How to draw an expanded diagram of a sphere?

In real life, the sphere can't be unfolded, and it can only be solved by projection.

1 can be expanded in abstract mathematics, which requires a series of changes in mathematical formulas, but this expansion is also infinite approximation, which means it is actually impossible.

2, this problem can be applied to map drawing to explain, because the earth is a sphere, it is impossible to spread the sphere on the plane in actual map drawing, and it can only be solved by projection.

3, the sphere unfolds ~ it can be imagined that it is cut into a crescent shape like a watermelon, and it will be the same when it is flat.

4. Strictly speaking, there is no expansion diagram of a sphere, because there is no plane on the sphere, and all are surfaces, because there are no three points on the sphere on the same plane. You can imagine peeling oranges.

Extended data

Basic concept of sphere

Definition of sphere

1. Definition: The space geometry in which a semicircle rotates one Zhou Suocheng around a straight line of its diameter is called a sphere, and the figure shown in the figure is a sphere.

2. A sphere is a three-dimensional figure with a continuous surface, and the geometry surrounded by the sphere is called a sphere.

There is no absolute sphere in the world. Absolute spheres exist only in theory.

4. But in weightless environment (such as space), the droplet will automatically form an absolute sphere.

Composition of sphere

1. The surface of a sphere is a curved surface, which is called a sphere.

2. A ball is similar to a circle, and it also has a center called the center of the ball.

Spherical characteristics

Cut a ball with a plane, the cross section is round. The cross section of the ball has the following characteristics:

1, the straight line connecting the center of the sphere and the center of the section is perpendicular to the section.

2. the distance d from the center of the sphere to the cross section has the following relationship with the radius r of the center of the sphere and the radius r of the cross section: r 2 = r 2-d 2.

3. A circle whose sphere is cut by a plane passing through the center of the sphere is called a great circle, and a circle cut by a section not passing through the center of the sphere is called a small circle.

4. On the sphere, the length of the shortest connecting line between two points is the length of a bad arc passing through the great circle between these two points. We call this arc length the spherical distance between two points.

References:

Baidu encyclopedia-ball