# Knowledge of Geometric progression in Vedas

The contribution of India to Mathematics is enormous. There are wonderful Sanskrit scriptures that explain various concepts in Mathematics. For Indians Vedas are the knowledge bases and have various values and virtues for better living. Though the Vedic scriptures are spiritualistic, there are also various descriptions about the knowledge of advance science concepts in Vedas. There is misinterpretation that is prevailing among the people that Vedas has the entire knowledge source that is required for the mankind. This thought is wrong. Though Vedas contain enormous amount of knowledge source, they did not go in depth about the concepts of science and technology. However there are some concepts used in the verses of Vedas that reveals the knowledge on Mathematics, Metallurgy etc. The following verses from Yajur Veda explain the knowledge of Geometric progression. In these verses the powers of 10 is used and the verses are framed in the manner of Geometric progression.

The above verses describe the numbers systematically with the power of ten and also have given a unique name for each and every value. The unique names are given to some extent till some large numbers. This naming of numbers in power of ten is used in Taithriya Samhitha in Krishna Yajur Veda as well as in Thaithariya Upanishad.

**What is Geometric Progression?**

Geometric progression is a sequence of numbers with a common ratio. The numbers after the first in the sequence will be a number arrived by multiplying the previous number in the sequence. By doing this a common ratio is maintained between the numbers in the sequence.

Example: 2,6,18,54….. In this Geometric progression the common ratio is 3.

The powers of a fixed numbers also forms a Geometric sequence. In the above example from Taithriya Samhita of Yajur Veda, the powers of ten is mentioned in geometric progression. Each value is also given a unique name which is yet another amazing factor.

Unique Name |
Value |
Powers of Ten |

Ekam |
1 |
100 |

Dasam |
100 |
101 |

Satham |
100 |
102 |

Sahasram |
1000 |
103 |

Ayutham |
10,000 |
104 |

Niyutham |
100,000 |
105 |

Prayutham |
1000,000 |
106 |

Arbudam |
10,000,000 |
107 |

Niarbudam |
100,000,000 |
108 |

Samudram |
1000,000,000 |
109 |

Madhyam |
10,000,000,000 |
1010 |

Anthyam |
100,000,000,000 |
1011 |

The description of names for the power of ten is also mentioned in two other Sanskrit texts such as Panchavimsa Brahmana and Samkyana Sutra. Also in the Indian epic Ramayana there is a verse where Suka, the spy appointed by Ravana describes about the army of Rama as follows.

1010 + 1014 + 1020 +1024+ 1030 + 1034 + 1040 + 1044+1052+1057 + 1062 + 5 men

Further the books that are dedicated to Mathematics describe more about the numbers, geometric progression and naming conventions of various number systems. There are also other places where the verses in the Vedas are used in the pattern of Geometric progression. Just because the Geometric progression is applied in the verses casually, it is more evident that the knowledge of advance concepts in mathematics was very common in ancient India.

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