Cartesian coordinate system, what are the types of Cartesian coordinate system?

is a planar Cartesian coordinate system.

It is also commonly called the Cartesian Cartesian coordinate system, and it was only after the introduction of the Cartesian coordinate system that people were able to use algebraic methods to study geometric problems, establish and improve analytic geometry, and establish calculus.

In 1637, Decart published "Geometry", created the Cartesian coordinate system, he used the distance from one point on the plane to two fixed straight lines to determine the position of a point, and used coordinates to describe the points in space, and then he founded analytic geometry, showing that geometric problems can not only be reduced to algebraic forms, but also can be found and proved by algebraic transformations. Descartes is one of the most influential giants in European philosophy and science in the 17th century, and is known as the "ancestor of modern science".

Yes, also known as a natural coordinate system, its origin is not fixed.

In 1637, Descartes published Geometry and created the Cartesian coordinate system.

The Cartesian coordinate system is a planar coordinate system.

two-dimensional coordinate system; Two number axes perpendicular to each other and with a common origin in the same plane constitute a plane Cartesian coordinate system, the two number axes are placed in the horizontal position and the vertical position respectively, and the right and upward directions are the positive directions of the two number axes, respectively. The horizontal number axis is called the x-axis, the vertical number axis is called the y-axis, the x-axis, and the y-axis are collectively called the coordinate axis, and their common origin o is called the origin of the Cartesian coordinate system, as shown in Figure 2.

three-dimensional coordinate system; The 3D Cartesian coordinates (x,y,z) are similar to the 2D Cartesian coordinates (x,y), that is, the z values are added on the basis of the x and y values, and the absolute coordinate values based on the origin of the current coordinate system or the relative coordinate values based on the previous input point can also be used, as shown in Figure 3.

The rule of the right hand: Hold the z-axis with your right hand, and when the four fingers of the right hand turn from the positive x-axis to the positive y-axis at an angle of 2, the thumb is pointing to the z-axis.

The three-dimensional form of space is absolutely real in the real world, and no matter which coordinate system is a relative datum, the coordinates under any coordinate system are relative coordinates. Therefore, under the Cartesian coordinate system, whether it is a two-dimensional (plane) coordinate system or a three-dimensional coordinate system, two different coordinate systems can be obtained by transforming the forward direction of the coordinate axis, namely the left-handed coordinate system (left-handed system) and the right-hand coordinate system (right-hand system).

Two ways:

1。Stretch out the right thumb, index, middle three fingers in a vertical shape, thumb - corresponding to the x-axis positive; Index finger - corresponding to the y-axis positive; Middle finger - corresponds to the z-axis positive.

2。Make a fist with the four fingers of the right hand from the X direction to the Y direction, and the thumb direction is the Z axis.

The Cartesian coordinate system is a collective term for the Cartesian coordinate system and the oblique coordinate system.

The two axes of number that intersect at the origin form a planar affine coordinate system. If the units of measurement on the two number lines are equal, the affine coordinate system is called the Cartesian coordinate system. A Cartesian coordinate system in which two axes of numbers are perpendicular to each other is called a Cartesian Cartesian coordinate system, otherwise it is called a Cartesian beveled coordinate system.

Affine coordinate system and Cartesian coordinate system planar to space generalization.

The three non-coplanar axes that intersect at the origin form the affine coordinate system of space. An affine coordinate system with equal units of measurement on three number axes is called a spatial Cartesian coordinate system. A Cartesian coordinate system with three number axes perpendicular to each other is called a spatial Cartesian Cartesian coordinate system, otherwise it is called a spatial Cartesian oblique coordinate system.

Cartesian coordinates, which represent the position of a point in space, are different from Cartesian coordinates, and the two coordinates can be converted to each other. For example, if the Cartesian coordinates of a point are 493, 454, 967, then its x-axis coordinates are 4+9+3=16, the y-axis coordinates are 4+5+4=13, and the z-axis coordinates are 9+6+7=22, so the Cartesian coordinates of this point are (16, 13, 22), and the coordinate values cannot be negative (because the sum of three natural numbers cannot be negative).

This should be.

The right-hand rule. In a three-dimensional coordinate system, the positive direction of the z-axis is determined according to the right-hand rule. The right-hand rule also determines the direction of positive rotation of any coordinate axis in 3D space.

To mark the positive direction of the x, y, and z axes, place your right hand with your back to the screen and your thumb pointing in the positive direction of the x-axis. Extend the index finger and middle finger, the index finger points to the positive direction of the y-axis, and the direction indicated by the middle finger is the positive direction of the z-axis.

Here's a picture.

1. Ellipse focal radius a+ex(left focus),a-ex(right focus),x=a c;

2. Double this rotten curve focal radius a+ex|(Left Focus)|a-ex|(right focus), alignment x=a c;

3. Parabola (y =2px) focal radius x+p 2 quasi-line x=-p 2;

The chord length k +1* (x1+x2) -4x1x2 and above is focused on the x-axis, and the y-axis only needs to be replaced by x.

Conical coordinates are a three-dimensional orthogonal coordinate system. Its three coordinate surfaces are concentric spheres, the cone axis is the cone of the x-axis, and the cone axis is the cone of the z-axis.

x+y=z is a curved bridge in three-dimensional spatial coordinates, which is a conical surface shaped like a funnel. The three-dimensional Cartesian coordinate system is formed by adding the three-dimensional coordinates (i.e., z-axis) of the Disen leak according to the right-hand rule on the basis of the two-dimensional Cartesian coordinate system.