goal of it is for each point in each set to satisfy one or more quantities of polynomial equations at the same time.
The approaches of algebraic geometry are based on polynomial equations and according to their degree. They go from those that define points, lines and planes; going through the linear; and those of second degree, which express objects with volume.
Projective geometry
Projective geometry studies projections on a plane of solids, so what is contained in the universe can be better explained. A line is determined by two points and two lines meet at a single point. Projective geometry does not use metrics, so it is said to be an incidence geometry; it does not have axioms that allow segment comparison.
It is obtained when it is observed from a certain point, in which the observer's eye will only be able to capture the points projected in that plane; It is also the one that is defined as the representation of a fragment of the three-dimensional space of the Euclidean, so that the lines could be represented by a point and the planes by a line.
Descriptive geometry
Descriptive geometry is responsible for projecting on a two-dimensional surface to three-dimensional space, which with an adequate interpretation can solve spatial problems. Descriptive geometry also pursues, in addition to those described above, several objectives, such as providing the fundamentals of technical drawing.
What is sacred geometry
This refers to the figures and geometric shapes found in structures in places that are classified as sacred. These can be temples, churches, basilicas, cathedrals, whose structures have symbols and elements with religious, esoteric, philosophical or spiritual meanings.
They relate to mathematics and geometry directly in the construction of the temples, and it is linked to Freemasonry, which is an enigmatic fraternity that seeks the truth through human study in a philosophical way, who took among its symbols the art of construction as emblem. Similarly, occultists use it for different purposes.
This tries to balance both hemispheres of the brain simultaneously: the mathematical logical area and the artistic visual spatial area. In this, proportions and elements such as the proportion or golden number, the number pi (which is nothing more than the relationship between the length of a circumference and its diameter), and other considerations developed by philosophers and understood in various disciplines are taken into account..
For the philosopher Plato, there are the so-called Platonic solids, which are five three-dimensional solids whose combination, according to him, God took as a reference to sketch the universe. For the theosophist Helena Blavatsky, this was the fifth key to understanding life, the other four being astrology, metaphysics, psychology, and physiology, the other two being mathematics and symbolism.
What is geometry dash
Geometry Dash is a video game designed by young developer Robert Topala and later developed by his company RobTop Games. In 2013 it was released for mobile phones and towards the end of 2014 for computers.
T his game consists of carrying a cube, which can be turned into different transport vehicles, and the objective is to avoid the obstacles that are crossed on the way until the end of the level without having crashed. Its method and controls are simple, since you only have to press the screen if it is a mobile device or click with the mouse if it is played on a computer, with which the cube will jump avoiding the obstacles that it has below, although also said jumps will ensure that the cube does not hit the ground.
There are different versions, which are Geometry Dash Sub Zero and Geometry Dash Meltdown, which include levels that the original did not include; the Lite version, which contains a few levels; and another version called Geometry Dash World, in which the user has the ability to create daily levels. To download Geometry Dash for PC, there are various sites online, and for mobile devices such as Android and Mac, they are found in the Play Store and App Store, respectively.
