Category Archives: Vedic Math

Ancient and religious calendar systems

Ancient and religious calendar systems

The Near East and the Middle East

The lunisolar calendar, in which months are lunar but years are solar—that is, are brought into line with the course of the Sun—was used in the early civilizations of the whole Middle East, except Egypt, and in Greece. The formula was probably invented in Mesopotamia in the 3rd millennium BCE. Study of cuneiform tablets found in this region facilitates tracing the development of time reckoning back to the 27th century BCE, near the invention of writing. The evidence shows that the calendar is a contrivance for dividing the flow of time into units that suit society’s current needs. Though calendar makers put to use time signs offered by nature—the Moon’s phases, for example—they rearranged reality to make it fit society’s constructions.

Babylonian calendars

In Mesopotamia the solar year was divided into two seasons, the “summer,” which included the barley harvest in the second half of May or in the beginning of June, and the “winter,” which roughly corresponded to today’s fall–winter. Three seasons (Assyria) and four seasons (Anatolia) were counted in northerly countries, but in Mesopotamia the bipartition of the year seemed natural. As late as about 1800 BCE the prognoses for the welfare of the city of Mari, on the middle Euphrates, were taken for six months.

The months began at the first visibility of the New Moon, and in the 8th century BCE court astronomers still reported this important observation to the Assyrian kings. The names of the months differed from city to city, and within the same Sumerian city of Babylonia a month could have several names, derived from festivals, from tasks (e.g., sheepshearing) usually performed in the given month, and so on, according to local needs. On the other hand, as early as the 27th century BCE, the Sumerians had used artificial time units in referring to the tenure of some high official—e.g., on N-day of the turn of office of PN, governor. The Sumerian administration also needed a time unit comprising the whole agricultural cycle; for example, from the delivery of new barley and the settling of pertinent accounts to the next crop. This financial year began about two months after barley cutting. For other purposes, a year began before or with the harvest. This fluctuating and discontinuous year was not precise enough for the meticulous accounting of Sumerian scribes, who by 2400 BCE already used the schematic year of 30 × 12 = 360 days.

At about the same time, the idea of a royal year took precise shape, beginning probably at the time of barley harvest, when the king celebrated the new (agricultural) year by offering first fruits to gods in expectation of their blessings for the year. When, in the course of this year, some royal exploit (conquest, temple building, and so on) demonstrated that the fates had been fixed favourably by the celestial powers, the year was named accordingly; for example, as the year in which “the temple of Ningirsu was built.” Until the naming, a year was described as that “following the year named (after such and such event).” The use of the date formulas was supplanted in Babylonia by the counting of regnal years in the 17th century BCE.

The use of lunar reckoning began to prevail in the 21st century BCE. The lunar year probably owed its success to economic progress. A barley loan could be measured out to the lender at the next year’s threshing floor. The wider use of silver as the standard of value demanded more flexible payment terms. A man hiring a servant in the lunar month of Kislimu for a year knew that the engagement would end at the return of the same month, without counting days or periods of office between two dates. At the city of Mari about 1800 BCE, the allocations were already reckoned on the basis of 29- and 30-day lunar months. In the 18th century BCE the Babylonian empire standardized the year by adopting the lunar calendar of the Sumerian sacred city of Nippur. The power and the cultural prestige of Babylon assured the success of the lunar year, which began on Nisanu 1, in the spring. When in the 17th century BCE the dating by regnal years became usual, the period between the accession day and the next Nisanu 1 was described as “the beginning of the kingship of PN,” and the regnal years were counted from this Nisanu 1.

It was necessary for the lunar year of about 354 days to be brought into line with the solar (agricultural) year of approximately 365 days. This was accomplished by the use of an intercalated month. Thus, in the 21st century BCE a special name for the intercalated month iti dirig appears in the sources. The intercalation was operated haphazardly, according to real or imagined needs, and each Sumerian city inserted months at will—e.g., 11 months in 18 years or two months in the same year. Later the empires centralized the intercalation, and as late as 541 BCE it was proclaimed by royal fiat. Improvements in astronomical knowledge eventually made possible the regularization of intercalation, and, under the Persian kings (c. 380 BCE), Babylonian calendar calculators succeeded in computing an almost perfect equivalence in a lunisolar cycle of 19 years and 235 months with intercalations in the years 3, 6, 8, 11, 14, 17, and 19 of the cycle. New Year’s Day (Nisanu 1) now oscillated around the spring equinox within a period of 27 days.

The Babylonian month names were Nisanu, Ayaru, Simanu, Duʾuzu, Abu, Ululu, Tashritu, Arakhsamna, Kislimu, Tebetu, Shabatu, Adaru. The month Adaru II was intercalated six times within the 19-year cycle but never in the year that was 17th of the cycle, when Ululu II was inserted. Thus, the Babylonian calendar until the end preserved a vestige of the original bipartition of the natural year into two seasons, just as the Babylonian months to the end remained truly lunar and began when the New Moon was first visible in the evening. The day began at sunset. Sundials and water clocks (clepsydra) served to count hours.

