Indian Mathematical Inventions: Who Changed the World indian inventions Mathematics is the subject (science) that deals with the logic of size, quantity, calculation and arrangement. Mathematics is all around us, everything we do. It is a designated place for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering and even sports. It represents the high level of abstraction achieved by the human mind.

#### mathematical inventions in ancient India

Mathematics has its roots in Vedic literature in India, which is about 4000 years old. 1000 BC And 1000 A.D. Between, various concepts on mathematics were given by Indian mathematicians. Which first included the concept of zero, techniques of algebra and algorithm, square root and cube root. There are various examples of mathematics of ancient India which are still applicable today.

#### Indian Mathematical Inventions: Who Changed the World

#### 1. Zero

- If this Indian mathematician-astronomer Aryabhatta were not there, the number would not have been zero. Although people have always understood the concept of nothing or nothing. It is a relatively new concept, it was fully developed in India around the fifth century. Earlier, mathematicians had struggled to make the simplest arithmetic calculation. Today, zero – both as a symbol (or digit) and a concept means the absence of any quantity. Zero allows us to perform paths, perform complex equations, and invent computers.

Peter Gobbets, secretary of the ZeroGrindia Foundation or Zero Project, said, “Zero is widely viewed as one of the biggest innovations in human history, a cornerstone of modern mathematics and physics.”

#### 2. Algebra

Today, as much as students hate it, India had a major contribution in the field of algebra in ancient times.

- In ancient India, traditional mathematics called Ganitam was known before the development of algebra. It originated from the name Algebra, which was given to the algebraic form of computation. Algebra means ‘other mathematics’ (Bija means second and Ganitam means mathematics).

- In India around the 5th century, a system of mathematics that made astronomical calculations easy. Its application at that time was limited to astronomy because its pioneers were astronomers. Because astronomical calculations are complex and involve many variables that go into the derivation of unknown quantities. Algebra is a small method of calculation and by this characteristic, it scores higher than traditional arithmetic.

#### 3. Trigonometry

- Trigonometry originated in ancient India. It traveled from India to the Middle East and people everywhere adopted it. From here it went through Arabs to Europe and went through many modifications to reach its present form. Trigonometry was considered a part of astronomy in ancient times.

We honor Siddhant (Sanskrit astronomical works) for his contribution towards the beginning of the Sine ceremony. Historians consider Aryabhatta, Brahmagupta, Bhaskara-I and Bhaskara-II to be the principal exponents of trigonometry. Bhaskar-I gave formulas to find the values of the sine function for angles greater than 90o (obtuse angle). On the other hand, Bhaskar-II gave precise expressions to calculate trigonometric ratios of acute angles such as 18o, 36o, 54o, and 72o.

#### 4. Decimal system and quadratic formula

- In the classical period of Indian mathematics (400 CE to 1600 CE), significant contributions were made by scholars such as Aryabhata, Brahmagupta, Mahavir, Bhaskar II, Madhava of Sangamagrama and Neelkanth Somayaji. The decimal number system in use worldwide today was first recorded in Indian mathematics.

- It was in the 7th century CE when Brahmagupta found the first general formula for solving quadratic equations. The decimal system (or Hindu number system), a precursor to the Arabic numerical system, developed in India between the 1st and 6th centuries CE.

#### 5. Fibonacci number

The Fibonacci sequence is a series of numbers where a number is found by adding two numbers before it. Starting from 0 and 1, the sequence progresses 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. It was first described by Virahanka, Gopal and Hemachandra as an outbreak of Pingala’s earlier writings.

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#### Indian Mathematical Inventions: Who Changed the World

#### 6. Length

- The scale is believed to have been used by the Indus Valley Civilization before 1500 BCE. Made of ivory, rulers found during excavations reveal the amazing accuracy of decimal subdivisions on it.

- Indus Valley Civilization found great accuracy in measuring length, mass and time. He was among the first to develop a system of equal weights and measures. A comparison of available items indicates large scale variation in the Indus regions. Their smallest division, inscribed on the scale of ivory found in Lothal, Gujarat, was about 1.704 mm, the smallest partition ever recorded on the Bronze Age scale.

#### 7. Weight

The history of measurement systems in India begins in the early Indus Valley Civilization, which is among the surviving specimens dating to the 5th millennium BCE. From the earliest times, the adoption of standard weights and measures shows the architectural, folk and metallic artifacts of the country. A complex system of weights and measures was adopted by the Mauryan Empire (322–185 BCE), which also made rules for the use of this system. Later, the Mughal Empire (1526–1857) used standard measures to determine land holdings and collect land taxes as part of Mughal land reforms.

A total of 558 weights were excavated from Mohenjodaro, Harappa and Chanhu-Daro, not including the poor ones. They did not find a statistically significant difference between weights, which were excavated from five different layers. The depth of each was about 1.5 meters. This was evidence that strong controls existed for a period of at least 500 years. The weight of 13.7-g is one of the units used in the Indus Valley. The notation was based on binary and decimal systems. 83% of the excavators from the above three cities were weight cubic and 68% were made of rag.

#### 8. Geometry

- Indian mathematicians also contributed to the field of geometry. There was a field of mathematical applications called Rekha Ganita (line count). The Sulva Sutra, which literally means ‘rule of law’ gives geometrical methods of constructing altars and temples. The layout of the temples was called Mandal. Some important works in this area have been done by Aapastamb, Boudhayan, Hiranyakeshin, Varaha and Vadhula.

#### 9. Infinite Series

Mathematicians in Kerala made rules for second order interpolation to calculate intermediate sine values. Madhava, a Kerala mathematician, must have discovered the sine and cosine series about three hundred years before Newton. In this sense, we can consider Madhav to be the founder of mathematical analysis. Madhav (circa 1340 – 1425 A.D.) was the first to take decisive steps to treat his boundary-crossing from the finite processes of ancient Indian mathematics to infinity. The mathematician Madhava also discovered infinite-series expansions of circular and trigonometric functions and finite-series approximations. His power series for the P and Sine and Cosin works is referred to by reverence by later writers.

#### 10. Binary Code

- Binary numbers form the basis for operating a computer. The binary number was discovered in the West in 1695 by the German mathematician Gottfried Leibniz. However, new evidence proves that binary numbers were used in India before the second century, more than 1500 years before their discovery in the West. The source of this discovery is a musical text by Pingala called “Chhandasastra” which means the science of meter.

This text falls under the category of “sutras” or erotic statements. Detailed discussion of these brief but profound statements is found in later observations. “Chhandashahstra” has been incarnated in the second century