Fascinating Ancient Numbers : Greek Numerals (Attic and Ionian)

The history of numbers is a fascinating journey through human civilization.

Early Beginnings: In prehistoric times, the earliest evidence of counting came from tally marks on bones and stones, dating back to around 35,000 BCE. The Ishango Bone, discovered in Africa, is a notable example. Also, humans likely used physical objects like pebbles, sticks, or knots in a string to keep track of numbers.

Ancient Civilizations: Around 3000 BCE, the Sumerians developed one of the earliest number systems, using a base-60 (sexagesimal) system. The Babylonians inherited and expanded this system, influencing their mathematics and astronomy. It inspired ancient Egyptians to create a decimal (base-10) system around 3000 BCE. Their hieroglyphs represented numbers and were used in administrative and architectural contexts.

Greeks: The Greeks used a variety of systems, including the Attic and the later alphabetic (Ionian) numerals, which assigned values to letters of their alphabet.

Attic: 

• 1: | (a vertical stroke)
• 5: Π (the first letter of "pente," meaning five)
• 10: Δ (the first letter of "deka," meaning ten)
• 50: ΠΔ (a combination of the symbols for 5 and 10)
• 100: Η (the first letter of "hekaton," meaning hundred)
• 500: ΠΗ (a combination of the symbols for 5 and 100)
• 1,000: Χ (the first letter of "chilioi," meaning thousand)
• 5,000: ΠΧ (a combination of the symbols for 5 and 1,000)
• 10,000: Μ (the first letter of "myrioi," meaning ten thousand)
  
  

    This system was additive, meaning that the values of the symbols were added together to form numbers. This system was additive, meaning that the values of the symbols were added together to form numbers. 

For example:  49 = 40 + 9 = ΔΔΔΔ + ΠΙΙΙΙ = ΔΔΔΔΠΙΙΙΙ

Ionian (Alphabetic):

• 1-9:
• 1: Α (alpha)
• 2: Β (beta)
• 3: Γ (gamma)
• 4: Δ (delta)
• 5: Ε (epsilon)
• 6: Ϛ (stigma)
• 7: Ζ (zeta)
• 8: Η (eta)
• 9: Θ (theta)
• 10-90:
• 10: Ι (iota)
• 20: Κ (kappa)
• 30: Λ (lambda)
• 40: Μ (mu)
• 50: Ν (nu)
• 60: Ξ (xi)
• 70: Ο (omicron)
• 80: Π (pi)
• 90: ϙ (koppa)
• 100-900:
• 100: Ρ (rho)
• 200: Σ (sigma)
• 300: Τ (tau)
• 400: Υ (upsilon)
• 500: Φ (phi)
• 600: Χ (chi)
• 700: Ψ (psi)
• 800: Ω (omega)
• 900: ϡ (sampi)

In this system, numbers were written by combining these letters. 

For example: the number 241 = ΣΜΑ (200 + 40 + 1).

The Ionian system was more efficient and flexible than the Attic system, leading to its widespread adoption throughout the Greek world. Thereafter the Roman numeral system, developed around 500 BCE, used combinations of letters from the Latin alphabet (I, V, X, L, C, D, M) to represent numbers.

        The Attic and Ionian numeral systems played a crucial role in various aspects of ancient Greek life, contributing to their economic prosperity, scientific advancements, cultural achievements, and administrative efficiency.

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Credits:

• OpenAI. (2024). ChatGPT [Large language model]. https://chatgpt.com/c/de7a198b-bf21-4493-84d4-35227eb07f58
• Attic numerals. (2023, June 1). In Wikipedia. https://en.wikipedia.org/wiki/Attic_numerals
• Apostol, Tom M. Introduction to analytic number theory. Springer Science & Business Media, 2013.

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Thank You

Alok Pradhan

30.07.2024

What is TRP and how it's calculated?

What is TRP?

TRP stands for Television Rating Point / Target Rating Point.

It shows the rating of TV channels and which shows are viewed the most.

Who calculates TRP?

TRP is calculated by a industry body called Broadcast Audience Research Council (BARC).

Before BARC, bam was the rating agency for measuring TRP.

BARC publishes the weekly rankings for channels.

How TRP is calculated?

To calculate TRP a device is used called peoplemeter.

Peoplemeter is installed with TV, it records how much time the channels are viewed.

As it is not possible to install this device in each television of the country, a sample size of 44000+ houses are selected.

It installs peoplemeter in the selective houses in different region of the country and each week measurement is taken from these households.

To install peoplemeter BARC has given contract to Hansa research.

