The civilizational achievements of ancient India

India is a melting pot of cultures. The country's unique historical background encompasses a variety of cultural trends from ancient times to modern times, from the West to the East, and from Asia to Europe. In addition, it is a country composed of five major ethnic groups, and it is like a large cultural museum. Mumbai, on the west bank of the capital New Delhi, is the center of culture, while Kolkata has news about culture every day. The diverse music, dance, dance dramas and comedy dazzle tourists and make them forget to leave.

After living in noisy big cities for a long time, people yearn to return to nature. The basis of Indian traditional music is "nature". It celebrates the relationship between people, the relationship between people and nature, and the relationship between people and God. The melodies of the four seasons are reflected in the traditional tune "raga" - legend has it that the ancients were inspired by the chirping of birds and the sound of burning branches in the forest to create the first "raga". As for the content of the song, it originated from North Indian religious rituals. To this day, traditional songs still retain the ancient pronunciation, and the singer's voice is pure, allowing the songs to maintain a simple and pure hymn feeling. Even if you don't understand the lyrics, you can still feel the sacredness and peace of nature.

Natyam, one of the oldest dances in India, means "the art of dance" in Hindi. In addition to emphasizing the rhythm of dance, it also emphasizes that the accompaniment music must be pleasant to the ear, consisting of solemn poetry and simple music. This dance was originally used for sacrifices and could fully reflect the emotions of the dancers. It was originally performed in temples by temple dancers. The key to this dance is to keep your upper body straight, your legs half-bent, your knees spread apart, and your feet like a half-open fan. Although there are strict movement specifications, every actor's performance is actually different, and most of the time the performances are improvised, so each Natyam has a very strong personal style.

This traditional dance is revived in a retro trend. However, in ancient times, Natyam was usually performed solo, while group dances were more popular. A group of graceful dancers in colorful traditional costumes dance like fairies to beautiful music, and the effect is even better than dancing alone. Today, Natyam has developed into a technical art system. Indian curry is famous all over the world, and many people think that rice and curry are the main food and seasonings of India. But in fact, only some places in India use rice as the staple food, and curry is an unfamiliar seasoning to most Indians. In fact, the lack of a unified style is the biggest feature of Indian cuisine. And not only are the eating habits very different between cities in India, but every family has a distinct eating style. But in general, chicken, fish and lamb are the most common. Gravy is a staple sauce in India and is popular throughout India. Of course, each place's gravy has its own distinctly local flavor. In Indian kitchens, only fresh green chillies and sun-dried red chillies are spicy. So tourists who don’t like spicy food don’t have to worry about not being able to eat authentic Indian food.

For tourists, India's most famous traditional dish has its origins in the Indian royal family. Stews, sauces and rice are the basis of three different cooking styles. But after all, royal food can only be eaten in specialized restaurants and big hotels, and ordinary people are not "cold" by it. In the local area, many popular Indian dishes are very popular at home, such as unleavened oatmeal bread and green mustard cooked over coal fire all night. Such a simple winter snack is popular among farmers and city dwellers alike. They all regard it as their favorite. In southern cities, authentic crispy pancakes and steamed rice cakes are famous. As for some coastal areas, in addition to seafood meals such as crabs, lobsters, tiger shrimps and shellfish, fragrant coconut is also the most commonly used ingredient.

The clay oven charcoal cooking method is a unique cooking method in India. It is very particular about time control. When the furnace temperature reaches 600°C, the cooking difference of one or two minutes, or even one or two seconds, affects the success or failure of cooking. The meat cooked in this way does not require oil, and is dipped in yogurt when eating. Even before the food is served, the sizzling sound of the charcoal fire and the lingering aroma will already make your index fingers tickle.

In addition, in many places in India, people like to use a large shallow plate called "thali" to serve food. When eating with "thali", you should taste it slowly as the locals do. Gobbling it up will only make the locals laugh. Since the Harappan culture period, ancient Indians have used the decimal system, but there was no place value method in the early days.

