Perpetual Calendar Formula 5gh18

Copyright © John Paul L. Botin 2021 ISBN: 978-0-557-98327-8 All Rights Reserved.

ABOUT THE BOOK

This book is the author’s attempt at explaining how he came up with a mental system of the calendar ( Julian and Gregorian ) which was later converted into a tangible prototype. Also attached herein is the author’s design for a two – dimensional perpetual calendar for both systems that can be used to check the veracity of one’s mental calculations.

Likewise, the process by which the codes were assigned or derived were also explained to establish the periodic cycles in both calendar systems. The rules for leap years for both systems were similarly discussed to illustrate the apparent difference between the Julian and Gregorian Calendar. Surprisingly, the Perpetual Calendar Formula itself only involves the operations addition and modulo seven if the final answer in not within the range of the Day Codes. Subtraction is only done for the dates in January and February of a leap year.

The ultimate goal is to be able to make the computations mentally and it requires memorization of the Codes for Days, Dates, Months, Years and Centuries as well as performing the correct addition and modulo application. With constant practice and active memorization, one can emerge as a human perpetual calendar.

DEDICATION

For Earl and Glenda, the Botin family, close friends and acquaintances and for all those who might benefit from the yields of an inquisitive mind.

ACKNOWLEDGMENT

The author manifests his gratitude to those who contributed largely to materialization of this endeavor, to wit:

Solomon+ and Erlina for the unwavering guidance beyond time and distance Annie, Fely, Patet, Louie, Lap, Tin & Toy for all the extended from the discovery of this method, writing of the College Research to its eventual Patent Application Friends from Pilar, Sorsogon for the tireless prodding to find the exact day of any given date thus strengthening my recall of the codes and its computation Earl and Glenda for the presence and encouragement to continuously persist even if the odds are not always even and favorable

May the ideas contained herein contribute to the constantly growing and evolving literature.

TABLE OF CONTENTS

About The Book Dedication Acknowledgment Road To Discovery Dates And Modulo 7 Month Codes Day Codes Year Codes Common Years And Modulo 4 Common Years Cycle Common And Leap Years Cycle Cycle Of 28 Julian Leap Years Julian Century Codes Transition From Julian Calendar To Gregorian Calendar Gregorian Rule For Leap Years Gregorian Century Codes Perpetual Calendar Formula

Final Words References Two – Dimensional Perpetual Calendar Julian Calendar Gregorian Calendar About The Author

ROAD TO DISCOVERY

Sometime in March 1998, the journey that eventually led me to the development of a Perpetual Calendar Formula all started with a 1998 calendar handed out by the staff of a politician running for a seat as Board Member in the province of Sorsogon, Philippines. Attached herein is the image of the same calendar from the internet for reference purposes.

Weeks before, I was told by my younger sister about a news feature wherein an elderly man can accurately guess the exact day of any random date. Since the likelihood of him giving the wrong answer is six out of seven, I started asking how it could possibly be that he gives the correct answer in matters of seconds every time. Then it dawned on me that there has to be a pattern associated thereto. Thus, using the card-size calendar, with the obverse side bearing the face of the aspiring politician, I began searching for that pattern and here is what I have found. It turns out that to be able to guess the exact day of any given date in 1998, I only have to memorize one date for each month as shown below.

MONTHS January February March April May June July August September October November December

1ST MONDAY 5 2 2 6 4 1 6 3 7 5 2 7

Number of Days 31 28 or 29 31 30 31 30 31 31 30 31 30 31

The listed dates are the first Monday of every month in 1998. Let us refer to this as the Month Keys. There are only seven days in a week which means that the same day will appear after that duration since it is a periodic cycle.

Sometimes, when finding the correct day of a date, the given date is too far from the month key or the date that was memorized for each month. We have to remove all the sevens from the date first so that it gets closer to the month key. Finally, once the given date is close enough to the first Monday as listed, we can simply perform simple calculations by counting backward or forward to get to the right answer.

