Perpetual Calendar

ABSTRACT OF THE DISCLOSURE A perpetual calendar that determines the day of any Gregorian calendar date that is in Anno Domini. This one-page perpetual calendar has five main tables: Days of the Week, Months, Days of the Month, Years and Leap Years. The Days of the 5 Week contains days (Sunday to Saturday) and numbers (0, 1, …, 6). The Days of the Week repeats twice here. The Months contains months (January to December). The Days of the Month contains whole numbers (1 to 31). The Years (a table with tables) has four tables: Thousands’ Place, Hundreds’ Place, Tens’ Place and Ones’ Place. The Thousands’ Place contains numbers (1000, 2000, …, 9000). The Hundreds’ Place 10 contains numbers (100, 200, …, 900). The Tens’ Place contains numbers (10, 20, …, 90). The Ones’ Place contains whole numbers (1 to 9). The Leap Years (a table with tables) has three tables: Leap Years Before a Centennial, Centennials and Millenniums. The Leap Years Before a Centennial contains numbers (4, 8, …, 96). The Centennials contains numbers (100, 200, …, 900). The Millenniums contains 15 numbers (1000, 2000, …, 9000). Methods that adhere to both the Gregorian calendar and the Fortunado’s algorithm (an algorithm for knowing the day of any Gregorian calendar date that is in Anno Domini) are used to determine which row and column the contents are placed. Modifications will be made to make a calendar for each year. Modifications will be made to know the day of any Gregorian calendar date later than 20 9999 Anno Domini. 25 PERPETUAL CALENDAR FOR THE GREGORIAN CALENDAR TECHNICAL FIELD HOW TO USE THIS PERPETUAL CALENDAR? (STEPS) Each part of the date has a value seen very left across (0 to 6). 5 2. In Years, look for the equivalent. Example: Year 2009 = 2000 and 9 (The hundred’s place is 0. The ten’s place is 0.) 3. In Leap Years, go to the nearest lower number if cannot be found. Example: Year 2009 = 2000 and 8. Last 2 digits 03, 02, 01 and 00 are 0. 4. Add the values of the Month, the Day of the Month, the Year and the Leap Year. 10 5. If the date be a leap year and (January or February), deduct 1. Note: A year is a leap year if it is exactly divisible by 4 but not exactly divisible by 100 unless also exactly divisible by 400. 6. If year is 12_ _, 13_ _, 16_ _, 17_ _, 32_ _, 33_ _, 36_ _, 37_ _, 52_ _, 53_ _, 56_ _, 57_ _, 72_ _, 73_ _, 76_ _, 77_ _, 92_ _, 93_ _, 96_ _ or 97_ _, add 1 15 (first two digits are) 7. Divide the value by seven and get the remainder. (mod 7) 8. The remainder has an equivalent day of the week seen left across which is the answer. Example: August 5, 2011 = (2+5+5+3+1+2+2)/7 and Get the remainder = 6 = 20 Friday FOR GREGORIAN DATES LATER THAN 9999 AD Make a table for Ten Thousand’s Place, … in addition to Years’ table. Make a table for (10000, 20000, …, 90000), … in addition to Leap Years’ table. 25 EXPLANATION OF THIS PERPETUAL CALENDAR This perpetual calendar adheres to both the Gregorian calendar and the Fortunado’s algorithm (an algorithm for knowing the day of any Gregorian calendar date that is in Anno Domini). 5 Why the Gregorian calendar? Other calendars (E.g. Julian calendar and Roman calendar) could be used but the Gregorian calendar is the internationally accepted civil calendar. Why the Fortunado’s Algorithm? It is the simplest algorithm for understanding how to know the day of any 10 given Gregorian calendar date that is in AD. It is also based on the Gregorian calendar which makes a perfect fit. It was analyzed to produce this perpetual calendar (other forms may be considered). 15 DERIVIATION OF THE PERPETUAL CALENDAR From the Gregorian calendar The five main tables signify the values of the basic components of any Gregorian calendar date that is in AD. (See the HOW TO USE THIS PERPETUAL 20 CALENDAR? portion.) Days of the Week determines what day the Gregorian calendar date that is in AD fell/falls/will fall after knowing the result of computations. (See the HOW TO USE THIS PERPETUAL CALENDAR? portion.) Months determines the value of the month. 25 3. Days of the Month determines the value of the day of the month. 4. Years determines the value of the years disregarding the leap years covered. 5. Leap Years determines the number of leap years that passed the year. Notes: (1) The tables are singular so I use singular verbs. (2)The months, the days of the month and the years are based in the Gregorian calendar (in Ad). 5 From the Fortunado’s algorithm The Days of the Week has two columns and seven rows. The first column comprises of days (Saturday to Friday). The second column comprises of numbers (0 to 6). The days and numbers are arranged increasing and each corresponds to a row. (for a reference to mod 7) 10 2. The Months has one column and seven rows. This table comprises of months (January to December). Each month has a value when evaluated that determines which row it is in. Mod 7 is used after knowing the value of the months. 