First, observe the special graphic method.
Directly observe the special surface in the target figure given by the topic, or the position of the connection of the special figure, and then compare the options to directly eliminate the inconsistency.
The left side of the example 1 shows the outer surface of the carton. Which of the following can be folded? ( )
Analyze and investigate the law of space folding. This question examines an irregular polyhedron. Looking directly at the figure on the left, we can find that there are two faces with special shapes, that is, "there are points on the top and grooves on the bottom". So choose A. (Tips: It is very important to observe the special aspects of space topics. Grasping special aspects often gets twice the result with half the effort. )
Example 2 The following is the outer surface of a given carton. Which of the following cartons can be folded from the above outer surface? ( )
Second, the relative surface non-adjacent method
The problem of space folding should be solved by exclusion method, and the most commonly used exclusion method is the principle that the opposite faces are not adjacent. That is to say, we must grasp the graphic characteristics of two adjacent faces or opposites, so that we can choose the correct answer through exclusion, and the wrong option is the one that violates these characteristics.
Characteristics and judgment methods of hexahedral opposites
1. Negative characteristics
In a hexahedral three-dimensional figure, only one of a set of opposite faces can be seen.
The hexahedron above can only see three faces at the same time. These three faces belong to two adjacent faces, and the opposite face is invisible.
2. The method of judging the negative side in the hexahedral plane development diagram.
The (1) interface is the opposite surface.
Among the above four surfaces, "1" and "3" are opposites, and "2" and "4" are opposites; Note: Alternating faces can only be separated by one face.
(2) The two ends of "Z" are opposite faces.
The faces at the two ends of the "Z" in the above three figures are opposite faces.
Example 3 If the six faces of a cubic box are colored with white, gray and black paints, and the colors on the two opposite faces are the same, which of the following can't be the expanded drawing of the external drawing of the box? ( )
Extended data:
Reasoning skills:
Introduction:
The main points of observing the rules of graphics are: the size of graphics, the straightness of strokes, the rotation of directions, the combination order of graphics, the superposition of graphics, seeking common ground and so on. The concrete forms of graphic reasoning's ability are: 1, graphic analogy reasoning 2, graphic sequence reasoning 3, graphic coordinate reasoning 4, graphic plane composition 5, and spatial reduction of plane graphics.
Problem solving skills:
1. Find the pattern
This is the key to solving the graphic reasoning problem. To find the law, we must first analyze the first set of figures. Some simple questions can be seen directly from the first set of figures. For some complex graphics, we need to combine the second set of graphics for analysis.
The law of graphic arrangement is ever-changing. As long as you carefully observe its changes, you will find its laws in the end. Law is the key to solve the problem: first, carefully observe the two groups of graphs given. The main points of observation are: the size change of graphics, the increase or decrease of graphic elements, the number of strokes of graphics, the rotation direction of graphics, the combination order of graphics, the superposition of graphics, whether there are the same graphics, etc.
This is the key to solving the graphic reasoning problem. Some simple questions can be seen directly from the first set of figures. For some complex graphics, we need to combine the second set of graphics for specific analysis. The law of graphic arrangement is ever-changing. As long as we carefully observe its changes, I believe we can find its internal law in the end.
2. Observation is the basis of solving problems: to be a graphic reasoning, you should learn to observe a given graph, including: the size change of the graph, the number of strokes of the graph, the rotation direction of the graph, the increase or decrease and combination of the graph components, the superposition of the graphs, the combination order of the graphs and whether there are the same graphs.
3. Break through the mindset to help solve problems: graphic reasoning and numerical reasoning should be organically combined.
After finding the pattern, you can choose the correct answer according to it. But you must be careful when choosing, and don't make visual mistakes. Of course, it is best to confirm the law I have summarized through the selected answers. If it conforms to the law, the selected answers are close to ten; If the answer you choose doesn't conform to your own rules, you need to ponder it carefully.
