Arithmetic progressions are some sort of sequence for numbers that are used in business and other calculations. This has been in practice for several years. Though this was named recently as Arithmetic progression, this has been in practice in India from the ancient days. Many great mathematic scholors of India like Aryabhatta, Bhaskaracharya etc have used this concept of Arithmetic progression that they have extracted from the Vedas. Vedas are the ancient source of knowledge for people of India for several thousand years that discuss about various sources of knowledge including Mathematics. It also has references to Geometric Progression where there are many places where the number series is used in this format.

What is Arithmetic Progression?
Arithmetic Progression is a sequence in Mathematics in which the numbers are entered in a manner such that the difference between the consequent number always gives a constant value. The following sequence can be given as an example for the Arithmetic Progression.

5,7,9,11,13,15,17….

In the above sequence the common difference is always 2. This concept of Arithmetic Progress was explained by Aryabhata in 499 AD in his Aryabhatiya (section 2.18). The source of knowledge for Aryabhatta was the Vedas that explains Arithmetic Progression in various instances.

 

Arithmetic Progression

 

Vedic Knowledge on Arithmetic Progression

Rig Veda is the oldest document known to the human race. Veda is a sanskrit work that comes with a meaning “Knowledge”. So basically Vedas are the collection of Knowledge. In ancient India, Vedas were thought to all the human race with the concept of Guru Shishya Parampara. It was merely a oral recitation until 5th century BC. Later after 5th century BC, Rig Veda was documented. There is no other document that is older than vedas with such advanced knowledge collection. The level of science and technological advancements in the Vedas are unimaginable to the human race. Vedas were categorised into 4 such as Rig, Yajur, Sama and Atharva. Each veda was actually categorised based on some significance and were practiced in Ancient India.

The knowledge of mathematics is vast in the Vedas. There are numerous references to Arithmetic Progression in Vedic verses. Rudhram is one among them. Rudhram is a part that comes in the Krishna Yajur Veda which consists of hymns that praise Lord Shiva. In the following verse of Rudhram Lord Shiva is praised based on the Arithmetic Progression.

एका च मे तिस्रश्च मे पञ्च च मे सप्त च मे
नव च म एकदश च मे त्रयोदश च मे पंचदश च मे
सप्तदश च मे नवदश च म एक विशतिश्च मे
त्रयोविशतिश्च मे पन्चविशतिश्च मे
सप्तविशतिश्च मे नवविशतिश्च म
एकत्रिशच्च मे त्रयस्त्रिशच्च मे
चतस्रश्च मेऽष्टौ च मे द्वादश च मे षोडश च मे
विशतिश्च मे चतुर्विशतिश्च मेऽष्टाविशतिश्च मे
द्वात्रिशच्च मे षट्त्रिशच्च मे चत्वरिशच्च मे
चतुश्चत्वारिशच्च मेऽष्टाचत्वारिशच्च मे
वाजश्च प्रसवश्चापिजश्च क्रतुश्च सुवश्च मूर्धा च
व्यश्नियश्चान्त्यायनश्चान्त्यश्च भौवनश्च
भुवनश्चाधिपतिश्च ॥ ११ ॥

The above verse clearly explains the knowledge of Arithmetic Progression in Vedas. The arithmetic progression in the above verse goes upto 33 starting from 1,3,5,7,9,11….. It is a wonderful factor to amaze that Yajur veda had even more wealth of knowledge on various fields in mathematics. The above verse from Yajur veda explains the knowledge of arithmetic progression and there are also many other references many other things in mathematics like geometric progression, knowledge on Zero, value of pi, pythagoras theorem, etc.  The knowledge source of our great Mathematicians of India are from the Vedas. They just extract or understand the concepts that are explained in the Vedas apply the concepts of Mathematics in their day today life.  Even though the verses in Vedas were not a direct definition or a formula or explanation of these mathematical and other concepts, it clearly shows that these advanced concepts were in practice. This has been a practice in India through oral recitation for many thousand years.

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