3. The Days of the Month has five columns and seven rows. This table comprises 15 of numbers (1 to 31). Mod 7 is used to determine which row a number would be in. 4. The Thousands’ Place has two columns and seven rows. This table has numbers (1000, 2000, …, 9000). Mod 7 is used to determine which row a number would be in. 20 5. The Hundreds’ Place has two columns and seven rows. This table has numbers (100, 200, …, 900). Mod 7 is used to determine which row a number would be in. The Tens’ Place has two columns and seven rows. This table has numbers (10, 20, …, 90). Mod 7 is used to determine which row a number would be in. 25 7. The Ones’ Place has two columns and seven rows. This table has numbers (1 to 9). Mod 7 is used to determine which row a number would be in. 8. The Leap Years Before a Centennial has four columns and seven rows. This table has numbers (4, 8, …, 96). Divide by 4 and mod 7 are used to determine which row a number would be in. 5 9. The Centennials has two columns and seven rows. This table has numbers (100, 200, …, 900). (In every 100 years but not in every 400 years, no adding of one leap year), divide by 4 and mod 7 are used to determine which row a number would be in. 10. The Millenniums has two columns and seven rows. This table has numbers 10 (1000, 2000, …, 9000). (In every 100 years but not in every 400 years, no adding of one leap year), divide by 4 and mod 7 are used to determine which row a number would be in. Note: The author arranged the contents to their proper columns to have a better presentation like the Gregorian calendar. 15 BACKGROUND OF THE UTILITY MODEL This perpetual calendar determines the day of any Gregorian calendar date that is in Anno Domini. Methods that adhere to both the Gregorian calendar and the 20 Fortunado’s algorithm (an algorithm for knowing the day of any Gregorian calendar date that is in Anno Domini) are used to make this perpetual calendar. Anno Domini (abbreviated as AD or A.D.) and Before Christ (abbreviated as BC or B.C.) are designations used to label or number years in the Christian Era (also known as the "Common Era" or the "Vulgar Era") used with 25 the Julian and Gregorian calendars. A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The Gregorian calendar, also known as the Western calendar, or Christian 5 calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter gravissimas. The reformed calendar was adopted later that year by a handful of countries, with other countries adopting it over the following centuries. The motivation for the Gregorian 10 reform was that the Julian calendar assumes that the time between vernal equinoxes is 365.25 days, when in fact it is presently almost exactly 11 minutes shorter. The error between these values accumulated at the rate of about three days every four centuries, resulting in the equinox occurring on March 11 (an accumulated error of about 10 days) and moving steadily earlier in the Julian calendar at the time of the Gregorian 15 reform. Since the Spring equinox was tied to the celebration of Easter, the Roman Catholic church considered that this steady movement in the date of the equinox was undesirable. A perpetual calendar (or forever calendar) is a calendar which is good for a span of many years, such as the Runic calendar. For the Gregorian calendar, a 20 perpetual calendar often consists of 14 one-year calendars, plus a legend to show which one-year calendar is to be used for any given year. Note that such a perpetual calendar fails to indicate the dates of moveable feasts such as Easter. There are other perpetual calendars which range from mechanical to others. In mathematics and computer science, an algorithm is an effective method 25 expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning. In simple words an algorithm is a step-by-step procedure for calculations. Fortunado’s algorithm is If the date was/is/will be a leap year and (January or February), use Formula 1 else 5 use Formula 2. Notes: We add another day (February 29) during a leap year. The difference (the use of two formulas) is told here. Formula 1: W=(D+M+Y–1) mod 7 Formula 2: W=(D+M+Y) mod 7 10 Note: mod is used in modular arithmetic. Where: W is the day of the week (0=Saturday, 1=Sunday, 2=Monday, 3=Tuesday, 4=Wednesday, 5=Thursday & 6=Friday). D is the day of the month. 