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Aryabhata has written Ganitapada. It is a poetic text talking about mathematics. Ganitapada has thirty-three verses. It is about theories of arithmetic and Algebra.
Arithmetic is the study of numbers, the operations that can be performed with them, and their relationships. Arithmetic involves using the operators +, -, *, and / to perform mathematical operations on numbers. We also use parentheses to group operations together and indicate the order of operations.
Ganitapada talks about topics mentioned below:
- Areas and Volume
- Trigonometry
- Decimal number system
- Progressions
- Squares and Cubes
- Linear equations
- Geometrical constructions
- Rule of three
Background History Of Aryabhata
Aryabhata was a well-known Gupta mathematician and astronomer. He is credited with inventing the decimal system. He was the first mathematician in India to study astrology and mathematics in various formats.
Indian scientists, for a long time, largely overlooked him. In the second half of the twentieth century, he came into the spotlight when Indian scientists launched the Aryabhata satellite in 1975.
Aryabhata was born in Kusumpur on April 13, 476. (Modern Patna).
The Verses of Ganitapada
The concepts given by Ganitapada are applicable even today. Here are some of its details:
Kuttaka (equations of the type): ax + b = cy + d (indeterminate equation of the first degree)
The conclusions reached in Ganitapada are still applicable today.
- Verse 1 is written in honour of Brahmadeva. He is considered to be the inventor of the universe.
- Verse 2 is about the number system.
- This means when the numbers are placed in sequence of 1,10, 100, 1000, 10000, 100000, 1000000, and so on, each successive number is ten times the previous number.
- Verse 3 is about cubes and Squares.
- A figure with four sides having all the sides and diagonals equal in measurement is a square. A cube is formed when a number is multiplied three times by itself.
- Verses 4 and 5 talk about obtaining the square root and cube root.
- For, e.g., the square root for 529 is 23. The cube root of 12167 is 23.
- Verse 6 is about the expansion of (x+y)2 and (x+y)3.
- Verses 7 talks about how the area of a circle is obtained.
- The area of a circle is obtained when you multiply half the circumference by half of the diameter of a circle.
- Verses 8 talks about calculating the area of a trapezium.
- Verses 9 is about calculating the area of a polygon.
- Verses 10 is about calculating the value of Pi.
- It is the ratio of the circumference of a circle to the diameter of a circle.
- Verses 11 to 14 talk about the properties of a circle. Chords are also mentioned.
- Verses 15 and 16 talk about the properties of a cone.
- Verses 17 and 18
- In the case of a right-angled triangle, the sum of squares of two sides = the square of its hypotenuse.
- Verses 19 to 22
- These verses are about Progressions. It is a sum to n terms.
- Verses 23 to 31
- The rule of three numbers is mentioned in these verses. They talk about the effect of two moving bodies: investment, interest, and profit and loss.
- Verses 32 and 33 talk about the linear equations of the form ax+b = cx+d.
Ganitapada exhibits the level of mathematics prevalent in ancient times, around 500 CE. Arithmetic also includes algebra and geometry. Algebra is the study of equations and systems of equations, which are mathematical models that describe real-world situations.
What Is Gnomon?
Gnomon (from the Greek word meaning “observer”) is a tool used in astronomy to measure the position of a celestial object. It is also known as a shadow clock, as it casts a shadow on a surface when the thing is located above it.
Notable Inventions Of Aryabhata
Aryabhata achieved extraordinary things relevant to the current times because of his great imaginative approach. Though most of his writings have been lost to time, Arya-Siddhanta and Aryabhatiya are two of his most important works.
Aryabhata examines astronomy and mathematics, as well as their relationship, in both volumes. He also talked about how mathematical equations could be used to figure out how the world works through astronomy.
Aryabhatiya
Ariyabhatiya, Aryabhata’s magnum opus, has 121 lines where he discusses astronomical treatises.
The mathematics section comprises 33 verses with 66 rules. Ganitapada (33 verses), Golapada (50 verses), Gitikapada (13 verses), and Kalakriyapada (13 verses) are the four chapters comprising the text (25 verses).
Aryabhatiya covers a wide range of topics, including the nature of the solar system, the system for calculating a planet’s position in space, and the explanations for lunar and solar eclipses.
Conclusion
Aryabhata is known as the “Father of Algebra” because he had a thorough grasp and explanation of the planetary system using the Sanskrutik method of computation, which was popular during the Vedic times.
Algebra, arithmetic, spherical trigonometry, and plane trigonometry are included in the mathematical section. Sums of power series, continuing fractions, the table of sines, and quadratic equations are all covered in Aryabhatiya. It is a highly influential piece of literature that presents many fundamental principles in modern mathematics and astronomy.
He established a “system of numerals” in Aryabhatiya, which used Indian alphabets to represent numbers. His number method ensured that numbers up to 1018 could be represented using alphabetical notation.
Aryabhata was thought to be familiar with the idea of zero and the place value system.
Prime Minister Narendra Modi visited Ireland on September 23, 2015. It was the second time an Indian Prime Minister had visited Ireland. The first being Jawaharlal Nehru’s visit in 1956. Ireland is an island nation located in Northwestern Europe and surrounded by the North Atlantic Ocean.
