What is a mathematical graph?
Mathematical graphics refer to graphics related to mathematics, such as geometric graphics and functional graphics. These include planar graphics (such as lines, curves, polygons and planar areas) and spatial graphics (such as spatial curves, surfaces, solids, spatial areas, etc.).
Mathematical graphics also include graphics drawn by applied mathematical software (Mathematica, Maple, MathCad, Matlab, and Geometric Sketchpad), computers and calculators (such as fractal graphics and solution curves of differential equations).
Classification:
Axisymmetric transformation
1. Fold a graph along a straight line, and the parts on both sides of the straight line can overlap each other, then this graph is called an axisymmetric graph, and this straight line is called an axis of symmetry.
2. The symmetry axis bisects the line segment connecting two symmetrical points.
3. Transforming from one graph to another and making these two graphs symmetrical about a straight line is called the axisymmetric transformation of graphs, also called reflection transformation, or reflection for short. The new figure obtained by transformation is called the image of the original figure.
4. Axisymmetric transformation will not change the shape and size of the original graphics.
Translation transformation
1. Convert from one drawing to another. In the process of change, all points on the original graph move the same distance in the same direction. This change of graphics is called translation transformation of graphics, which is called translation for short.
2. Translation transformation will not change the shape, size and direction of the graph.
3. The line segments connecting the corresponding points are parallel (or on the same straight line) and equal.
Rotational transformation
1. When changing from one graphic to another, all points on the original graphic revolve around a fixed point in the same direction and angle. Such a graphic change is called graphic rotation transformation, or rotation for short. This fixed point is called the center of rotation.
2. Rotation transformation will not change the shape and size of the graph.
3. The distance from the corresponding point to the rotation center is equal. The angle formed by the connecting line between the corresponding point and the rotation center is equal to the rotation angle.