15 M is the number of days of the month (January=0, February=31, March=59, April=90, May=120, June=151, July=181, August= 212, September=243, October=273, November=304 and December=334.). Notes: Add the days that passed after the month. There is a separate computation for leap years. We use February having 28 days regardless if it is a leap 20 year. E.g. March = January (31 days) + February (28 days) Y is the number of days of the year (year times to 365 + year/4, disregard the fraction – year/100, disregard the fraction + year/400, disregard the fraction). Note: year times to 365 = year because using distributive law results to 365 mod 7=1 and any number times to 1 is itself. 25 Y becomes year + year/4, disregard the fraction – year/100, disregard the fraction + year/400, disregard the fraction. Notes: Leap years are computed in the years. 365 could be subtracted from the number of days of the year but doing this will change the algorithm affecting the date to fit the day and so another adjustment takes place in the day of the week. 5 Note: Rules for determining leap years A year is a leap year if It is exactly divisible by 4 BUT NOT exactly divisible by 100 UNLESS ALSO exactly divisible by 400. 10 In mathematics, modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus. The Swiss mathematician Leonhard Euler pioneered the modern approach to congruence in about 1750, when he explicitly introduced the idea of congruence modulo a number N. Modular arithmetic was further advanced by Carl 15 Friendrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there 20 is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Since the hour number starts over after it reaches 12, this is arithmetic modulo 12. 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 ≡ 0 mod 12. Modular arithmetic can be handled mathematically by introducing 25 a congruence relation on the integers that is compatible with the operations of the ring of integers: addition, subtraction, and multiplication. For a positive integer n, two integers (a and b) are said to be congruent modulo n, written: If their difference (a – b) is an integer multiple of n, the number n is called 5 the modulus of the congruence. For example, because 38 − 14 = 24, which is a multiple of 12. 10 Advantages of this perpetual calendar It is made up of simple materials (ink for the contents and paper for where the contents be placed). It has least contents compared to other perpetual calendars. Modifications can be easily made to have a calendar for each year. 15 4. Modifications can be easily made to know the day of any Gregorian calendar date later than 9999 Anno Domini. 5. The greatest coverage with no adjustments or extended computations needed. (It is originally from year 1 to year 9999 Anno Domini.) Disadvantages of this perpetual calendar 20 Disadvantages could be disregarded because The materials used can be changed. (for presentation and longer time use) The contents can be modified. (for appropriate use) DETAILED DESCRIPTION 25 General Description Use an A-4 paper (3-ply Bristol board is used here). Use India ink or its equivalent for the contents. Contents are numbers, days and months. (no use of italics, boldface or underline) The fonts are Times New Roman. All the font sizes are 10. Only names of tables use boldface. (Names are placed on top.) The Main Tables 10 The basic compositions of this calendar are five tables. The five tables’ names are Days of the Week, Months, Days of the Month, Years and Leap Years. The Years (a table with tables) has four tables: Thousands’ Place, Hundreds’ Place, Tens’ Place and Ones’ Place. The Leap Years (a table with tables) has three tables: Leap Years Before a Centennial, Centennials and 15 Millenniums. Construction of this Perpetual Calendar The calendar has three portions: the top, the middle and the bottom. The top portion has the Days of the Week, the Months and the Days of the 20 Months. The Days of the Week is located left (right of the paper). The Months is located in the middle. The Days of the Month is located right (left of the paper). The middle portion has the Days of the Week and the Years. The Days of the Week is located left (right of the paper). The Years is located right (left of the paper). Thousands’ Place is located right the Days of the Week. The 25 Hundreds’ Place is located right the Thousands’ Place. The Tens’ Place is located right the Hundreds’ Place. The Ones’ Place is located right the Tens’ Place. The bottom portion has the Days of the Week and the Leap Years. The Days of the Week is located left (right of the paper). The Leap Years is located right (left of the paper). The Leap Years Before a Centennial is located right 5 the Days of the Week. The Centennials is located right the Leap Years Before a Centennial. The Millenniums is located right the Centennials. The other tables are aligned to the Days of the Week. (E.g. The first row of the Days of the Week is aligned to the first row of the Months., …) The Days of the Week