Here are the preliminary steps that we have to do: Identify the month key for the given date Remove all the sevens from the given date When the reduced date is close enough to the month key, perform backward or forward counting of days

Let us have the date 18 January 1998 as our example to illustrate how it works. The key for the month of January is 5. We have to make 18 close enough to the key for that month so we remove all the sevens thereon. The computation becomes 18 – 14 = 4. In other words, the dates January 4 and 18 should fall on the same day. If January 5 is a Monday, the day before it, which is January 4, has to be a Sunday. It only means that the given date 18 January 1998 is also a Sunday.

This time, let us try 02 May 1998. The month key for May is 4 and the given date is 2. We can just count backwards once again. May 4 is a Monday, May 3 is

a Sunday and 02 May 1998 has to be Saturday. We will use a formula later on so we that will not rely so much on counting the days forward or otherwise. The original formula involves addition and subtraction. It was later revised so that the operation involved will only be addition of all the codes. Subtraction will only happen if the given is a date in January or February of a leap year.

DATES AND MODULO 7

As what is universally known, there are seven days in a week. And because of such, we expect the same day to appear very often owing to this pattern. The following months contain thirty ( 30 ) days -- April, June, September and November . All the rest of the months have thirty – one (31) days except February which can either have 28 days in a common year or 29 days during a leap year.

In Mathematics, there is an operation which is called Modulo. Since there are seven days in a week and it repeats perpetually, it is safe to assume that the days follow a Modulo 7 cycle. Modulo is basically the remainder when a number is divided by another number called divisor. Let us try the date 25 and reduce it by using Modulo 7. Once 25 is divided by 7, it gives a quotient of 3 and a remainder of 4. It simply means that, in the syntax of Microsoft Excel or Google Sheets, =Mod(25,7) should give a return value of 4 since it is the remainder. We will use the codes in the table below later on when we discuss the Perpetual Calendar Formula in the ensuing chapters. The values in red will be the Date Codes for the specific dates.

0 DATES 7 14 21 28

CODE 1 8 15 22 29

2 1 9 16 23 30

3 2 10 17 24 31

4 3 11 18 25

5 4 12 19 26

6 5 6 13 20 27

It will be very useful if we start memorizing the Date Codes early on. For easier memorization, we have placed here the first line of the dates. The succeeding dates will just be an addition of a multiple of seven. In other words, to get the code for any date, simply apply Modulo 7 to remove all the sevens on it.

0 DATES

CODE 1 7

2 3 4 5 6 1 2 3 4 5 6

MONTH CODES

Going back to the Month Keys or the 1 st Mondays of 1998 , let us add a number to the dates so that the total becomes 7 and it becomes the Month Codes . MONTHS January February March April May June July August September October November December

Month Keys 5 2 2 6 4 1 6 3 7 5 2 7

Month Codes 2 5 5 1 3 6 1 4 0 2 5 0

Let us summarize the Month Codes by grouping the months with exactly the same codes. Take the time to memorize these codes as well.

0 MONTHS DEC

CODE 1 SEP JUL

2 3 4 5 6 APR JAN MAY AUG FEB JUN OCT MAR NOV

DAY CODES

The assignment of the Day Codes is actually arbitrary. But for the purpose of our explanation and its eventual use in the formula, we are asg the codes for the days as follows:

0 DAYS

CODE 1 FRI

2 3 4 5 6 SAT SUN MON TUE WED THU

Similarly, since the Month Keys fall on a Monday in 1998 and the code for Monday is 3, it follows that the Year Code for 1998 should be 3. In essence, we are simply looking for the day wherein the Month Keys fall on a particular year and use its corresponding equivalent in the day codes to determine the ensuing year code of any given year. Aside from that we also consider the given century and its corresponding code.

YEAR CODES

The designation of the Year Codes follows a different pattern. It is principally based on the corresponding day where the Month Keys are located in a particular year. In other words, there has to be a separate code for the years and the centuries. A separate discussion will be provided in determining the Century Codes using the Year Codes as basis for both the Julian and Gregorian Calendars.

