What geometry does plane rotation produce?

Geometric bodies that can be rotated by plane figures in life are: cylinder, sphere, cone, frustum and ellipsoid.

1, cylinder-rectangle or square rotation.

A rectangle rotates clockwise or counterclockwise on one side, and the space it passes through forms a cylinder.

Translation definition can also form a cylinder, that is, with a circle as the bottom, it moves up or down for a certain distance, and the space it passes through forms a cylinder.

2. Ball-circle rotation.

Any circle takes its diameter as its axis of rotation, and the geometric figure formed by rotation is a sphere. Rotating a semicircle with the diameter as the axis of rotation can also form a sphere.

3. Right cone-right triangle rotation.

A right cone is a geometric figure obtained by a right triangle rotating around one of its right angles. The hypotenuse of this right triangle is the generatrix of the cone. The projection of the vertex on the bottom surface is not on the center of the circle. Such a cone is an oblique cone. A regular cone can be obtained from a plane truncated cone, but an oblique cone cannot. The geometric shape obtained by cutting a conical surface with an inclined plane is called an elliptic cone.

4, frustum of a cone-right trapezoid rotation.

The frustum of a cone is a geometric body surrounded by a curved surface formed by the straight line rotation of the waist perpendicular to the bottom of a right-angled trapezoid.

You can also use a plane parallel to the bottom of the cone to truncate the cone, and the part between the bottom and the cross section is a truncated body.

5. Ellipsoid-rotating ellipse.

A solid surrounded by an ellipse that rotates once around its major or minor axis. Like football.

Extended data:

First, the rotation characteristics

1, the distance between the corresponding point and the rotation center is equal.

2. The included angle of the connecting line between the corresponding point and the rotation center is equal to the rotation angle.

3. The figures before and after rotation are congruent, that is, the size and shape of the figures before and after rotation have not changed.

4. The rotation center is the only fixed point.

5. The angle of the straight line where the connecting line of a group of corresponding points is located is equal to the rotation angle.

Second, the symmetrical transformation of points

The symmetry of (1) point about the origin.

When two points are symmetrical about the origin, the signs of their coordinates are opposite, that is, the symmetrical point of point P(x, y) about the origin is P'(-x, -y).

(2) The characteristics of the points that are symmetrical about the X axis.

When two points are axisymmetrical about X, in their coordinates, X is equal and the sign of Y is opposite, that is, the point where point P(x, y) is axisymmetrical about X is P'(X, -y).

(3) The characteristics of the point symmetrical about the Y axis

When two points are symmetrical about Y, Y is equal, and the sign of X is opposite in its coordinates, that is, the point where P(x, y) is symmetrical about Y is P'(-x, y).

(4) Symmetry of the straight line y = x.

When two points are symmetrical about the straight line y=x, the abscissa and ordinate are reversed, that is, the symmetrical point of P(x, y) about the straight line y=x is P'(y, x).

(5) When two points are symmetrical about the straight line y=-x, the abscissa and ordinate are opposite to those before, that is, the symmetrical point of P(x, y) about the straight line y=x is P'(-y, -x).

Note: A straight line with y=x is the bisector of an angle passing through one or three quadrants, and a straight line with y=-x is the bisector of an angle passing through two or four quadrants.

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