(1) Simplex, as shown in Figures 9 and 1, Take a single geometric figure as the whole trademark. This kind of example is rare, and it is mostly the deformation of the basic figure.
(2) Fractal. Divide a basic geometric figure into several parts as shown in Figure 3 (equilateral triangle is divided into three parts), Figure 5 (pentagon is divided into a triangle) and Figure 12 (circle is divided into upper and lower parts).
(3) Similar (identical) group shape. As shown in Figure 1 (composed of three isosceles trapeziums), Figure 2 (composed of three equilateral diamonds) and Figure 11 (composed of five small circles with holes).
(4) It is transformed from a basic geometric figure, as shown in Figure 8 (obtained by changing the rhombus), Figure 9 (obtained by changing the parallelogram) and Figure 1 (obtained by changing the rectangle).
Group shape. It is composed of two or more different basic geometric figures. This situation is common, as shown in Figure 4 (composed of a circle and a square) and Figure 7 (composed of an isosceles right triangle and a rectangle).
(6) Fitting shape. Geometric figures or their group shapes are used to simulate objects and characters to achieve vivid and expressive effects. There are also many such examples. The red circle is like a pill), Figure 14 (like the sun coming out of the mountain), Figure 17 (like the letter "m").
(7) Mixed shape. As shown in Figure 6, it can be regarded as a cube and its shadow, and the effect is the same from four directions. The author has made such an experiment: students at different ages (from junior high school students and college students) And draw one or two. As a result, almost all the trademarks made up of regular geometric figures (hereinafter referred to as geometric figure trademarks), such as "Peking University Founder", "Mitsubishi" and "Xugong", etc.
This gives us an inspiration: geometric figure trademarks, among many types of trademarks, have obvious advertising advantages and are worth mathematicians. Especially the attention of middle school mathematics teachers. The basic geometric figures in middle school mathematics-triangle, rectangle, square, trapezoid, diamond, circle, ellipse, etc.-enter the trademark design and play an increasingly important role, opening up an effective way for middle school geometry knowledge to integrate with practice and serve the market economy. We might as well try to combine mathematics teaching.
1 Features and advantages of geometric figure trademarks
1 From this, we can see that geometric figure trademarks have the following obvious characteristics:
(1) The composition is simple and lively, and the three-dimensional sense is strong. This is determined by the basic geometric figure shape rules, so it gives people a clear and outstanding overall impression.
(2) There are significant differences between them. It is easy for people to identify and recognize. Because different kinds of geometric figures have different essential attributes, people's visual effects are very different. Even if they are both linear figures, they will show great differences due to different combinations and colors of basic geometric figures, so they are not easy to be confused. < P > (3) They are standardized and easy to make, and geometric figures, especially basic geometric figures, have established standards and practices. Moreover, it can be done only by using compasses and rulers, which brings great convenience to the production of geometric figure trademarks. Once the drawing specifications are determined, geometric figure trademarks of various sizes can be produced uniformly. < P > 1.2 This brings good advertising effect to geometric marks (which is the main value of trademarks):
(1) Strength and beauty. Linear, thick and powerful. Curved shape, beautiful and full of aesthetic feeling. Symmetrical shape, showing symmetrical beauty; Asymmetric shape, showing harmonious beauty. Black and white graphics, solemn and powerful; Colored graphics are bright and pleasing to the eye.
(2) It is easy to arouse association and imagination. The rough geometric trademarks (as shown in Figures 1, 2 and 3) remind people of the solid and reliable quality of products; Elegance reminds people of the beauty and dexterity of products. Some of them are so closely combined with the names of commodities or manufacturers that their names can be known at a glance (as shown in Figure 4-"Red Square"). Some of them are thought-provoking, while others are ingenious and intriguing. < P > 1.3 Because of this, many famous trademarks at home and abroad use geometric figures. China and the United States "SmithKline", Meiling Electric Appliances, and Founder Computer of Peking University, Lenovo Group, etc.
2 Types of geometric figure trademarks
3 Designs of geometric figure trademarks
3.1 The following ways can often be used to create geometric marks:
(1) Select or construct appropriate geometric figures with images to symbolize the name, shape and attributes of products, or the name of the manufacturer and the scenery where the factory is located. In order to achieve the effect of the integration of form and object, as shown in Figure 2, Figure 4 and Figure 6, the name of the factory (group) is symbolized.
(2) Geometrical figures are constructed to express the performance and quality of products, or the ambition and desire of the manufacturer, so as to achieve the effect of advertising. As shown in Figure 1, the quality of construction machinery is reliable with thick straight lines; Fig. 4 is a metaphor for the connection between brain thinking and the outside world, thus achieving the meaning of "association"; Fig. 1, which means that all directions eat the medicines of this factory, and the manufacturers have the ambition to develop in all directions. Fig. 13, which means that "people take medicines".
(3) Beauty is embodied in form, and beauty is contained in geometric trademarks with clever ideas and beautiful coloring, so that people can feel beautiful and attract customers. Clever combination and bright colors make consumers feel pleasing to the eye. Therefore, they have a sense of identity with their products.
3.2 Problems that should be paid attention to in design
(1) Deal with the dialectical relations between circle and square, curve and straight, skillful and clumsy, symmetrical and asymmetrical, dynamic and static.
Because geometric figures are always associated with concrete things in real life, they also have emotional colors. For example, circular and curved figures are beautiful and flexible; Square and straight lines are solid and steady. Symmetric figures have symmetrical beauty, while asymmetrical figures have singular beauty. We should make full use of this in trademark design and handle these dialectical relations well.
(2) We should give a clear drawing specification, especially for non-basic geometric figures or combined geometric figures. It is best to give a method in mathematical language or an analytical expression (as shown in the figure). Even if it is used, it must be visualized and patterned.
In short, the use of geometric figures in trademark design can add vivid content to middle school mathematics teaching, improve students' interest in learning geometry (one of the difficult points in junior high school mathematics) and cultivate their creativity.
References
1 Ye Jinwen. Collection and creation of trademarks composed of geometric figures. Mathematics Teaching, 1994, (4)