The influence of the Babylonian calendar was seen in many continued customs and usages of its neighbour and vassal states long after the Babylonian empire had been succeeded by others. In particular, the Jewish calendar in use at relatively late dates employed similar systems of intercalation of months, month names, and other details (see below The Jewish calendar). The Jewish adoption of Babylonian calendar customs dates from the period of the Babylonian Exile in the 6th century BCE.

Other calendars used in the ancient Near East

The Assyrians and the Hittites

Of the calendars of other peoples of the ancient Near East, very little is known. Thus, though the names of all or of some months are known, their order is not. The months were probably everywhere lunar, but evidence for intercalation is often lacking; for instance, in Assyria. For accounting, the Assyrians also used a kind of week, of five days, as it seems, identified by the name of an eponymous official. Thus, a loan could be made and interest calculated for a number of weeks in advance and independently of the vagaries of the civil year. In the city of Ashur, the years bore the name of the official elected for the year; his eponym was known as the limmu. As late as about 1070 BCE, his installation date was not fixed in the calendar. From about 1100 BCE, however, Babylonian month names began to supplant Assyrian names, and, when Assyria became a world power, it used the Babylonian lunisolar calendar.

The calendar of the Hittite empire is known even less well. As in Babylonia, the first Hittite month was that of first fruits, and, on its beginning, the gods determined the fates.


At about the time of the conquest of Babylonia in 539 BCE, Persian kings made the Babylonian cyclic calendar standard throughout the Persian empire, from the Indus to the Nile. Aramaic documents from Persian Egypt, for instance, bear Babylonian dates besides the Egyptian. Similarly, the royal years were reckoned in Babylonian style, from Nisanu 1. It is probable, however, that at the court itself the counting of regnal years began with the accession day. The Seleucids and, afterward, the Parthian rulers of Iran maintained the Babylonian calendar. The fiscal administration in northern Iran, from the 1st century BCE, at least, used Zoroastrian month and day names in documents in Pahlavi (the Iranian language of Sāsānian Persia). The origin and history of the Zoroastrian calendar year of 12 months of 30 days, plus five days (that is, 365 days), remain unknown. It became official under the Sāsānian dynasty, from about 226 CE until the Arab conquest in 621. The Arabs introduced the Muslim lunar year, but the Persians continued to use the Sāsānian solar year, which in 1079 was made equal to the Julian year by the introduction of the leap year.

The Egyptian calendar

The ancient Egyptians originally employed a calendar based upon the Moon, and, like many peoples throughout the world, they regulated their lunar calendar by means of the guidance of a sidereal calendar. They used the seasonal appearance of the star Sirius (Sothis); this corresponded closely to the true solar year, being only 12 minutes shorter. Certain difficulties arose, however, because of the inherent incompatibility of lunar and solar years. To solve this problem the Egyptians invented a schematized civil year of 365 days divided into three seasons, each of which consisted of four months of 30 days each. To complete the year, five intercalary days were added at its end, so that the 12 months were equal to 360 days plus five extra days. This civil calendar was derived from the lunar calendar (using months) and the agricultural, or Nile, fluctuations (using seasons); it was, however, no longer directly connected to either and thus was not controlled by them. The civil calendar served government and administration, while the lunar calendar continued to regulate religious affairs and everyday life.

In time, the discrepancy between the civil calendar and the older lunar structure became obvious. Because the lunar calendar was controlled by the rising of Sirius, its months would correspond to the same season each year, while the civil calendar would move through the seasons because the civil year was about one-fourth day shorter than the solar year. Hence, every four years it would fall behind the solar year by one day, and after 1,460 years it would again agree with the lunisolar calendar. Such a period of time is called a Sothic cycle.

Because of the discrepancy between these two calendars, the Egyptians established a second lunar calendar based upon the civil year and not, as the older one had been, upon the sighting of Sirius. It was schematic and artificial, and its purpose was to determine religious celebrations and duties. In order to keep it in general agreement with the civil year, a month was intercalated every time the first day of the lunar year came before the first day of the civil year; later a 25-year cycle of intercalation was introduced. The original lunar calendar, however, was not abandoned but was retained primarily for agriculture because of its agreement with the seasons. Thus, the ancient Egyptians operated with three calendars, each for a different purpose.

The only unit of time that was larger than a year was the reign of a king. The usual custom of dating by reign was “year 1, 2, 3,…of King So-and-So,” and with each new king the counting reverted back to year 1. King lists recorded consecutive rulers and the total years of their respective reigns.The civil year was divided into three seasons, commonly translated: Inundation, when the Nile overflowed the agricultural land; Going Forth, the time of planting when the Nile returned to its bed; and Deficiency, the time of low water and harvest.

