How to express complex mathematical concepts with simple shapes and symbols?

It is an effective way to express complex mathematical concepts with simple figures and symbols, which can help us better understand and convey mathematical ideas. Here are some common methods and techniques:

1. Expressing relationships with graphs: By drawing graphs, the relationships between mathematical concepts can be displayed intuitively. For example, use straight lines, curves or line charts to represent the changing trend of functions; Use coordinate system to represent points and vectors in two or three-dimensional space.

2. Simplify the expression with symbols: Mathematical symbols are concise and accurate expressions, which can greatly simplify the expression of mathematical concepts. For example, a plus sign (+) indicates addition, a minus sign (-) indicates subtraction, a multiplication sign (×) indicates multiplication, and a division sign () indicates division.

3. Use charts and tables: charts and tables can present a large amount of data and information in a concise way, helping us to better understand and analyze mathematical concepts. For example, histograms are used to compare different categories of data; Show the relationship between variables with scatter diagram, etc.

4. Use schematic diagrams and flowcharts: schematic diagrams and flowcharts can be used to describe the steps and ideas of solving mathematical problems and help us better understand and master mathematical methods. For example, the flow chart is used to represent the execution process of the algorithm; Illustrate the application of geometric theorem with schematic diagram.

5. Use colors and shadows: Colors and shadows can be used to highlight important information and relationships and help us better understand and remember mathematical concepts. For example, different colors are used to distinguish different variables or data; Use shadows to represent different parts of three-dimensional graphics, etc.

In a word, it is an effective way to express complex mathematical concepts with simple figures and symbols, which can help us better understand and convey mathematical ideas. Through the flexible use of various figures and symbols, abstract mathematical concepts are transformed into intuitive visual expressions, and the learning effect and application ability are improved.