What is a point, line, and surface in math common sense?

Points, lines, and surfaces are geometry.

The concept of is the basic element of flat space. The philosophical meaning of the point: The point is the origin of the universe.

There is no volume that is crammed into the universe"Edge";Points are the foundation of all graphics. The philosophical meaning of the line: the line is made up of countless dots. The philosophical meaning of the surface: The surface is made up of countless lines. in geometry, topology.

And in related branches of mathematics, a point in space is used to describe a particular kind of object in a given space, in which there are similarities like volume, area, length, or other high-dimensional analogues. A point is a zero-dimensional object, and a point as the simplest geometric concept is usually used as a geometric, physical, and vector figure.

and other areas of the most basic components. Points form lines, lines form surfaces, and points are the most basic components of geometry. In the usual sense, points are treated as zero-dimensional objects, lines as one-dimensional objects, and faces as two-dimensional objects.

The jog becomes a line, and the line moves into a surface. Composition of ordered points: This mainly refers to the shape and area, position or direction of the points, and other factors, arranged in a regular form, or the same repetition, or orderly gradients, etc.

The points are often arranged through sparse and dense arrangements to form the expression needs of the graphics in the space, and at the same time, the rich and orderly point composition will also produce a sense of space with delicate layers and form a three-dimensional.

In the composition, the relationship between the points forms the whole, and their arrangement is combined with the space of the whole, so the visual tendency of the points is the line and surface, which is the rational composition of the points. Linearly, the lines have neat and upright geometric lines, as well as free-form lines drawn freehand. The object itself does not exist, the turn of the surface forms a line, and the form is defined by the line, which is what we call the outline line, which is a generalized form expression of the artist to the material.

It is the most expressive and dynamic component of the image and picture space, and it is also the visual expression element that has always been loved by Chinese and foreign artists in ancient and modern times. Our aesthete Yang Xin wrote about our Neolithic Banshan faience pottery:"Its pattern decoration is a line, from a single line to produce a variety of different lines, such as thick line, thin line, toothed line, wavy line, red line, black line, etc., the use of repeated, staggered methods, the combination of many regular lines, so that people feel coordinated, as if composed with lines'A silent symphony'"。

The composition of the surface is the composition of the form, and it is also the key point that needs to be learned and mastered in the composition of the plane, which involves concepts such as basic type and bones, which we will discuss one by one in the following chapters. Here we will first discuss the compositional relationships between faces in a flat space, when two or more faces appear at the same time in a flat space (our picture), there will be a variety of compositional relationships between them.

The enlarged point forms the polygon, and a closed line creates the polygon. Dense dots and lines can also form polygons. In morphology, the surface also has modeling elements such as size, shape, color, texture, etc., and at the same time, the surface is"image", so the surface is"shape"。

The composition of free points: here it mainly refers to the shape and area, position or direction of the points, and other factors, arranged in a free, irregular form, this composition often presents a rich, flat, and scattered visual effect. If you use this to represent parts of space, you can use them to their strengths, such as symbolizing the stars in the sky or as a decoration for the shading of graphics.

1. Point

In plastic arts, a point is a point with an area, a shape, a color, a concreteness, and an image. A point represents a position, which has neither length nor width and is the smallest unit. In planar composition, the concept of a point is only a relative, it exists in contrast, which is shown by comparison.

2. Line

The shapes of the lines are extremely rich, including straight lines, broken lines, curves, cross lines, etc., and they have a strong emotional and emotional expressiveness. A line is the trajectory of a point movement. In the geometric definition, a line has only a position and length, but not a wide slag thickness and thicknessFrom the perspective of plane composition, a line can have both length and width.

3. Surface

In the plastic arts, points, lines, and surfaces are relative, and surfaces are shapes that are larger than points and wider than lines. The surface is formed by the continuous movement of the line to the end of the mark. Faces have length, width, and no thickness, and straight lines move parallel to rectangles; Straight line rotation moves into a circle; Moving freely in a straight line to form an organic shape; Straight lines and arcs combine to form irregular shapes.

Characteristics of point, line, and surface:

Because the infinitesimal infinitesimal of the body, surface, and line (permanently greater than zero) is not equal to zero, the beam is destroyed and there is no limit. So, here we must not mistake the tangible point (of the theoretical application of Cavalliri and Kepler) into the microscopic realm for being equal to the intangible point. Invisible points can only be reflected through the contrast between positive, positive, and positive lines composed of tangible points and negative, negative, and negative lines.

The body (positive body and negative body): it is the collection of positive body points and positive body points to form a positive body; Negative points and a set of negative points form a negative body.

(positive and negative) in the surface: it is the set of positive points and positive points that form a positive one; The negative points and the set of negative points make up a negative.

1. Jog into a line: For example, when a dot matrix printer is typing, a line is formed by dots. When a car travels a certain distance, the distance it travels is a line.

2. Linear surface formation: For example, when the laser knife is used in the medical field, the knife edge formed at the place where the laser passes. A stick rotates around an end to draw a circle, and the circle forms a surface.

3. The surface is moving: For example, when we brush our teeth, the toothpaste mouth is a round surface, and when we squeeze the toothpaste, it forms a cylinder. When a fan is fanned, the space where the fan crosses the air is the body of the face.

The relationship between points, lines, and surfaces.

1. The most important function of the point is to indicate the position and focus, the point and the surface are compared and formed, the same point, if it covers the whole or a large area of the plane, it is the surface, if it appears many times in a plane, it can be understood as a point.

2. The connection between points forms a line, or the regular extension of a point along a certain aspect can become a line, and the line emphasizes the direction and shape.

3. The connection of more than three points on the plane can form a surface, and at the same time, the closure of the plane line or the line can also form a surface, and the surface emphasizes the shape and area.

The knowledge of the composition of points, lines, and surfaces is as follows:

1. All elements in nature can be regarded as points, lines, and planes. Fully grasp the composition principle of points, lines and surfaces, and use them reasonably, you can form an excellent graphic design work, coupled with the understanding of the color principle, it will make the work more perfect.

2. Points are the most basic and important elements, and if a smaller element appears in a diagram or two or more non-linear elements appear in a diagram at the same time, we can treat it as a point.

3. A line is a kind of geometry with position, direction and length, which can be understood as the formation of point movement.

4. The dotted line has the advantages of the line, and it has some characteristics, which is a design method that is used more.

5. Point expression method and effect: different tools and different paper draw different point effects; The same tool and different drawing methods will have different effects on the points. Generally speaking, the smaller the area, the stronger the sense of the point, and the larger the area, the more the sense of face, but the smaller the point, the weaker the visual presence.

The visual image of a point can be real or imaginary; It can be positive or negative, and the effect is different.