The months of the civil calendar were numbered according to their respective seasons and were not listed by any particular name—e.g., third month of Inundation—but for religious purposes the months had names. How early these names were employed in the later lunar calendar is obscure.

The days in the civil calendar were also indicated by number and listed according to their respective months. Thus a full civil date would be: “Regnal year 1, fourth month of Inundation, day 5, under the majesty of King So-and-So.” In the lunar calendar, however, each day had a specific name, and from some of these names it can be seen that the four quarters or chief phases of the Moon were recognized, although the Egyptians did not use these quarters to divide the month into smaller segments, such as weeks. Unlike most people who used a lunar calendar, the Egyptians began their day with sunrise instead of sunset because they began their month, and consequently their day, by the disappearance of the old Moon just before dawn.

As was customary in early civilizations, the hours were unequal, daylight being divided into 12 parts, and the night likewise; the duration of these parts varied with the seasons. Both water clocks and sundials were constructed with notations to indicate the hours for the different months and seasons of the year. The standard hour of constant length was never employed in ancient Egypt.



Introduction of Vedic Math

Introduction of Vedic Math

Vedic Maths is a super-fast method of making all math calculations straightforward and easy. It mainly deals with mental calculations. When it comes to kids, it helps in increasing concentration power, memorizing formulas, and makes long calculations very simple and less tedious than before.

Vedic Maths Tricks saves a lot of time. The Math trick makes it possible for students to multiply a 13 digit number by a 12 digit number without using pen and paper. It boosts confidence in one’s ability to tackle mathematical problems easily. Formulas for special numbers and Dodging Times Tables up to 99 are much easier with the help of Vedic Maths. It not only helps for calculating magic numbers like multiplication of 999, 5’s, 11, 12, 13,… but also helps for all other numbers.

The Vedic Math Tricks mainly helps children in solving basic concepts under Arithmetic operations like additions, subtractions, multiplication, division, fractions, squares, cubes, and a few Algebraic operations. When compared to the conventional or usual method, the Vedic method has more tricks and easy ways to calculate.

The most important thing about Vedic Mathematics is that it teaches you how to think logically. The method is based on the principle that everything can be reduced to numbers. This means that you will learn to use your intuition as well as logic when doing mathematics.

Vedic Mathematics is a great way to improve your child’s overall intelligence quotient (IQ).

History and Importance of Vedic Math

In the Golden Age Period, about 5000 years ago, people were able to calculate correctly and mentally, without even using a pen or a piece of paper, in no time. Education at that time was exclusively verbal. As time passed, it was felt necessary to document the knowledge of that era for future generations and different Vedas were being composed. We are familiar with four major Vedas: the Rigveda, Samaveda, Yajurveda, and Atharvaveda. The subject matter of each varies. As such, Atharvaveda contains all kinds of sciences, such as architectural science, astronomical science, engineering science, and mathematics.

Europeans showed a great deal of interest in ancient Sanskrit texts at the beginning of the 20th century. Atharvaveda contains some texts called “Ganit Sutras” that contain mathematical conclusions, but no one was able to use them since no one could find mathematics in them.

Vedic Maths is an ancient method of mental calculations that was discovered by “Late Swami Shri Bharti Krishna Tirthaji” (1884-1960)”, the Shankaracharya of Puri, who is known as “The Father of Vedic Maths”. was a great scholar of Sanskrit, English, Mathematics, History, and Philosophy. He studied these texts called “Ganit Sutras” in deep silence in the forests of shingeri for a period of 8 long years.

He reconstructed 16 main Vedic sutras or formulae and 13 sub-sutras, covering a wide range of Arithmetical computation and Algebraic operations. These formulas are in the form of sutras and they are short, easy to remember, and very easy to apply.

All the sutras are in Sanskrit words, he has given English translation and mathematical meaning for all of them and it is clearly explained for the understanding of all age groups. Through the Math techniques explained here, everyone will be able to cut out their dependency on calculators.

Students from grade 3-12, need to learn the Vedic sutras from scratch, it is the foundation. Now is where they will understand the difference between Conventional maths and Vedic Maths. In conventional maths, the steps will be longer, but in Vedic maths, the accurate answers can be found in one straight line. Here is where the students become even smarter. They will start enjoying their school life without any math phobia.

When it comes to competitive exams, students appearing for any government exams, banking, railway, SSC, UPSC, CET, GMAT, etc,.. can easily clear the papers on time with the help of Vedic tricks and it gives quick and accurate results. For this, you need to have a very good practice and tricks should be on your fingertip. It isn’t that easy, but having good practice on concepts of mathematics makes you perfect. So over a period of time, you will get a hang of the math trick. That’s where it sharpens your mind, speed of calculation increases confidence level, and improves mental ability.

