When a set of numbers follows a particular discipline, it becomes a Pattern or Sequence of Numbers.
The simplest pattern is the "Natural Numbers" or "Counting numbers". The discipline or rule followed by this sequence is just a difference of 1 to any number. We get the sequence by adding 1 to any number. So, if we start with 0, we get 0, 1, 2, 3, 4, 5, 6, ..... and so on all the way to infinity. If we start with -100, we get the sequence -100, -99, -98, -97,...., -1, 0, 1, 2, 3, etc. These are also called Integers.
Addition by 1 gives us this sequence. Addition by 1 can also be called “One more than the one before” or the Vedic sutra “Ekadhikena Purvena”. Interesting, Subtraction by 1 also gives the same sequence of numbers. Subtraction by 1 can also be called “One less than the one before” or the Vedic sutra “Ekayunena Purvena”.
We have already seen “Ekadhikena Purvena” and “Ekayunena Purvena” in the article http://www.vedmath.com/vedmath-vedic-maths-blogs/numberline-and-vedicmaths
If we start with 1 and take alternate numbers, the pattern or sequence is 1, 3, 5, 7, 9, ....and so on. This sequence is called “Odd Numbers”. If we start with 0 and take alternate numbers, the pattern or sequence is 0, 2, 4, 6, 8, 10...and so on. This sequence is called “Even Numbers”. Considering both positive and negative numbers, we get the following patterns:
Thus, Odd numbers and Even numbers are simple patterns of numbers.
(a) If we start with 2 and take alternate numbers, we end up with the pattern:
(b) If we start at 3, and instead of taking alternate number, if we skip 2 numbers, we get:
3, 6, 9, 12,.....+infinity
(c) If we start at 4, and skip 3 numbers, we get:
This can go on and we can get all the Tables we learnt in school. The Tables are nothing but different patterns in numbers. Vedic maths leverages these simple properties of numbers to achieve powerful solutions and help us in solving problems quickly, elegantly and effectively.
These patterns and more including 9 point circle, etc are taught in the courses taken by VedMath Academy: both at our classes in our centres as well as online Vedic maths.