0 YEAR 07 12 18 29 35 40 46 57 63 68 74 85 91 96

CODE 1 01 13 19 24 30 41 47 52 58 69 75 80 86 97

2 02 08 14 25 31 36 42 53 59 64 70 81 87 92 98

3 03 15 20 26 37 43 48 54 65 71 76 82 93 99

4 09 10 21 27 32 38 49 55 60 66 77 83 88 94

5 04 11 16 22 33 39 44 50 61 67 72 78 89 95

6 05 00 06 17 23 28 34 45 51 56 62 73 79 84 90

Since it is apparently difficult to memorize all the dates and its corresponding codes, we will use a representative portion for each Year Code. It is advised to memorize this table because the ultimate aim of this endeavor is to be able to mentally compute for the exact day of any date from the year 0001 – 9999 covering both the Julian and Gregorian Calendars.

0 YEAR 07 12 18

CODE 1 01 13 19 24

2 02 08 14 25

3 03 15 20 26

4 09 10 21 27

5 04 11 16 22

6 05 00 06 17 23

By memorizing only this portion of the table, we get to the codes for the rest of the years not shown. All years, regardless of being an ordinary year or leap year, periodically follows a 28 - year cycle. For common years, there is also periodic cycle in between which can either be every 5, 6, 11, 17 or 22 years but all years will have exactly the same calendar pattern of dates and corresponding days every 28 years. If the given date is higher than any of the numbers shown on the list, apply modulo 28.

To illustrate, let us attach a century to the given table. It only means that 2001, 2007 and 2018 will have exactly the same dates appearing on the same day. For 2012, only the months from March until December will match with the years previously mentioned since 2012 is a leap year. The Day, Date, Month and Year Codes are common for Julian and Gregorian calendars. The only difference will be in the century codes owing to the difference in the period of time it was used and the conditions that determine whether a year that is divisible by four should be a leap year or not.

COMMON YEARS AND MODULO 4

The location of a particular year is determined using Modulo 4. That being said, the focus will be on the last two digits of a given year. The resulting remainder is the location of the year and the same location is crucial in finding other years with exactly the same calendar patterns. In the example below, the years 2000 and 2004 are both leap years and divisible by four which explains the remainder of zero. 2001 then is a year in the first location, 2002 is on the second location and 2003 is on the third location.

Year 2000 Modulo 4 0

2001 1

2002 2

2003 3

2004 0

COMMON YEARS CYCLE

Common or ordinary years are those years which, when divided by four, gives a remainder of 1, 2 or 3. The same remainder is similarly indicative of the year’s location as first, second or third. For the common years, the exact calendar pattern appears every 6 or 11 years depending on its location. If the initial location of a year is on the first, a similar calendar pattern is found six years after it. However, if the location is either second or third, the pattern repeats every eleven years. Regardless of the location of a common or ordinary year, the same pattern is expected to appear after every 28 years.

LOCATION 1 2 3

Addend 6 11 11

1st 3 1 2

Addend 11 6 11

2nd 2 3 1

Addend 11 11 6

3rd 1 2 3

The previous table shows the year locations and the respective addends for each. For common years, it only takes 3 iterations before it completes the 28 - year cycle. Simply put, a year in the first location once added with six with give a result that is found in the third location. Similarly, a year in the third location once added with eleven will give a result in the second location. Finally, a year in the second location, once added by eleven, will give a year in the first location

LOCATION 1 2 3

1st 6 11 11

2nd 11 6 11

3rd 11 11 6

The cumulative addends for each iteration for specific year locations are as follows: LOCATION 1 2 3

1st 6 11 11

2nd 17 17 22

3rd 28 28 28

Let use the year 1993 to illustrate the process:

1993 is a year in the first location (1993 divided 4 gives a remainder of 1) 1993 + 6 = 1999 (a year in the third location) 1999 + 11 = 2010 (a year in the second location) 2010 + 11 = 2021 (a year in the first location)

As shown in the computations and the attached calendar containing the first three months, all the years have exactly the same dates and corresponding days and it’s all because of the periodic occurrence of the calendar pattern every so often. Thus, we have established the fact that the years 1993, 1999, 2010 and 2021 have exactly the same calendar pattern.

