Description: Take the transcendental number e =1+11! + 1/2! + 1/3! +...= 2.7 1828 ... logarithm with base.

Usage:

1. standard writing ln(x) (note: the value range of x is 0.

2. The number set should be LN (pi, pi/3, pi/6) =1.1447 0.0461-0.647.

3. The combined application of LN (SIN (PI/4+6)+LG (SIN (1)) =-1.9177).

Details:

Also known as hyperbolic logarithm. Take the transcendental number [fc (] e =1+11! + 12! + 13! +…? =2? 7 1828 ...[fc]] is the base logarithm. Represented by the symbol "ln". There is a natural logarithm table to look up.

When x approaches positive infinity or negative infinity, the limit of [1+( 1/x)] X is equal to e, which is actually discovered through this limit. It is an infinite cyclic decimal. Its value is approximately equal to 2.7 1828 1828. ...

Represented by e.

Logarithms based on e are usually used for.

E is a transcendental number.

E is widely used in science and technology, and the logarithm with the base of 10 is generally not used. Taking e as the base can simplify many formulas, and it is the most "natural", so it is called "natural logarithm"

Vortex or spiral is a very common form of natural things, such as: a wisp of smoke curling into the blue sky, a ripple swaying gently on the blue lake, several snails climbing slowly on the fence, and countless stars dancing in the quiet night sky. ...

The aesthetic significance of spiral, especially logarithmic spiral, can be expressed in exponential form:

φkρ=αe

Where α and k are constants, φ is polar angle, ρ is polar diameter, and E is the base of natural logarithm. For the convenience of discussion, we define e or the form composed of e as "natural law" Therefore, the core of "natural law" is E, and its value is 2.7 1828 ... This is an infinite cyclic number.

The Beauty of "Natural Law"

"natural law" is the form of e and e after certain transformation and compound. E is the essence of "natural law", which is a function in mathematics;

( 1+ 1/x)^x

The limit when x approaches infinity.

People should study some practical problems, such as the cooling of objects, the reproduction of cells and the decay of radioactive elements.

( 1+ 1/x)^x

The x power of x, the limit when x approaches infinity. It is this finiteness obtained from infinite change that develops from two opposite directions (when X tends to positive infinity, the limit of the above formula is equal to E = 2.7 1828 ..., and when X tends to negative infinity, the result of the above formula is also equal to E = 2.7 1828 ...), which fully embodies the formation of the universe.

Modern cosmology shows that the universe originated from the Big Bang and is still expanding. This description is consistent with the entropy law, that is, the second law of thermodynamics, which is one of the two great discoveries in the second half of19th century. The law of entropy points out that the evolution of matter is always in the direction of destroying information and disintegrating order, and gradually degenerates from complex to simple and from high to low. The limit of degradation is disorderly balance, that is, the state of maximum entropy, a state of inaction and death. What is this process like? It is not difficult to understand just by looking at the photos of spiral galaxies in astrophotography. If we must find the motive force that Aristotle said, then we can regard the universe as a clockwork mechanism that is wound up in advance, or simply regard the whole universe as a huge clockwork. History is just the process of this clockwork constantly striving for freedom and releasing energy.

The evolution of organisms has opposite characteristics, which is very different from the entropy described by the second law of thermodynamics. It enables organisms to avoid the decline of trends and environment. Any life is a dissipative structure system, and the reason why it can avoid the death state approaching the maximum entropy is because life can continuously absorb negative entropy from the environment through metabolic processes such as eating, drinking and breathing. The essence of metabolism is to let the organism successfully eliminate all the entropy it has to produce when it is alive.

On the one hand, the "law of nature" embodies the collapse process of natural systems in the direction of chaos (such as the decay of elements), on the other hand, it shows the essence that life systems can maintain their stability and promote their development (such as cell reproduction) only through an orderly process. It is precisely because of this feature that order and disorder, vitality and death are in the same form, and "natural law" has important aesthetic value.