Why calculate mentally if I have a calculator?

Vedic Maths is full of math tricks and gives quick answers and removes the confusion in the school method. Also helps in solving any difficulty level in maths calculation. Even a person from a non-maths background can easily learn Vedic Maths.

The human brain is capable of working faster than the world’s fastest computer.

Performing mental calculations is the best exercise for the brain, just like exercising our bodies to stay healthy. Exercising the brain will not only help us calculate fast but also help us in our daily lives as well.

With a calculator, we don’t participate in the calculation process at all. This is highly dangerous over time, as we lose our ability to calculate in a day-to-day situation and our thinking abilities are also affected.

As a result, our brain must be exercised as frequently as possible to become smart and fast, and mental calculations serve as a kind of brain gym. The ability to think faster and smarter keeps the brain active and the body healthy.

5 Interesting Vedic Maths Sutras or Tricks:-

Vedic Maths Is all about the Collection of Sutras and their benefits which can be used with the school curriculum. Here are a few basic operations that will boost you to get started with.

Vedic Sutra 1- Ekadhikena Purvena:-

English Translation:- One more than the previous one

Mathematical meaning:- To obtain the next number, add one to the previous one.

This is the formula used for calculating Squares Of Numbers Ending In 5:-

Eg:- Find the Square of 25.

Solution:- 1st step:- Multiply the number (except last 5) by one more than it.

i.e., 2x(2+1) = 2×3 = 6

2nd step:- Write Square of 5, i.e., 25 after it.

5×5 = 25.

Together (join both the steps), in one line, 2x(2+1) and write 25 = 625.

Therefore, the answer is 625.

Vedic Sutra 2 – Nikhilam Navatascharamam Dasatah:-

English Translation:- All from nine and last from ten.

Mathematical Meaning:- To find the complement (deficiency) of any number to the next base (nearest base, also called working base), subtract all the other digits (except last) from 9 and the last digit from 10.

Eg:- To find the complement of 38 (to the working base 100), subtract:-

Solution:- 3 from 9 = 6 and 8 from 10 = 2, i.e., 62.

Therefore, the complement of 38 (100-38) is 62.

Vedic Sutra 3 – Ekanyunena Purvena:-

English Translation:- One less than the previous one.

Mathematical Meaning:- One number less than the previous number.

This method is used for calculating Multiplication by 9,99,999,…

Formula:- 1st step- Left part- One less than the multiplicand, i.e., (multiplicand – 1)

2nd step- Right part- The deficiency of multiplicand, i.e., (base – multiplicand)

Eg:- Multiply 57 by 99:- (base is 100)

Solution:- step1 – 57-1= 56

step2- 100-57= (9-5=4, 10-7=3)= 43

57 x 99 = (57 – 1) (100 – 57) = 5643

Therefore, 57 x 99 = 5643.

Vedic Sutra 4 – Anthyayordasakepi:-

English Translation:- When final digits add upon ten.

Mathematical Meaning:- The sum of final digits is the base. Eg- 14+16 = (4+6) =10 as base. Multiplication – When the sum of final digits is the base and previous parts are the same.

Formula:- 1st step- Left part- Multiply the previous part by one more than itself

2nd step- Right part- Multiply the last digits (whose sum is the base).

Eg:- Multiply 36 by 34:-

Solution:- Here sum of last digits 6 and 4 is 6+4=10 (base)

36 x 34 = (3x (3+1) (6×4) =(3 x 4) (24) =1224.

Therefore, 36 x 34 = 1224.

Vedic Sutra 5 – Yavadhunam

English Translation:- Whatever the extent of the deficiency.

Mathematical Meaning:- The deficiency (to the nearest base).

This method is used for calculating Squares Of Any Number.

Formula:- 1st step- Right part- Square the deficiency

2nd step-Left part- Subtract the number by its deficiency plus carry over.

Eg:- Find the square of 96.

Solution:- The deficiency is 4 with working base 100.

Step1- Right part:- Square of deficiency (4)²

Step2 – Left part:- Subtract the number by its deficiency (96-4)

(96 – 4) (4)² = (92) (16)

Therefore, 96² = 9216.

Who Can Benefit from Vedic Maths?

Vedic Mathematics is applicable for students from grades 3-12 (age 8-17), students writing competitive exams, and also helps in our day-to-day activities. I have been training teachers and homemakers for improvising their mathematical skills and it also helps homemakers to have an identity and it provides them an extra source of income.

Vedic Maths is the gift of the Veda for solving the “Maths Anxiety” problem in Math education worldwide. It’s a very special feature, it mainly converts the dry tedious Maths into a playful and joyful subject, which children enjoy learning with a smile.