The Prime Minister of Ireland, Enda Kenny, had hosted PM Modi during his visit. The PM was attended by other dignitaries such as the Minister of Foreign Affairs and Trade, Charles Flanagan, and Ireland’s Ambassador to India, Feilim McLaughlin. The main aim of the visit was to create stronger ties and improve trade and cultural relations. Described below is the impact of the PM’s Ireland visit.
Impact on trade and commerce
India and Ireland have strong bilateral trade and business relations. Before the PM’s visit, trades with Ireland were valued at €650 million in business in 2014. This included exports worth €248m and imports worth €402 million.
The indigenous exports increased from €32 million in 2012 to €55 million in 2014. In 2019, the total bilateral trade was around €1.2 billion. The exports and the imports have also increased to €636 million and €480 million respectively. Currently, the total trade between India and Ireland is valued at €4.2 billion. This resulted from improved bilateral ties between the two nations, owing to Prime Minister Modi’s visit to Ireland.
Indian Companies in Ireland
Many Indian companies carry out trade and commerce in Ireland. They provide services to Irish markets and consumers across various industries. Pharmaceutical giants such as Reliance Genemedix and Amneal Pharmaceuticals operate in Ireland. Major IT companies such as Wipro, Infosys, TCS, and HCL also have a strong presence in the country. The trade relations were bolstered after Indian Prime Minister Narendra Modi visited Ireland.
Other companies like Crompton Greaves, Deepak Fasteners, Jain irrigation systems, and Shapoorji Pallonji provide consumer goods and services. Likewise, many Irish companies conduct their business in the Indian market. These companies include pharmaceutical and nutrition players like ICON and Glanbia, IT firms like Globoforce and other companies like Keventer, CRH Taxback Group, and Connolly Red Mills.
Impact on Education
Ireland has been a coveted destination for higher education for Indian students. Over 5000 Indian students have enrolled for higher studies in various institutions in Ireland. The students are admitted to engineering, technology, medicine and management colleges. More than 30 research agreements have been signed between the two nations that allow institutes in both countries to collaborate.
Many reputed institutes like Trinity College, Dublin, and Thapar University, Patiala, have signed MOUs for engineering and science disciplines programmes. Thus, Ireland is an essential collaborator in graduate and doctoral research. This collaboration is also considered an impact of the PM’s Ireland visit.
Indian Community in Ireland
Ireland is diplomatically significant for India also due to the large number of Indian citizens residing there. The Indian origin population is approximately 45,000 people, of whom 18,500 are Non-Resident Indians (NRI), and others are Persons of Indian Origin (PIO). The majority of the residents are working professionals employed in engineering, healthcare and management positions.
It has helped in establishing many policies for the Indian origin population. Two such policies in practice are wearing hijab as a part of the police uniform and the non-requirement of obtaining an additional work permit for the spouse or the partner of Critical Skill Employment Permit holders.
Cultural Impact
As a result of a large population of Indian origin citizens in Ireland and the relationship between the two nations, Ireland promotes Indian culture in various forms. One such example is the celebration of Diwali in Ireland since 2008. The event is organised every year in collaboration with Irish and Indian committees.
Further, an annual contemporary film festival is also a part of the celebration of Indian culture. The promotion of such events indicates the importance of cultural exchange between the two nations. The Irish communities also take a keen interest in conventional practices such as cultivating and consuming Indian herbs and spices. This connects the agricultural practices between the two nations. The cultural ties between the countries were strong, and Prime Minister Modi’s visit to Ireland helped strengthen them further.
Another significant practice is the celebration of International Yoga Day in Ireland. The Irish communities have accepted Yoga as a form of a healthy lifestyle. The practice is similar to the Indian tradition.
Tourism
India attracts around 44,000 Irish tourists every year. Indian tourists too visit Ireland in similar numbers. This was facilitated by the introduction of the common British-Irish visa scheme. This scheme allows the tourists to visit the U.K. and Ireland under one visa, rather than applying for two separate visas. It is valid for short stays. India also extended its Electronic Tourist Visa facility to Ireland to digitally facilitate visa approval and generation. The impact of the PM’s Ireland visit was such that it has also helped establish the tourism sector in both countries.
Conclusion
The diplomatic ties between Ireland and India have been impacted positively after Prime Minister Modi visited Ireland in 2015. It was an essential step toward strengthening the bilateral relationship between these two nations. India and Ireland have been important to each other since the 1900s.
In 2010 and 2017, two honorary consulates were established in Chennai and Kolkata. Later in 2019, a formal and fully functional consulate general in Mumbai. Ireland and India have also shown their allegiance to fighting terrorism after the Pulwama attack. India has also hosted several Irish dignitaries on various occasions. These visits were directed toward engagement in business, education, health and tourism.
Further, many agreements were signed to provide opportunities for employment to people of both countries. Prime Minister Modi’s visit to Ireland helped revive relatively stagnant relations between these two nations. Several cultural and historically similar instances bind these two nations. From Yeats and Tagore to cricket and Diwali, the cultural semblance between these two nations has helped create a strong tie between them.