If the barren desert is the entropy increasing state of "natural law" in disorder and death, then the vast and vibrant grassland is the dynamic and stable structure of "natural law" in order and prosperity. Therefore, the desert makes people feel solemn, boundless and thought-provoking, reminding people of all kinds of difficulties and bumps in the course of life; Grassland, on the other hand, makes people excited, happy and feel the joy and happiness of life.

E = 2.7 1828 ... is a quantitative expression of "natural law". The image expression of "natural law" is a spiral. There are five mathematical expressions of spiral: (1) logarithmic spiral; (2) Archimedes spiral; (3) interlocking helix; (4) Hyperbolic spiral; (5) spiral. Logarithmic spiral is the most common spiral in nature, and other spirals are also related to logarithmic spiral, but at present we have not found the general formula of spiral. The logarithmic spiral was introduced by Descartes in 1638. Later, Swiss mathematician Jacob Bernoulli made a detailed study on it, and found that the involute and extension line of logarithmic spiral are still logarithmic spiral, and the tangent of each point and pole of logarithmic spiral is still logarithmic spiral, and so on. Bernoulli was surprised by these interesting properties and left a will on his tombstone to draw a logarithmic spiral.

Willianm Hogarth, a famous British painter and art theorist, deeply felt that spirals or spirals gradually narrowed towards their centers, which were all beautiful shapes. In fact, we can easily find the spiral in the works of ancient and modern artists. Why can our feelings, our "spiritual" eyes, often be satisfied instinctively and intuitively from such a spiral form? Doesn't this mean that there is a more primitive isomorphic correspondence between our spirit, our "inner" world and the external world than history?

As we know, protein, as the basic substance of life phenomenon, participates in all the work of life process in life, and its function is so complex, efficient and mysterious that it is closely related to its structure. Chemists found that protein's titanium chain is mainly spiral, and the nucleic acid structure that determines heredity is also spiral.

The ancient Greeks had a musical instrument called Feng Qin Ming. When its strings vibrate in the wind, it can make a beautiful tone. This tone is called "vortex tail effect". It is thought-provoking that the inner ear structure, an auditory organ formed by human beings through long-term evolution, also has a vortex shape. Is this for the convenience of enjoying the ancient Greek wind chimes? And our fingerprints, hair clips, etc. The physiological structure of this aesthetic subject corresponds to the isomorphism of the external world and is the natural basis for the harmony between "inside" and "outside".

Some people say that the beauty of mathematics is the brilliance of "one", which is invariant under the action of as many transformation groups as possible, that is, it is the expression of the universal law of nature and the unity of "many" and "one", so "natural law" also flashes the brilliance of "one". Who can say how much convenience and success E = 2.7 1828 ... have brought to mathematicians? People praise the rigidity, clarity and truthfulness of straight lines and appreciate the beauty, change and implication of curves, but they don't know that any straight line and curve can be composed of enough parts on the spiral. Some people say that beauty is the unity of subject and object, the unity of inner spiritual world and outer material world, so "natural law" also has this unity. Human understanding develops according to the law of negation of negation, and the history of society and nature also follows this dialectical development law. What gives this form a vivid expression? Spiral!

Some people say that beauty lies in the rhythm of things, and the "laws of nature" also have this rhythm; Some people say that beauty is a dynamic balance and eternal change, so "natural law" is also a dynamic balance and eternal change; Some people say that beauty lies in the dynamic structure of things, so the "laws of nature" also have this structure-such as hairspring in watches, clockwork in machines and so on.

"Natural law" is the unity of formal reasons and dynamic reasons, the image expression of things, and the same expression of concrete and abstract. Limited life is rooted in infinite nature, and the pulse of life consciously adjusts its movement and rhythm according to the melody of the universe ... organic and inorganic, internal and external, social and natural, and all things are one. Is this all the aesthetic mystery revealed by the "laws of nature"? Don't! "Natural law" always has endless aesthetic connotation, because it symbolizes the vast and profound nature. Because of this, it attracts people worthy of unremitting exploration, thus showing the essential power of human evolution.

The above information comes from practical mathematics software.