"Projection" Projection and View PPT Courseware 8

"Projection" Projection and View PPT Courseware 8

teaching objectives

knowledge and abilities

Understand the concepts of projection and be able to identify the projection of objects based on the direction of light.

Learn the meaning of central projection and parallel projection and their simple applications through examples.

Understand the meaning of orthographic projection and be able to draw the orthographic projection of simple plane figures based on the properties of orthographic projection.

Process and Method

Through students' recall, operation, imagination, reasoning, communication and other mathematical activities, students can initially establish spatial concepts and develop geometric intuition.

Emotional attitudes and values

Be willing to be exposed to mathematical information in the social environment, be willing to talk about certain mathematical topics, be able to play an active role in mathematical activities, and feel the wisdom of the ancient Chinese working people and the profoundness of the traditional Chinese culture.

Important and difficult points in teaching

Distinguish between parallel projection and central projection, and their applications in life.

Understand the meaning of orthographic projection and be able to draw the orthographic projection of simple plane figures based on the properties of orthographic projection.

Analysis and application of comprehensive problems in mathematics and physics.

Knowledge points

Generally, when an object is illuminated with light, the shadow obtained on a certain plane (floor, wall, etc.) is called the projection of the object.

review

In Chapter 2 "Light Phenomena" of "Eighth Grade Physics Volume 1", we learned the concept of light.

In order to represent the propagation of light, we usually use a straight line with an arrow to represent the path and direction of light. Such straight lines are called rays.

Projections formed by parallel rays are parallel projections.

observe

What is the difference between the projected lines in the two images below?

What projections do they form?

Knowledge points

The projection produced by the projection line perpendicular to the projection surface is called orthographic projection.

Fix the projection surface and change the position and direction of the stick. What changes will happen to its shadow?

When a certain surface of an object is parallel to the projection surface, the orthographic projection of this surface will be exactly the same shape and size as this surface.

example

Draw the orthographic projection of the cube placed as shown in the figure on the projection plane P.

(1) One face ABCD of the cube is parallel to the projection plane P;

(2) One surface ABCD of the cube is inclined to the projection surface P, and the upper bottom surface ADEF is perpendicular to the projection surface P.

Class summary

1. Projection: When an object is illuminated by light, it will leave its shadow on the ground or wall. This is projection.

2. Parallel projection: Generally, the projection formed by parallel light rays is parallel projection.

3. Central projection: The projection formed by the light rays emitted from the same point (electric light source) is called central projection.

Practice in class

1. The picture below is the shadow of two trees at the same time. Please draw the light rays that create the shadow of the tree in the picture. Are these rays of sunlight or lights?

Because the light is not parallel light, it is not sunlight, but the light of the light. The light of the light is emitted from one point.

2. The picture below is the shadow of two trees at the same time. Please draw the light rays that create the shadow of the tree in the picture. Are they sunlight or lights? Draw the shadow of the flagpole at the same moment.

3. Given the two wooden poles and their respective shadows, determine the location of the street light bulb.

Solution: Draw a straight line through the top of one wooden pole, and then draw a straight line through the top of the other wooden pole. The two straight lines intersect at point O. Point O is where the street light bulb is.

4. Opposite a street lamp, there is a glass curtain wall. There is a pot of flowers and a tree on the ground in front of the curtain wall. At night, the curtain wall reflects the street light, forming the shadow of the potted flower, and the tree shadow is formed by the street light. Can you determine the location of the street light source at this time?

5. Xiao Ming and his father are walking on the beach in the sun. He doesn’t want his father to see his shadow. Can you draw the approximate range of Xiao Ming’s activities?

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