According to rough statistics and classification, geometric trademark graphics generally fall into the following categories:

(1) Simplex. As shown in Figures 9 and 10, a single geometric figure is used as the entire trademark. Such examples are rare. And most of them are deformations of basic graphics.

(2) Fractal. Divide a basic geometric figure into several parts, as shown in Figure 3 (an equilateral triangle is divided into three parts), Figure 5 (a pentagon is divided into a triangle), and Figure 12 (a circle is divided into upper and lower parts).

(3) Similar (same) group shapes. It is composed of several similar or identical basic geometric figures, as shown in Figure 1 (composed of three isosceles trapezoids), Figure 2 (composed of three equilateral rhombuses), Figure 11 (composed of five perforated small circles) ．

(4) Deformation. It is derived from a basic geometric figure. As shown in Figure 8 (obtained by changing the rhombus), Figure 9 (obtained by changing the parallelogram), and Figure 10 (obtained by changing the rectangle).

(5) Formation. It is composed of two or more different basic geometric figures. This situation is relatively common. As shown in Figure 4 (formed by superimposing a circle and a square), Figure 7 (formed by splicing an isosceles right triangle and a rectangle).

(6) Simulation. Use geometric figures or their combinations to simulate objects and words to achieve expressive and expressive effects. There are many such examples. As shown in Figure 5 (superposition of two Vs), Figure 13 (imagined as a "person", and the red circle as a pill), Figure 14 (imagined as the sun rising from the mountain), Figure 17 (imagined as the letter "M").

(7) Mixed form. Use a mix of techniques. As shown in Figure 6, it can be regarded as consisting of a cube and its shadow, and the effect is the same from four directions. The author has conducted such an experiment: among students of different ages (from junior high school students to college students), they were asked to name a few trademarks they saw on the street or on TV, and to draw one or two. ． As a result, almost all trademarks mentioned are trademarks composed of regular geometric figures (hereinafter referred to as geometric trademarks) - such as "Peking University Founder", "Mitsubishi", "Xugong", etc.

This gives us a revelation: geometric trademarks, among various types of trademarks, have significant advertising advantages and deserve the attention of mathematics workers, especially middle school mathematics teachers. Basic geometric figures in middle school mathematics - triangles, rectangles, squares, trapezoids, rhombuses, circles, ellipses, etc. have entered trademark design and played an increasingly important role, opening up a new path for connecting middle school geometry knowledge with practice and serving the market economy. As an effective way, we might as well try it in conjunction with mathematics teaching.

1 Characteristics and advantages of geometric trademarks

1 It can be seen that geometric trademarks have the following obvious characteristics:

(1) The composition is simple, lively and three-dimensional Feeling strong. This is determined by basic geometric shape rules. Therefore, the overall impression it gives people is clear and prominent.

(2) They are significantly different from each other and easy for people to identify and identify. Because the essential attributes of different types of geometric figures are different, people's visual effects are very different. Even if they are both linear figures, they will show great differences due to different combinations of basic geometric figures and different colors. So it is not easy to be confused.

(3) It is highly standardized and easy to make. There are established standards and methods for drawing geometric figures, especially basic geometric figures, and it can be completed with only two tools: compass and ruler. ． This brings great convenience to the production of geometric trademarks. Once the drawing specifications are determined, geometric logos of various sizes can be produced uniformly.

1.2 This has brought good advertising effect to the geometric trademark (this is the main value of the trademark):

(1) Strength and beauty. Straight lines are thick and powerful; curves are graceful and aesthetic. Symmetrical shape shows the beauty of symmetry; asymmetrical shape shows the beauty of harmony. Black and white graphics are solemn and powerful; colored graphics are bright and pleasing to the eye.

(2) Easy to trigger association and imagination. Among the geometric trademarks, the rough ones (as shown in Figures 1, 2, and 3) remind people of the solid and reliable quality of the product; the elegant ones remind people of the beauty and dexterity of the product. Some are so closely combined with the name of the product or manufacturer that you can know the name at a glance (Figure 4 - "Red Square"). Some are full of changes and thought-provoking, and some are cleverly conceived and thought-provoking.

1.3 Because of this, many famous trademarks at home and abroad use geometric figures.

SmithKline, Meiling Electric, Peking University Founder Computer, Lenovo Group, etc.

2 Types of geometric trademarks

3 Design of geometric trademarks

3.1 The following methods can often be used to create geometric trademarks:

(1) To image objects. Select or construct appropriate geometric figures to symbolize the name, shape, and attributes of the product, or the name of the production plant, the scenery of the factory location, etc., to achieve the effect of integrating form and matter. Figure 2, Figure 4, and Figure 6 represent the name of the factory (group).

(2) Metaphorical meaning. Construct geometric figures to express the performance and quality of the product, or the ambition and desire of the manufacturer, so as to achieve the effect of advertising. As shown in Figure 1, a thick straight line graphic is used to metaphor the quality and reliability of engineering machinery; Figure 4 is a metaphor for the connection between the brain's thinking and the external world, thereby achieving the meaning of "association"; Figure 10 is a metaphor for the fact that people from all over the world take the medicine of this factory. Manufacturers have the ambition to develop in all directions. Figure 13 is a metaphor for "people taking medicine".

(3) Use shapes to embody beauty, use ingenious conception and beautiful coloring to embody beauty in geometric trademarks, making people feel beautiful, thereby achieving the purpose of attracting customers. The ingenious combination and bright colors give consumers a pleasant and beautiful feeling, thus creating a sense of identification with their products.

3.2 Issues that should be paid attention to when designing

(1) Handle the dialectics of circle and square, curve and straight, cleverness and clumsiness, symmetry and asymmetry, movement and stillness, etc. relation.

Because geometric figures are always related to specific things in real life, they also have emotional color. For example, circle and curve shapes are beautiful and flexible; square and straight lines are solid and steady. Symmetrical figures have the beauty of symmetry, while asymmetrical figures have the beauty of singularity. We should make full use of this in trademark design and handle these dialectical relationships.

(2) It is necessary to give clear drawing specifications, especially for non-basic geometric figures or combined geometric figures.

This kind of drawing specifications is best given in mathematical language. method, or give analytical expressions (such as line segment proportions, joint point coordinates, curve function relationships, etc.).

(3) Geometric trademark graphics should be used as little or as little as possible with words (Chinese, English or pinyin abbreviations); even if they are used, they must be visual and patterned.

In short, using geometric figures in trademark design can add vivid content to middle school mathematics teaching, improve students' interest in learning geometry (one of the difficulties in junior middle school mathematics), and cultivate their creative talents.

References

1 Ye Jinwen. Collection and creation of trademarks composed of geometric figures. Mathematics Teaching, 1994, (4).

2 Yan Shijian． China’s mathematics education reform facing the 21st century. Journal of Mathematics Education, 1996(1).