Second, we should learn geometry language well. Geometric language is divided into literal language and symbolic language, which are always associated with graphics. For example, the literal language: ∠ 1 and ∠2 are complementary, and the figure is as follows. Symbol language: ∠ 1+∠ 2 = 180.
Thirdly, we should think intuitively, that is, make some figures with cardboard and bamboo chips, and make detailed observation and analysis according to the figures in the book, which can not only help us deepen our understanding of the theorems and properties in the book, but also cultivate our observation ability step by step.
Fourth, be imaginative. Some problems need to rely on graphics and abstract thinking. For example, the "point" in geometry has no size, only position. There is a size between the point in real life and the point actually drawn. So the "point" in geometry only exists in the brain's thinking. The same is true of "straight lines", which can extend indefinitely. Who can draw a straight line to Mars and then to the Milky Way? Straight lines exist only in people's minds.
Fifth, we should study, summarize and improve. Geometry is more systematic than other disciplines, so we should summarize, sort out, summarize and summarize the knowledge we have learned. For example, is there any way to prove that two straight lines are parallel except by definition? What are the properties of two parallel lines? In real life, where are parallel lines used? As long as you observe carefully, it is not difficult to find parallel lines everywhere on both sides of the classroom wall, on doorframes, on tables, on stools, on glass plates, on pages, on matchboxes and on most packaging boxes.
Geometry is the only mathematical work written by Descartes, a French mathematician. Published on 1637, as one of the three appendices of Descartes' masterpiece "Methodology for Better Guiding Reasoning and Seeking Scientific Truth" (or "Methodology" for short).
Geometry accounts for about 100 page in Methodology, and is divided into three volumes, all of which are about geometric drawing. In this book, Descartes combined logic, algebra and geometric methods to outline the method of analytic geometry. He said, "When we want to solve any problem", "Give a name to the line segments to be used in drawing" and "Express the relationship between these line segments in the most natural way until we can find two ways to express the same quantity, which will form an equation".
In the first volume, Descartes explained the geometry of algebra and went further than the Greeks. For the Greeks, one variable is equivalent to the length of a line segment, the product of two variables is equivalent to the area of a rectangle, and the product of three variables is equivalent to the volume of a cuboid. The product of more than three variables, the Greeks have no way to deal with. Descartes didn't think so. He thinks that X2 should be the fourth term of the proportional formula 1: x = x: x2 instead of the area. In this way, we only need to give a unit line segment, and we can express the product of a variable and multiple variables with any power and the length of the given line segment.