4. Train of thought analysis
The key to graphic reasoning is to find out the rules in the first set of figures. After finding the rule, it can be easily applied to the second group of graphics. There may not be many elements that can be observed, but when used, especially when used in combination, its laws can be ever-changing.
Candidates should look for its changes according to the observation elements, so as to find its laws, and then apply them to the second set of graphs to get the correct answers. Let's take several commonly used laws as examples to specifically talk about how to do graphic reasoning problems in order to attract more attention. As long as the candidates can draw inferences, this kind of problem will not be too headache.
Reasoning skills:
Graphic reasoning is to sum up the laws of graphic changes according to several figures, and then choose the right options according to the summarized laws of changes. Therefore, it is very important to be a graphic reasoning, that is, "change" is constant, and the constant is "law"
Graphic reasoning is called "cultural fairness" test because it tests the examinee's abstract reasoning ability, is independent of specific things and is less influenced by knowledge and culture.
To solve the graphic reasoning problem, we should pay attention to the following skills:
First, establish the concept of "element". Think of each figure as an inseparable "element". And careful observation, good at refining. Elements generally include points, lines, faces and bodies. Judging from the real questions in the past two years, the main investigation is "body", that is, small graphics make up large graphics.
Whether the number of each element changes, whether the rotation or rotation direction is regular, whether the graphics overlap each other and whether the shapes are equal. So be careful when choosing the answer, and don't make visual mistakes. You should also learn to use mutated thinking. For example, sometimes an element is missing, but it can be said that there are laws of "being" and "not being".
Second, look for the law of change. The law of its change can be seen from many angles. Compared with many previous series types and calculation methods, the law of graphic change is more complicated and may be an unheard of "law", which depends on the logical thinking ability and flexibility of candidates to deal with and solve.
Third, special rules should be adopted for special graphics. For example, the law of element combination reasoning of element combination graphics. If there are four "circles", it can only be regarded as "circles" without counting the number of "circles", that is to say, it has great interference to the problem that the local content of a graphic "constitutes an element".
Here is also a summary of some problem-solving laws that are easy to appear in graphic reasoning:
In comparative reasoning, it generally includes: the changing rules of the size and shape of graphics, the changing rules of the number of graphics, the rules of strokes, the corresponding similarity, the rules of removing co-existence or different storage and co-existence, the rules of graphic rotation or turnover, the rules of graphic movement, the rules of axial symmetry and central symmetry, and the rules of shadow graphics.
In addition, the types of laws in deferred reasoning are similar to those in comparative reasoning, so I won't repeat them here. In addition, there are some special laws, such as the interval law of even and odd terms, the left-right symmetry law centered on the third figure, and the comprehensive law (using multiple laws at the same time).
In the process of splitting and reassembling, the most critical condition is to require the new graphics to be on the same plane, and change the direction and position on this basis. If you turn them over or fold them, you will get the wrong figure. In addition, pay attention to split the original image and compare it with the options. Some need to move on the same plane, and the direction and position will change to get it.
The essence of "Jiugongge" reasoning is to apply some laws of graphic contrast reasoning and visual reasoning, and apply these laws many times and in many directions. To solve this kind of test questions, we should see clearly the requirements of the test questions, observe them from the horizontal and vertical directions according to the example specifications, find out a suitable law and apply it comprehensively.
In folding graphics, it is wrong to grasp the situation that two faces are relatively adjacent, and it is relatively impossible to be adjacent and adjacent. If there are options that violate these characteristics, they are wrong options. In addition, we should also pay attention to the rotation law of three-dimensional graphics.
Graphic reasoning is a big problem that puzzles many candidates. Therefore, the key to graphic reasoning is to master the transformation rules of various figures and practice them frequently. As the saying goes, practice makes perfect. I believe that after a period of training according to methods and rules, the effect is very remarkable.
References:
Baidu Encyclopedia-graphic reasoning