On the basis of the sample size a statistical data, rating is given to the channels.

This Rating shows which channels are popular or seen most throughout the country.

Example:

Suppose there are  2 channels named A&B.

A is seen by 6 peoples for 10 minutes by each.

B is seen by 4 people for 20 minutes by each.

Total time watched for A = 10*6 = 60 min for B=20*4=80 min.

So B's Rating is higher than that of A.

Why TRP is important:

•Higher TRP attracts advertisers as their ad will reach more audience. It enables advertisers to determine which channels are viewed most and which show is popular.

•TRP rating enables broadcaster to charge advertiser accordingly. It means higher TRP of a channels implies higher earning through advertisement.

Loophole of TRP:

It doesn't matter how many people are watching a particular channel, but how much time a channels is seen matters. So isn't it easy to manipulate the TRP by luring the viewers where peoplemeter are used.

There are about 20 Crore TV sets and about 80 Crore people watch TV in India.

Only 44000 peoplemeter or TRP meter are installed which is only 0.00022 percent or 22 peoplemeter for  every 1 lakh TV. It means 22 people decides what 1 lakh people are watching.

It's not that each of the  44000 peoplemetre measures all type of channels of a TV set.

•23760 (54%) device are used for HIndi entertainment only.

•Only 8000 (20%) devices are used Hindi News channels.

i,e. 4 TV user decides what 1 lakh TV users are watching.

•Only 700 devices are used for English News channels.

i,e. 35 TV for every 1 Crore. 35 people decides what 1 Crore people are watching.

What do you think?

Is this the proper way of measuring TRP? 

The likes and dislikes of 20,00,00,000 TV users are being measured by only 44,000 TV users.

TRP can be easily manipulated by bribing the TV users where peoplemeter is installed and a channel's rating can be easily increased.

Comment below what do you think about it and in your opinion how TRP can be calculated authentically.

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Light Year | Distance

 Light Year is a unit of Distance.

Light Year is defined as the distance traveled by light in one year.

Generally in our day to day life we use centimetre, metre, kilometre, mile, inch, foot etc. to measure distance between two points.

But in astronomy or space science to measure distance between astronomical objects like planets, stars and between galaxies these units are not suitable, hence Light Year is used.

1 Light Year = 9.4607×10¹² km 

•Light travels at the rate of 3×10⁸ m/sec in vacuum.

•Light travels at the rate of 2.2×10⁸ m/sec in water.

•Light travels at the rate of 2×10⁸ m/sec in glass.

DO YOU KNOW?

•Milky Way galaxy is about 1,000,000,000,000,000,000 km (about 100,000 light years).

There are billions of galaxy in the observable universe.

•Nearest galaxy to our Milky Way galaxy is Andromeda Galaxy which is 2.3 million light years away.

Just imagine how long the distance is and how big our universe.

•The radius of observable universe is 46.508 billion light years.

Think how our science has developed that we can study the planets,stars,galaxies up to this huge distance.

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If you know more interesting facts like this then comment below.

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How a day, a month and a year is defined?

DAY:

A Day is defined as the time taken by earth to complete one rotation around its axis.

Earth takes approximately 23 hour and 56 minutes to complete one rotation around its axis. So one day of earth is taken as 24 hours. 

Now let's see how much time planets in our solar system take to complete one rotation around its axis.

MONTH:

Generally a  Month is defined as time taken by MOON to complete one revolution around earth which is approximated to 30 days.

YEAR:

A Year is defined as the time taken by earth to complete one revolution around Sun.

Earth takes 365.242  days to complete one revolution around sun.

Every year is considered as 365 days and to adjust 0.242 day which is approximately equal to 0.25 day, in every fourth year one day is added which is called Leap Year.

This extra day is added to the month February, which becomes 29 days. 

see, how long it takes by the planets of our solar system to complete one revolution around sun (in earth days)

Thank You...

For any query or suggestion comment below

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PIN Code and what does its each digit mean

 PIN stands for Postal Index Number.

A PIN refers to a six digit code in the Indian Postal System used by India Post.

HISTORY:

India Post is a government-operated postal system that was established in 1854, this is the largest postal service or most widely distributed postal service in the world.

It had some limitations like manual sorting of posts and delivery of posts by eliminating confusion over names of similar places, and incorrect delivery addresses.

To simplify this PIN system was launched on 15th August 1972 by the Ministry of Communication. This system divided India into 9 different zones and each zones into many sub-zones. The first eight zones i,e. digits 1 to 8 are divided geographically and the digit 9 is reserved for Army Postal.

