First, explain the concept of geography with mathematical knowledge.

1. Explain geographical concepts with mathematical formulas.

This method is often used to reflect the distribution and change of area and distance or the relationship between individual and whole, part and whole. For example, scale can be expressed by mathematical formula: scale = distance on map/actual distance. Explaining the application of mathematical knowledge after showing formulas;

Calculation rules of (1) scale: the units in calculation should be unified, generally in centimeters; Generally, the distance on the map is one centimeter, and the actual distance remains an integer.

(2) Scale size comparison: in fact, it is to compare scores: in the case of the same numerator, the larger the denominator, the smaller the score, that is, the smaller the scale. (3) Relationship between scale and figure: the smaller the scale, the longer the actual distance, the larger the area represented by the map sheet and the simpler the geographical things reflected; On the contrary, the opposite is true. This expression not only explains the calculation and size of scales intuitively and concisely, but also enables students to understand the related characteristics of scales. Similar applications include the teaching of concepts such as population density and forest coverage. In this way, through the application of mathematical knowledge, on the basis of strengthening understanding, flexible application can replace rote learning, thus achieving the dual purposes of improving teaching effect and reducing learning burden.

2. Explain geographical concepts with mathematical figures.

(1) Explain the related concepts reflecting the proportional relationship with statistical graphs. If a concept is formed, a fan-shaped statistical chart can be displayed first, and then illustrated graphically, that is, the percentage of each component of a geographical thing, and its total amount is 1. This leads to similar concepts related to it, such as the composition of the earth's atmosphere, the material composition of the earth's crust, the composition of energy consumption, the composition of agricultural output value, the composition of industrial output value, the composition of industry and the composition of population. , vividly illustrates the relative proportional relationship between the components. Then it is extended to similar concepts, such as the regional distribution composition of hydropower reserves in China, the reserves composition of major oil distribution areas in the world, and the output composition of major oil producing areas. , and vividly illustrates the general spatial distribution of a geographical thing from the perspective of local and overall. The combination of mathematical graphics and geographical language deepens the understanding of geographical concepts.

(2) Geometry clarifies the concept of geographical space. For example, the intersection of yellow and red is such a typical concept. It is necessary to explain the concept with the help of geometric figures and three-dimensional models, and to understand the concept and its influence with geometric knowledge. The concept of ecliptic angle-that is, the angle between the revolution plane (ecliptic plane) and the rotation plane (equatorial plane) is a dihedral angle formed by the two planes.

The size of the intersection angle between yellow and red determines the scope of the five regions. As far as the northern and southern hemispheres are concerned, the tropics are areas with direct sunlight, the size of which is equal to the degree of intersection between yellow and red; The frigid zone is an extreme zone day and night, which ranges from the pole to the polar circle, and the temperate zone between the two is equal to the complementary angle of twice the angle of intersection between the yellow and the red. When the declination angle increases, that is, the range of tropical and cold zones increases and the range of temperate zones decreases; On the contrary, the opposite is true.

The concepts and characteristics of latitude and longitude, latitude and longitude, horizon height, sun height, angular velocity and linear velocity give students an intuitive and vivid impression, which helps students understand the concepts correctly and profoundly, thus playing the role of grasping key points and breaking through difficulties.

Second, use mathematical knowledge to quantitatively explain the characteristics and relationships of geographical things.

1, using data to illustrate the absolute quantitative characteristics of geographical things.

For example, the cycle of the earth's rotation and revolution, the total population of China, the total population of the world and the total resources of China. To enable students to establish intuitive impressions and feelings.

2. Compare and summarize the data to explain the differences and connections between different things.

For example, when talking about the judgment of climate types in the world, let students compare and summarize the differences of different climate zones from the aspect of temperature, then compare the differences of different climate types in the same climate zone from the aspect of precipitation, establish the most basic basis for climate type discrimination, master the most basic methods for climate type discrimination, and provide a premise for accurate analysis and judgment in the future. In this way, through data comparison, students can intuitively feel the differences and connections between different geographical things, and are deeply impressed by what they have learned. At the same time, it can also cultivate their ability to read data information and use data information for analysis and judgment.

Third, explain the changing law of geographical things with mathematical figures.

1, using statistical graphs to illustrate the law of time change.

Generally, the abscissa of this kind of statistical chart is time, and the ordinate is geographical element. It includes two forms: one is graphics, which can reflect the changes of one or more geographical elements with time, as well as the mutual combination and comprehensive effect of multiple geographical elements. For example, the daily variation of solar height, the annual variation of solar height at noon, the daily and annual variation of temperature and precipitation, and the variation map of precipitation and flow of rivers. The other is a point statistical chart, that is, two geographical elements are abscissa and ordinate respectively, and there are several points on the chart, and the points are marked with time. Such as climate type map, annual growth map of industry and agriculture, etc.

2. Explain the law of geographical spatial distribution with statistics.

This kind of graph often has one coordinate related to geographical space elements such as distance, longitude or latitude and height, and the other coordinate is other geographical elements. It is often expressed in the form of charts, line charts and bar charts. For example, the latitude distribution law of sun height at noon or day and night, the latitude distribution law of precipitation, the latitude distribution law of seawater salinity or temperature, the latitude distribution law of snow line height, etc.

Fourthly, apply mathematical knowledge to explain geographical principles and conclusions.

1. Explain the differences and connections between geographical concepts by combining mathematical logic knowledge with graphics.

Many geographical concepts, how to accurately grasp their differences and connections is of great significance for correctly understanding the knowledge learned, expressing geography in a standardized, scientific and accurate way, and effectively improving the academic performance of geography. Proper application of mathematical logic knowledge can play an unexpected role.

2. Quantitatively judge and describe geography by mathematical operation.

Use mathematical addition and subtraction to calculate the geographical differences in latitude and longitude, time difference, height difference and nutritional level difference. Calculate tropospheric temperature, fixed energy of trophic level in ecosystem, population density, per capita resources and forest coverage rate by mathematical multiplication and division. Conversion of time, composition of energy consumption and composition of industrial and agricultural output value between different longitudes are calculated by comprehensive algorithm. Using mathematical problem-solving methods, such as the extreme value method in mathematics, we can deduce the maximum and minimum values of cliff height on the contour line in geography.

3. Prove geographical principles and conclusions with mathematical proof methods.

For example, it is proved by "reduction to absurdity" that if sidereal day and the solar day are different, under three hypothetical conditions, different conclusions can be drawn by negative reasoning: when the earth only rotates but does not revolve, sidereal day is equal to the solar day; When the rotation of the earth is opposite to the revolution direction, the sidereal day is greater than the solar day; When the rotation and revolution of the earth are opposite at the same time, the sidereal day is smaller than the solar day. It is concluded that sidereal day is smaller than the solar day because the earth rotates around the sun at the same time, and the two directions are the same.

4. Break through the reading difficulties of geo-statistical maps by mathematical map reading.

Observe the principle from simple to complex, from single to comprehensive, read out the composition of a single element, the changes and characteristics in time and space, and then comprehensively analyze the relationship and function between them. For example, when reading and analyzing the relationship diagram between solar activity and annual precipitation, we should first analyze their respective changes, then analyze their corresponding relations, and then compare the differences in different places, so as to correctly draw the relationship between them. Another example is the reading of triangular coordinate graphics. We can judge the origin of coordinates by mathematical drawing, then find the ordinate, and read out the values of the three coordinates respectively according to the method that the connecting lines of points with equal abscissas are parallel to the ordinate.