COMMON AND LEAP YEARS CYCLE

Because of the addition of one day ( February 29 ) in a leap year, the month codes will not fall on the same days. If the codes for January and February fall on a Monday , the codes from March until December falls on the day after which is a Tuesday . We will use the day where the majority of the month codes fall and just deduct 1 day in our computation for the dates in January and February of a leap year. In of the Perpetual Calendar Formula , the only difference between the common years and the leap year is the subtraction of one from the latter.

Unlike the common years, with the inclusion of a leap year in the cycle, it takes four iterations before the years complete the 28 - year cycle. The addends and the resulting location are listed in the ensuing table. LOCATION 0 1 2 3

6 6 11 5

1st 2 3 1 0

11 5 6 6

2nd 1 0 3 2

6 6 5 11

3rd 3 2 0 1

5 11 6 6

4th 0 1 2 3

Again, let use the year 1993 to illustrate the process: 1993 is a year in the first location (1993 divided 4 gives a remainder of 1) 1993 + 6 = 1999 (a year in the third location) 1999 + 5 = 2004 (a leap year) 2004 + 6 = 2010 (a year in the second location) 2010 + 11 = 2021 (a year in the first location) The addends per iteration is shown in the table below.

LOCATION 0 1 2 3

1st 6 6 11 5

2nd 11 5 6 6

3rd 6 6 5 11

4th 5 11 6 6

The cumulative addends for each iteration for specific year locations including leap years are as follows:

LOCATION 0 1 2 3

1st 6 6 11 5

2nd 17 11 17 11

3rd 22 17 22 22

4th 28 28 28 28

Here is an image of a 2004 calendar and it shows that the dates January 5 and February 2 are Mondays while the rest of the month keys from March until December are all Tuesdays.

CYCLE OF 28

The cycle of 28 is true to both common and ordinary years. For the common years, it only takes about 6 or 11 years for the same calendar pattern to appear. But for leap years, it takes 28 years to have exactly the same calendar pattern. Let us have the calendar for 2032 which shows the same calendar pattern as 2004 .

JULIAN LEAP YEARS

The rule on leap years for the Julian Calendar explicitly says all years divisible by four (4) are leap years. As a result of the excessive declaration of leap years, the Julian calendar eventually became behind by in days relative to the supposed actual date and the season. By 04 October 1582 , the discrepancy already amounted to ten days. Because of that, Pope Gregory XIII decreed to drop ten days from the Julian Calendar to rectify the error. As a result, the starting date of the Gregorian Calendar became 15 October 1582 which is actually the date after 04 October 1582 in the Julian Calendar . Some countries continued to use the Julian Calendar even with its apparent inaccuracy before adopting the Gregorian Calendar system years later.

In recent centuries, the use of the Gregorian Calendar has proliferated worldwide and it also has employed specific rules and measures to avoid future errors in designating years as leap years or not.

JULIAN CENTURY CODES

The basis for the Century Codes for the Julian Calendar will be the Year Code and the actual day in the calendar wherein the Month Codes are found. The next image indicates that the Month Keys fall on a Wednesday on the year 0001 of the Julian Calendar . The Year Code for the 01 is 1 and the only code missing is the one for the century. The formula for finding the actual code of the year is Century Code + Year Code . Since the missing value is the Century Code, we can simply subtract the resultant code by the Year Code. When the result is a negative number, add seven to it. If the result is a number greater than seven, apply modulo 7. The Year Code for 00 is 6 while for 99 it is 3. Also, all years ending in two zeroes are leap years in the Julian Calendar.

