Can a master talk about how to look at a curve, what kind of curve is good?

Didn't the next door tell you, it's the Divine Comedy! You go next door and talk about it, this is the curve measured by Level B15A, and see what compliments people will have View the original post

Trouble, thanks!

If you are interested in learning, you can learn about frequency response curves, phase, transient response, T60 reverberation time, waterfall diagrams, group delays, equalizers, isoecho curves, occlusion effects, distortion, spatial acoustics principles, sound testing, etc., all of which will help you understand and debug the system. View the original post

How to know this graph such as dive there , good or bad View the original post

For example: place two ping pong balls.

Placed at the starting point of the curved track and the straight track of the same height, the experimental results show that the ball of the curved track reaches the end point first. The ball on the curved track reaches the highest speed first, so it reaches the finish line first. It is the cycloidal that connects the start and end points.

Ignoring other factors, the cycloidal is the fastest descending line.

Beyond the two-dimensional plane, the curve is shorter than the straight line. The earth is round, and any point cannot be connected with another point in the form of a straight line, and if you want to connect it in a straight line, you must fly out in the direction of the tangent line, and it is difficult to connect them together. The curve connection is the shortest distance.

The shortest straight line between two points is only applicable to the two-dimensional plane, and the shortest straight line between two points is not applicable when it is separated from the two-dimensional plane. In addition, the conclusion that the straight line between two points is the shortest is theoretically true, and the one that is not linked in real life is true. Two points in different dimensions cannot be connected in a straight line, and if they are connected in a straight line, the distance will be correspondingly farther.

In the same way, this method is correct in theory, but it cannot be applied in practice.

On an inclined plane, there are two tracks, one straight and one curved, and the height of the start point is the same as the height of the end point. Balls of the same mass and size slide from the starting point at the same time, and the curved balls go to the end point first. The curve ball arrives at the end point first because the ball on the curve track reaches the highest speed first, and the highest speed will arrive first.

There is only one straight line between two points, and there are countless curves, so which one is the fastest? Galileo.

The same question was posed in 1630, which he thought should be a straight line, which was later found to be wrong. In 1696, Bernoulli solved this problem as a challenge to other mathematicians. Newton, Leibniz.

Scientists such as Lobida and Bernoulli solved the problem. This maximum speed curve is the cycloid, which is scientifically known as the rotor line.

Galileo Galilei posed the analytic question in 1630: "A mass is under gravity, from a fixed point to a point not below the vertical, regardless of friction."

What curve takes the shortest time. "Curves are circles, that's wrong.

Bernoulli asks for answers to the question of the fastest curve. capacity, the average speed is the fastest.

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Problem description: A definite curve is required.

Analysis: What is a curve? According to the classical definition, a continuous mapping from (a,b) to r3 is a curve, which is equivalent to saying:

i) The curve in r3 is a continuous image of one-dimensional space and is therefore one-dimensional.

ii) The curves in R3 can be obtained by making various twists in straight lines.

iii) To say a certain value of a parameter is to say a point on the curve, but not necessarily the other way around, because we can consider the self-intersecting curve.

Differential geometry is the study of geometry using calculus, and in order to be able to apply the knowledge of calculus, we cannot consider all curves, even continuous curves, because continuity is not necessarily differentiable. This brings us to the differential curve. But differentiable curves are also not good, because there may be some curves where the direction of the tangent is not determined at a certain point, which makes it impossible for us to start with the tangent, which requires us to study this kind of curve where the derivative is not zero everywhere, we call them regular curves.

Regular curves are the main research objects of classical curve theory.

Hyperbola. 1) Definition The absolute value of the difference between the distance from the two fixed points f1,f2 in the plane is equal to the fixed value 2a(0<2a<|f1f2|) of the point.

The ratio of the distance to the fixed point is e(e 1).

2) Geometric properties:

Focus: Vertices:

Axis of symmetry: x-axis, y-axis.

Eccentricity: The larger the e, the wider the opening.

Alignment: Asymptote:

Focal radius: The line segment connecting any point m on the hyperbola with the focal point of the hyperbola is called the focal radius of the hyperbola.

The focal radius formula for hyperbolic Huai search with a focus on the x-axis:

The focal radius of the hyperbola focusing on the y-axis is this formula:

where are the lower and upper focus of the hyperbola).

left plus right subtraction, down plus subtraction", and the parabolic note Sen Mingqin is the opposite, and the ellipse note is the same, but with more absolute values).