Approximately after the 7th century AD, place value notation was introduced in ancient India, but at the beginning there was no "0" symbol, only a blank space was used to represent it. In the second half of the 9th century AD, there was a symbol for zero, written as "."

The decimal place value method was adopted by many ethnic groups in Central Asia and spread to Europe through the Arabs, gradually evolving into the "Arabic notation" commonly used in the world today. Therefore, Arabic numerals were not created by the Arabs, they just played a role in spreading them. It was the ancient Indians who really contributed to Arabic numerals.

The "Principle Sutra" is the earliest extant mathematical work in ancient India. It is a book about the construction of altars. It was written approximately between the 5th and 4th centuries BC. It contains some geometric knowledge. . This book shows that they already knew the Pythagorean Theorem at that time and used pi to be 3.09. The ancient Indians had already used triangles in astronomical calculations. The mathematical content of "The Collection of Holy Messengers" written in 499 AD ***There are 66 items, including arithmetic operations, exponentiation, square root and some rules of algebra, geometry and trigonometry.

The Holy Messenger also studied the problem of adding two irrational numbers and obtained the correct formula. In terms of trigonometry, he also introduced the positive vector function, and the π he calculated was 3.1416.

The 7th to 13th centuries AD were the most glorious period of mathematical achievements in ancient India. Famous figures during this period include Brahma Zang (about 589~?), Mahavira (9th century), and Sri Tuora (999~?). ) and Zuo Ming (1114~?).

Fan Zang wrote "Brahma Mingmansidanta" in about 628, which conducted in-depth discussions on many mathematical problems. Fanzang was the first person in ancient India to introduce the concept of negative numbers. He also proposed the concept of negative numbers. Operation method.

Fanzang already understood zero as a number, but he mistakenly believed that dividing zero by zero still equals zero. He proposed the rules for understanding general quadratic equations, and concluded that the root of the quadratic equation x+px-q=0 is Fanzang. He also gave the integer solution of ax+by=0 and the method of dealing with the indefinite equation ax+1=y. . His most important achievement was the correct formula for finding the final term of an arithmetic sequence and the sum of the sequence.

In terms of geometry, Sanskrit has the correct formula for calculating the area of ??a quadrilateral based on the side lengths of the quadrilateral, that is, S=√(s-a)(s-b)(s-c)(s-d) (√ is the square root of meaning), S is the area of ??the quadrilateral, a b c d is the length of each side.

Nobita continued the work of his predecessors. His main work is "The Essence of Computing". He realized that zero multiplied by any number equals zero, but he mistakenly believed that dividing a number by zero still equals that number.

Nobita’s research on fractions is also very meaningful. He realized that dividing one fraction by another fraction is equivalent to reversing the numerator and denominator of the fraction and multiplying them.

The existing mathematical works of Sri Tuara include "Summary of Algorithms", and it is said that he also has a book dedicated to quadratic equations. His main work is to study the solution of quadratic equations.

During this period, the greatest achievement in mathematics was made by Zuo Ming. The "Xi You Zhang" and "Factor Algorithm Chapter" in his "Lishu Quanshu Touzhu" reflect the highest achievements of ancient Indian mathematics and are representative works of that period.

Zuo Ming conducted further research on zero and correctly pointed out that dividing a number by zero is infinite. He continued to study the problem of solving quadratic equations and learned that the square root of a number has two numbers, one positive and one negative.

He also clearly pointed out that the square root of a negative number is meaningless. Zuo Ming made very remarkable achievements in the study of indefinite equations. He used ingenious methods to solve the problems of finding integer solutions to many indefinite equations.

The following equations are as follows:

6x+2x=y, 5x-100x=y,

He also gave two values ??of pi, namely π= 3927/1250=3.1416 and π=22/7=3.1429, and pointed out that the former value is more accurate. Since this statement, the development of ancient Indian mathematical science has slowed down, and there is nothing more eye-catching.