x + 0 = 5 x = 5

CENTURY 0 YEAR 01 001 CENTURY 0 YEAR 01 001 CENTURY 0 YEAR 99 099

CODE ? 0 5 CODE 5 0 5 CODE 5 3 1

x + 6 = 3 x = 4

CENTURY 1 YEAR 00 100 CENTURY 1 YEAR 00 100 CENTURY 1 YEAR 99 199

CODE ? 6 3 CODE 4 6 3 CODE 4 3 0

x + 6 = 2 x = 3

CENTURY 2 YEAR 00 200 CENTURY 2 YEAR 00 200 CENTURY 2 YEAR 99 299

CODE ? 6 2 CODE 3 6 2 CODE 3 3 6

x + 6 = 1 x = 2

CENTURY 3 YEAR 00 300 CENTURY 3 YEAR 00 300 CENTURY 3 YEAR 99 399

CODE ? 6 1 CODE 2 6 1 CODE 2 3 5

x + 6 = 0 x = 1

CENTURY 4 YEAR 00 400 CENTURY 4 YEAR 00 400 CENTURY 4 YEAR 99 499

CODE ? 6 0 CODE 1 6 0 CODE 1 3 4

x + 6 = 6 x = 0

CENTURY 5 YEAR 00 500 CENTURY 5 YEAR 00 500 CENTURY 5 YEAR 99 599

CODE ? 6 6 CODE 0 6 6 CODE 0 3 3

x + 6 = 5 x = 6

CENTURY 6 YEAR 00 600 CENTURY 6 YEAR 00 600 CENTURY 6 YEAR 99 699

CODE ? 6 5 CODE 6 6 5 CODE 6 3 2

x + 6 = 4 x = 5

CENTURY 7 YEAR 00 700 CENTURY 7 YEAR 00 700 CENTURY 7 YEAR 99 799

CODE ? 6 4 CODE 5 6 4 CODE 5 3 1

The summary of the Century Codes for the Julian Calendar are as follows:

5 JULIAN CENTURY 07 14

CODE 4 00 08 15

3 2 1 0 6 01 02 03 04 05 06 09 10 11 12 13

For easier memorization, focus only on the first line of the codes since we can apply modulo 7 on any century in the Julian Calendar.

5 JULIAN CENTURY

CODE 4 00

3 2 1 0 6 01 02 03 04 05 06

TRANSITION FROM JULIAN CALENDAR TO GREGORIAN CALENDAR

Mainly because of the inaccuracy of the Julian Calendar, Pope Gregory XIII heeded the suggestion to rectify the same and align the date with the season. As a result, 10 days were dropped from the calendar in 1582. The day after 04 October 1582 (Thursday) became 15 October 1582 (Friday). Some countries did not accede to the same suggestion thinking that it is but a means of the papacy to maintain control over their herd. Referring now to the next image, it shows there that the dates October 5 – 14 are missing in the 1582 calendar.

GREGORIAN RULE FOR LEAP YEARS

Here are the conditions that determine whether a year in the Gregorian Calendar is a leap year or not.

All years divisible by four (4) are leap years. Years ending in two zeroes (00) are leap years if the year is divisible by 400. The years 1700, 1800 and 1900 are common or ordinary years but 1600 and 2000 are both leap years. Years ending in three zeroes (000) are leap years except if it is divisible by 4000. Hence, the years 5000, 6000 and 7000 are leap years but 4000 and 8000 are common or ordinary years.

GREGORIAN CENTURY CODES

Just like the Julian Calendar, the basis for the Century Codes of the Gregorian Calendar will be the Year Code and the actual day in the calendar wherein the Month Keys are found. Unlike the other calendar system, years ending in two zeroes are not necessarily leap years. As previously stated, only the years evenly divisible by 400 will be designated as a leap year. All else will be common years.

The process by which the Century Code is derived is the same for both calendar systems and an image of the actual calendar bearing the first three months will show proof of the actual days where the month codes are found for the century in consideration. If the given year is a leap year, the dates January 5 and February 2 are found on the same day but the date March 2 is the day after. However, if the given year is a common year all the stated dates will fall on exactly the same day. The difference in the pattern is occasioned by the additional date (February 29) in a leap year.