Focus chord: The intersecting chord formed by the recant of the congregation that crosses the focal point.

Diameter: Intersecting chord that is over focus and perpendicular to the axis of symmetry The focal chord formula is applied directly

A curve is a line formed by a continuous change in direction when a moving point moves. It can also be thought of as a curved wavy line. Any continuous line is called a curve, including straight lines, polylines, line segments, arcs, and so on. Curves can be used as a mathematical term, but they can also refer to the lines of the human body in particular.

If a point is on a curve.

Let the curve equation be y=f(x) and a point on the curve is (a,f(a)) and find the derivative of the curve equation to obtain f'(x), substituting a point to get f'(a), which is the tangent slope of the crossing point (a, f(a)), is obtained from the point oblique equation of the straight line. y-f(a)=f'(a)(x-a)

If a point is not on the curve.

Let the curve equation be y=f(x), and a point outside the curve is (a,b) to find the derivative of the curve equation to obtain f'In the open state (x), let the tangent point be (x0,f(x0)), and substitute x0 into f'(x) to get the tangent slope f'(x0), the equation y-f(x0)=f of the tangent line is obtained from the point oblique equation of the straight line'(x0)(x-x0), because (a,b) is on the tangent, substituting the obtained tangent equation, has: b-f(x0)=f'(x0)(a-x0), x0 is obtained, and the tangent equation of the mountain macro is obtained by substitution, that is, the tangent equation is obtained.

1. Curve definition: Any continuous line is called a curve, including straight lines, broken lines, bumper letter line segments, arcs, etc.

2. According to the classical definition, the continuous mapping from (a, b) to r3 is a curve, which is equivalent to saying:

1) The curve in R3 is a continuous image of a one-dimensional space and is therefore one-dimensional.

2) The curve in R3 can be obtained by making various twists in the straight line.

3) To say a certain value of a parameter is to say a point on the curve, but not necessarily the other way around, because we can consider a self-intersecting curve.

3. Differential geometry is the discipline that uses calculus to study geometry, and in order to be able to apply the knowledge of calculus, we can't consider all curves, even continuous curves, because continuity is not necessarily differentiable. This brings us to the differential curve. But differentiable curves are also not very good, because there may be some curves, the direction of the tangent at a certain point is not determined, which makes it impossible to start from the tangent, which requires us to study this kind of curve where the derivative is not zero everywhere, we call them regular curves.

4. Regular curves are the main research objects of classical curve theory.

5. Curve: Any continuous line is called a curve, including straight lines, broken lines, line segments, arcs, etc.

6. The curve is a 1-2 dimensional graph, refer to "Fractional Dimensional Space".

7. The curve that turns everywhere generally has an infinite length and an area of zero, and at this time, the curve itself is a space greater than 1 and less than 2 dimensions.

The formation of a curve can be seen as formed in the following three ways: first, a curve can be obtained by depicting the trajectory of a moving point with a continuous change of direction, or by depicting the set of a series of continuous points on its trajectory; Woo Trousers

Second, the intersection line between the surface of the hole balance and the simple surface of the cavity or the surface and the plane after the intersection is the curve;

Third, the envelope during the movement of a line (straight or curved).

envelopes of a line family or curve family), the line produced when each line of the line family is tangent to the envelope is a curve.

What are the types of curves? Curves can be classified according to different criteria: first, curves can be divided into planar curves and spatial curves based on whether all points are in the same plane or not.

No. First of all, it is necessary to clarify what a line segment is: the part between two points of a straight line and the part between them is called a line segment.

Therefore, the line segment must be part of a straight line. There are endpoints at both ends of the line segment, which cannot be extended, which is different from straight lines and rays. Of all the lines connecting two points, the line segment is the shortest.

Abbreviated as the shortest line segment between two points.

Introduction to curvesCurves are one of the main objects of differential geometry research. In the view of straight crack spring, the curve can be regarded as the trajectory of the movement of the spatial particle. Differential geometry is the study of geometry using calculus.

In order to be able to apply the knowledge of calculus, we cannot consider all curves, or even this and continuous, because continuity is not necessarily differentiable. This brings us to the differential curve.

But the differential curve is also not very good, because there may be some curves, the direction of the tangent at a certain point is not determined, which makes it impossible for us to start from the tangent, which requires us to study this kind of curve where the derivative is not zero everywhere, and we call them regular curves. Regular curves are the main research objects of classical curve theory.