Pingalacharya's Counting 0 to 31 with Five fingers!

Counting 0 to 31 with Five Fingers! 

Powers of 2= 2^5, if we allowed folding the finger into half (as tripathaka in Natya Shastra), three possibilities for one finger makes it 3^5=243 numbers with just five fingers! :) 

With 10 fingers we could count up to fifty nine thousand and forty nine! 

So thumb represents 2 power 0=1

Index finger represents 2 power 1 = 2

Middle finger represents 2 power 2 = 4

Ring finger represents 2 power 3 = 8

Little finger represents 2 power 4 = 16

So any number from 0 to 31 can be represented as a combination of sum of (1,2,4,8,16)

Example 17= 1+16 so 10001. Open only thumb and little finger.

11= 1+2+8 so 11010. Open thumb index and ring fingers.

It is important for children to learn about mathematics of counting, arithmetic, geometry, algebra, on the way to the beautiful early Calculus, that our great Madhavacharya of Sangamagrama gifted the world more than 300 years before Newton or Leibniz who fight to take credit! 

We can count upto 1023 using 10 fingers

Each new finger will represent the numbers 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. That is why you could count upto 31 with 5 fingers.

With 5 fingers.. Each finger has  2 states - open or close that is 1 or 0..  So with 5 fingers we can represent 2 power 5 (32 numbers, that is 0 to 31)

0 0 0 0 0 = 0 (all fingers closed)

10000  = 1 ( only thumb open)

01000 = 2 ( only index open)

11000 = 3 (1+2 = both thumb and index open)

00100=4

10100=5

01100=6

11100=7

00010=8

10010=9

01010=10

11010=11(1+2+8)

00110=12

10110=13

01110=14

11110=15 (1+2+4+8)

00001=16

10001=17

01001=18

11001=19

00101=20

10101=21

01101=22(2+4+16)

11101=23

00011=24

10011=25

01011=26

11011=27

00111=28

10111=29

01111=30

11111=31

Similarly with 10 fingers 2 power 10=1024 numbers can be represented. (0-1023)

This later formed the basis of binary system that computers use today!