x + 6 = 0 x = 1

CENTURY 19 YEAR 00 1900 CENTURY 19 YEAR 00 1900 CENTURY 19 YEAR 99 1999

CODE ? 6 0 CODE 1 6 0 CODE 1 3 4

x + 6 = 6 x = 0

CENTURY 20 YEAR 00 2000 CENTURY 20 YEAR 00 2000 CENTURY 20 YEAR 99 2099

CODE ? 6 6 CODE 0 6 6 CODE 0 3 3

x + 6 = 4 x = 5

CENTURY 21 YEAR 00 2100 CENTURY 21 YEAR 00 2100 CENTURY 21 YEAR 99 2199

CODE ? 6 4 CODE 5 6 4 CODE 5 3 1

x + 6 = 2 x = 3

CENTURY 22 YEAR 00 2200 CENTURY 22 YEAR 00 2200 CENTURY 22 YEAR 99 2299

CODE ? 6 2 CODE 3 6 2 CODE 3 3 6

x + 6 = 0 x = 1

CENTURY 23 YEAR 00 2300 CENTURY 23 YEAR 00 2300 CENTURY 23 YEAR 99 2399

CODE ? 6 0 CODE 1 6 0 CODE 1 3 4

x + 6 = 6 x = 0

CENTURY 24 YEAR 00 2400 CENTURY 24 YEAR 00 2400 CENTURY 24 YEAR 99 2499

CODE ? 6 6 CODE 0 6 6 CODE 0 3 3

Here is the list of all the Century Codes in the Gregorian Calendar. It looks a lot but just like the other table of codes, we will only memorize a representative portion. And since there are only four codes, if the given century is way beyond our codes, apply modulo 4.

0 GREGORIAN CENTURY 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96

CODE 5

3

1 15

17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97

18 22 26 30 34 38 42 46 50 54 58 62 66 70 74 78 82 86 90 94 98

19 23 27 31 35 39 43 47 51 55 59 63 67 71 75 79 83 87 91 95 99

For easier memorization, focus only on the first line of the codes since we can apply modulo 4 on any century in the Gregorian Calendar. If the remainder is 1 the code is 5. If the remainder is 2, the code has to be 3. But if the remainder is 3, the code is 1. If there is no remainder, the code should be 0 as well.

0 GREGORIAN CENTURY 16

CODE 5

3

1 15

17

18 19

PERPETUAL CALENDAR FORMULA

There is only one general formula for common or ordinary years that we will use in the computation of the correct day of any given date in both Gregorian and Julian Calendars. If necessary, apply modulo seven so that the final answer is within the range of the Day Codes. The general formula is shown below as:

Common Year Formula Date Code + Month Code + Century Code + Year Code = Day Code

The other formula which is used for the dates in January and February of the Leap Year is derived from the first one. The only reason for the inclusion of a minus 1 in the formula is because the keys for January and February on a leap year falls a day earlier. Leap Year Formula Date Code + Month Code + Century Code + Year Code – 1 = Day Code

In illustrating the process of computation, we will employ a template done in Microsoft Excel containing a dropdown list of all the inclusive dates, months, centuries and years for both calendar systems. The cells filled with green is where the list will be populated and the adjacent cells contain a Vlookup formula to fetch the codes for each value. The final result as the exact day of the given date is also a Vlookup formula that converts the numerical value to its right with its corresponding day. Lastly, the merged cell on top of the given and the code is a concatenation of the values list on the filled cells.

Gregorian Calendar Given Date

Code

Month Century Year Day

For our first example, let us have the first date in the Gregorian calendar and explain the computational process involved thereto.

Gregorian Calendar Given Date Month Century Year Day

15 October 1582 Code 15 October 15 82 Friday

1 2 1 3 0

The code for the given date 15 is 1. The month October has 2 as its code. The century 15 has 1 as its code while the year 82 has 3 as its code. Apply modulo 7, if necessary. The operation then resolves to:

1 + 2 + 1 + 3 = n 7 = n 0 = n 0 = Friday

Referring now the final answer of 0 against the Day Codes will give the result Friday. This only means that the given date 15 October 1582 is actually a Friday.

Let us take the last day in our range -- 31 December 9999 and employ the same process of computation. to remove all sevens in the final answer by applying modulo 7. For January and February of a leap year, subtract 1 from the final answer.

Gregorian Calendar Given Date Month Century Year Day

31 December 9999 Code 31 December 99 99 Friday

3 0 1 3 0

3 + 0 + 1 + 3 = n 7 = n 0 = n 0 = Friday

The next examples are dates in January or February of a leap year in the Gregorian Calendar.