PIN STRUCTURE

Each digit of PIN code is assigned to a specific region/location. 

First digit of the PIN refers to the zone.

• 1- Delhi, Haryana, Punjab, Himachal Pradesh, Jammu & Kashmir, Ladakh, Chandigarh
• 2- Uttar Pradesh, Uttarakhand
• 3- Rajasthan, Gujarat, Daman and Diu, Dadra and Nagar Haveli
• 4- Maharastra, Goa, Madhya Pradesh, Chhatisgarh
• 5- Telengana, Andhra Pradesh, Karnataka
• 6- Tamilnadu, Kerala, Puducherry, Kerala
• 7- West Bengal, Odisha, Nagaland, Arunachal Pradesh, Tripura, Mizoram, Tripura, Meghalaya, Assam, Sikkim, Andaman & Nichobar Island.
• 8- Bihar, Jharlhand
• 9- Army Post Office(APO), Field Post Office(FPO)

Army Postal Service is a government operated postal service for the delivery of mail of army.

Field Post Office is set up at the time of war or military exercise.

Second digit indicate the sub-zone.

Second digit along with the first digit indiate a sub-zone or a circle.

• 11 - Delhi
• 12,13 - Haryana
• 14,15 - Punjab
• 16 - Chhatisgarh
• 17 - Himachal Pradesh
• 18,19 - Jammu & Kashmir, Ladakh
• 20 to 28 - Uttar Pradesh, Uttarakhand
• 30 to 34 - Rajasthan

• 36 to 39 - Gujurat
• 40 to 44 - Maharstra
• 45 to 49 - Chhatisgarh, Madhya Pradesh
• 50 to 53 - Andhra Pradesh, Telengana
• 56 to 59 - Karnataka
• 60 to 64 - Tamil Nadu
• 67 to 69 - Kerala
• 70 to 74 - West Bengal
• 75 to 77 - Odisha
• 78 - Assam
• 79 - North Eastern State
• 80 to 85 - Bihar, Jharkhand
• 90 to 99 - Army Postal Service

Third digit refers to a geographical region (excluding in the case of functional zone of Army)  called sorting District i,e. headquartered at the main post office of the largest city of the region.

Fourth digit represent the route on which a post office is located. The digit 0 is for offices which are nearer to the sorting district.

Fifth and Sixth digit together represent a specific Post Office starting from 01.

Thank You...

For any query or suggestion comment below 

                                                                  

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Co-prime numbers

Set of  numbers that have only common divisor as 1 are called co-prime numbers.

Co-prime numbers are also known as Mutually prime number or Relatively prime numbers.

How to Check weather two numbers are Prime or not?

Consider any two numbers, if no positive integer divide both the numbers except 1 then the two numbers are called Relatively Prime or Co-prime.

Example1: are 15 and 22 co-prime?

Answer: 

Divisors of 15: 1, 3, 5, 15

Divisors of 22: 1,2,11,22

Since 15 and 22 don't have any common divisor they are co-prime.

Example2: are 20 and 34 co-prime?

Answer: 

Divisors of 20 : 1,2,4,5,10,20

Divisors of 34 : 1,2,17,34

These two numbers have 2 as the common divisors so they are not co-prime.

FACTS:

• Every number is co-prime with 1.
• Two even number can never be co-prime because every even number is divisible by 2.
• Every Prime number is co-prime to each other. 
• Any two consecutive number are always co-prime. Take any two number like (1,2), (2,3), (3,4)... (501,502).... are always co-prime.

                                                            

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Roman Number System

7 symbols are used to represent the whole number system in Roman Number System.

The seven symbols are given as:

I = 1

V = 5

X = 10

L = 50

C = 100

D = 500

M = 1000

The value of the numeral is the sum of the values of the symbols.

like:

1=I

2=II

3=III

4=IV

5=V

6=VI

7=VII

8=VIII

9=IX

10=X

In this system the symbols are read from left to right.

You must have noticed IV and VI having same symbols represent different value. But why?

There are specific rules to write the roman number system.

• We can't write the same symbol more than three times.

    we can't write 4 as IIII. it's wrong . 4 is written as IV.

• When a symbol appears after a larger or equal symbol, then it's added.

VI= 5+1=6

XI=10+1=11

XX=10+10=20

•When a symbol appears after a smaller symbol, then the smaller symbol is subtracted from the larger symbol.

as

IV=5-1=4

IX=10-1=9 

LCXIV= (100-50) + 10 + (5-1)  = 64

Thank You.

For any query comment below.

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