has two columns and seven rows. The first 10 column comprises of days (Saturday to Friday). The second column comprises of numbers (0 to 6). The days and numbers are arranged increasing and each corresponds to a row. Saturday is in row 1, Sunday is in row 2, Monday is in row 3, Tuesday is in row 4, Wednesday is in row 5, Thursday is in row 6, Friday is in row 7, 0 is in row 1, 1 is in row 2, 2 is in row 3, 3 is in row 4, 4 is 15 in row 5, 5 is in row 6 and 6 is in row 7. The Months has one column and seven rows. This table comprises of months (January to December). Each month has a value when evaluated that determines which row it is in. (January = 0 (row 1), February = 31 (row 4), March = 59 (row 4), April = 90 (row 7), May = 120 (row 2), June = 151 (row 20 5), July = 181 (row 7), August = 212 (row 3), September = 243 (row 6), October = 273 (row 1), November = 304 (row 4) and December = 334 (row 6).) Note: Mod 7 is used to determine which row a month (number) would be in. (E.g. January = 0, 0 mod 7 = 0 = row 1.) 25 The Days of the Month has five columns and seven rows. This table comprises of numbers (1 to 31). 1 is in row 2, 2 is in row 3, 3 is in row 4, 4 is in row 5, 6 is in row 7, 7 is in row 1, …, 30 is in row 3 and 31 is in row 4. Notes: 1 to 6 are in column 1, 7 to 13 are in column 2, 14 to 20 are in column 3, 21 to 27 are in column 4 and 28 to 31 are in column 5. Mod 7 is 5 used to determine which row a number would be in. (E.g. 1 mod 7 = 1 = row 2.) The Thousands’ Place has two columns and seven rows. This table has numbers (1000, 2000, …, 9000). 1000 is in row 7, 2000 is in row 6, 3000 is in row 5, 4000 is in row 4, 5000 is in row 3, 6000 is in row 2, 7000 is in row 1, 10 8000 is in row 7 and 9000 is in row 6. Notes: 1000 to 7000 are in column 1 and (8000 and 9000) are in column 2. Mod 7 is used to determine which row a number would be in. (E.g. 1000 mod 7 = 6 = row 7.) The Hundreds’ Place has two columns and seven rows. This table has 15 numbers (100, 200, …, 900). 100 is in row 3, 200 is in row 5, 300 is in row 7, 400 is in row 2, 500 is in row 4, 600 is in row 6, 700 is in row 1, 800 is in row 3 and 900 is in row 5. Notes: 100 to 700 are in column 1 and (800 and 900) are in column 2. Mod 7 is used to determine which row a number would be in. (E.g. 100 mod 7 20 = 2 = row 3.) The Tens’ Place has two columns and seven rows. This table has numbers (10, 20, …, 90). 10 is in row 4, 20 is in row 7, 30 is in row 3, 40 is in row 6, 50 is in row 2, 60 is in row 5, 70 is in row 1, 80 is in row 4 and 90 is in row 7. 25 Notes: 10 to 70 are in column 1 and (80 and 90) are in column 2. Mod 7 is used to determine which row a number would be in. (E.g. 10 mod 7 = 3 = row 4.) The Ones’ Place has two columns and seven rows. This table has numbers (1 to 9). 1 is in row 2, 2 is in row 3, 3 is in row 4, 4 is in row 5, 5 is in 5 row 6, 6 is in row 7, 7 is in row 1, 8 is in row 2 and 9 is in row 3. Notes: 1 to 6 are in column 1 and 7 to 9 are in column 2. Mod 7 is used to determine which row a number would be in. (E.g. 1 mod 7 = 1 = row 2.) The Leap Years Before a Centennial has four columns and seven rows. This table has numbers (4, 8, …, 96). 4 is in row 2, 8 is in row 3, 12 is in row 10 4, 16 is in row 5, 20 is in row 6, 24 is in row 7, 28 is in row 1, 32 is in row 2, …, 92 is in row 3 and 96 is in row 4. Notes: 4 to 24 are in column 1, 24 to 52 are in column 2, 56 to 80 are in column 3 and 84 to 96 are in column 4. Divide by 4 and mod 7 are used to determine which row a number would be in. (E.g. (4/4) mod 7 = 1 = row 2.) 15 The Centennials has two columns and seven rows. This table has numbers (100, 200, …, 900). 100 is in row 4, 200 is in row 7, 300 is in row 3, 400 is in row 7, 500 is in row 3, 600 is in row 6, 700 is in row 2, 800 is in row 6 and 900 is in row 2. Notes: 100, 200, 300, 600 and 700 are in column 1 and the rest (400, 20 500, 800 and 900) are in column 2. (In every 100 but not in every 400, no adding of one leap year), divide by 4 and mod 7 are used to determine which row a number would be in. (E.g. (100/4 – 1) mod 7 = 3 = row 4.) The Millenniums has two columns and seven rows. This table has numbers (1000, 2000, …, 9000). 1000 is in row 5, 2000 is in row 3, 25 3000 is in row 7, 4000 is in row 5, 5000 is in row 2, 6000 is in row 7, 7000 is in row 4, 8000 is in row 2 and 9000 is in row 6. Notes: 1000, 2000, 3000, 5000, 7000 and 9000 are in column 1 and the rest (4000, 6000 and 8000) are in column 2. (In every 100 but not in every 400, no adding of one leap year), divide by 4 and mod 7 are used to determine 5 which row a number would be in. (E.g. (1000/4 – 8) mod 7 = 4 = row 5, (2000/4 – 15) mod 7 = 2 = row 3, ...) 