Gregorian (Leap Year) Given Date Month Century Year Day

29 February 2004 Code 29 February 20 04 Sunday

1 5 0 4 2

1 + 5 + 0 + 4 - 1 = n 9 = n 2 = n 2 = Sunday

Gregorian (Leap Year) Given Date Month Century Year Day

18 January 7960 Code 18 January 79 60 Monday

4 2 1 4 3

4 + 2 + 1 + 4 – 1 = n 10 = n 3 = n 3 = Monday

Let us have some examples from the Julian Calendar.

Julian Calendar Given Date Month Century Year Day

4 October 1582 Code 4 October 15 82 Thursday

4 2 4 3 6

4 + 2 + 4 + 3 = n 13 = n 6 = n 6 = Thursday

Julian Calendar Given Date Month Century Year Day

1 January 001 Code 1 January 0 01 Saturday

1 2 5 0 1

1 + 2 + 5 + 0 = n 8 = n 1 = n 1 = Saturday

Here is January or February of a leap year in the Julian Calendar.

Julian Calendar (Leap Year) Given Date Month Century Year Day

29 February 200 Code 29 February 2 00 Friday

1 5 3 6 0

1 + 5 + 3 + 6 - 1 = n 14 = n 0 = n 0 = Friday

Julian Calendar (Leap Year) Given Date Month Century Year Day

15 January 1492 Code 15 January 14 92 Sunday

1 2 5 2 2

1 + 2 + 5 + 2 - 1 = n 9 = n 2 = n 1 = Sunday

There are countless other possible dates to solve for its exact day. As shown in the preceding examples, the computation will be a lot easier if only the corresponding codes come in handy. The real challenge lies in the memorization of the codes and performing the correct sequence of operations. But once you have found your own way of memorizing the codes, the computation becomes relatively effortless.

FINAL WORDS

Months after I discovered the formula, I used to impress my friends that I can guess the exact day of any given date at random. And since cellular phones were not yet available during those times to check the correctness of my answer, I usually have a set of pocket calendars from 1976 – 1998. Then I would ask them to pick any date from the calendar they have. After a few seconds, I would give them the correct answer once I have correctly recalled the specific codes for the given date and performed addition and modulo 7, if necessary.

It took some years more before I was able to come up with a much simpler method with a greater expanse of century range. And the method is exactly the formula that we have shown earlier.

As a bonus for reaching this far, and if memorizing the codes still pose a challenge, I have appended here my version of the Two - Dimensional Perpetual Calendars for both Julian and Gregorian Calendar system. It works exactly as the method previously discussed but instead of memorizing the codes, you only have to mark the given date, month, century or year then add all the codes to arrive at an answer found in the range of the Day Codes. Again, apply modulo seven if the final answer is a number greater than seven. For January and February of a leap year, do not forget to deduct one from the final answer.

REFERENCES

www.timeanddate.com

www.generalblue.com

TWO – DIMENSIONAL PERPETUAL CALENDAR

JULIAN CALENDAR

GREGORIAN CALENDAR

ABOUT THE AUTHOR

The author is a Bicolano who hails from Binanuahan, Pilar, Sorsogon, Philippines. He discovered a mental system of the calendar for both the Julian and Gregorian Calendar ( January 1, 0001 – December 31, 2899 ) sometime in March 1998 . He later used the same study as his College Research which earned for him the “ Best Research Award ” in March 2000 at Bicol University College of Industrial Technology ( BUCIT ) in Legazpi City.

He later converted his mental system of a calendar to a tangible prototype. His first attempt was a Two – Dimensional Perpetual Calendar similar to the illustration found at the last pages of the book. He then revised the prototype and applied for a Philippine Patent for a “Cylindrical Perpetual Calendar” covering the dates ranging from January 1, 0001 until December 31, 9999. He is now awaiting the release of the patent for a utility model since it has already been published initially in the official publication of the Intellectual Property Office of the Philippines.

Among his other notable works include “Encounters with the Pen” (Ukiyoto Publishing, 2021), “Street-Smart Google Sheets” and “Hand Abacus”.

For other inquiries you may email him at [email protected]