10 15 20 25 CLAIMS Having fully disclosed my utility model in accordance with the requirements of the statutes, my claims are (What I claim and desired to be protected by means of letters Patent in the Philippines are) 5 1. A perpetual calendar for indicating dates comprising of three portions: the top, the middle and the bottom; the top portion has the Days of the Week, the Months and the Days of the Months; the Days of the Week is located left (right of the paper); the Months is located in the middle; the Days of the Month is located right (left of the paper); the middle portion has the Days of the Week and the Years; the Days of the 10 Week is located left (right of the paper); the Years is located right (left of the paper); the Thousands’ Place is located right the Days of the Week; the Hundreds’ Place is located right the Thousands’ Place; the Tens’ Place is located right the Hundreds’ Place; the Ones’ Place is located right the Tens’ Place; the bottom portion has the Days of the Week and the Leap Years; the Days of the Week is located left (right of 15 the paper); the Leap Years is located right (left of the paper); the Leap Years Before a Centennial is located right the Days of the Week; the Centennials is located right the Leap Years Before a Centennial; the Millenniums is located right the Centennials; the other tables are aligned to the Days of the Week (E.g. The first row of the Days of the Week is aligned to the first row of the Months., …); the Days of the Week has two 20 columns and seven rows; the first column comprises of days (Saturday to Friday); the second column comprises of numbers (0 to 6); the days and numbers are arranged increasing and each corresponds to a row (for a reference to mod 7); the Months has one column and seven rows (this table comprises of months (January to December)) (each month has a value when evaluated that determines which row it is in) (mod 7 is 25 used after knowing the value of the months); the Days of the Month has five columns and seven rows (this table comprises of numbers (1 to 31) ) (mod 7 is used to determine which row a number would be in); the Thousands’ Place has two columns and seven rows (this table has numbers (1000, 2000, …, 9000)) (mod 7 is used to determine which row a number would be in); the Hundreds’ Place has two columns 5 and seven rows (this table has numbers (100, 200, …, 900) ) (mod 7 is used to determine which row a number would be in); the Tens’ Place has two columns and seven rows (this table has numbers (10, 20, …, 90) ) (mod 7 is used to determine which row a number would be in); the Ones’ Place has two columns and seven rows (this table has numbers (1 to 9)) (mod 7 is used to determine which row a number 10 would be in); the Leap Years Before a Centennial has four columns and seven rows (this table has numbers (4, 8, …, 96)) (divide by 4 and mod 7 are used to determine which row a number would be in); the Centennials has two columns and seven rows (this table has numbers (100, 200, …, 900) ) ((In every 100 years but not in every 400 years, no adding of one leap year), divide by 4 and mod 7 are used to determine which 15 row a number would be in); the Millenniums has two columns and seven rows (this table has numbers (1000, 2000, …, 9000)) ((In every 100 years but not in every 400 years, no adding of one leap year), divide by 4 and mod 7 are used to determine which row a number would be in). 2. The perpetual calendar as defined in claim 1 when modifications are made 20 to make other forms of this calendar such as the Days of the Month can be deleted (In the HOW TO USE THIS PERPETUAL CALENDAR? portion (step 1 and step 44rtion (step 1 and step 5n and get the remainder.), just add the day of the month, not knowing the value seen very left across.), Leap Years can be deleted but combined to the year (In doing this, the perpetual calendar may will very much look like other perpetual calendars.) and the Days of the Week 25 can be not repeated (In doing this, all the other tables must be aligned to the Days of the Week (still located left which is right of the paper).). 3. The perpetual calendar as defined in claim 1 when modifications are made to make a calendar for each year. 4. The perpetual calendar as defined in claim 1 when modifications are made 5 to make any perpetual calendar later than 9999 Anno Domini. 5. The perpetual calendar as defined in claim 1 when any improvements are made by making it having rotating parts, changing the general description, rearranging the tables (even making adjustments or modifications) and rearranging the contents (even making adjustments or modifications) of the tables using the 10 Fortunado’s algorithm (even varying some constants) are not allowed (improved or distributed) in any form or means without the permission of the maker. 15 Engr. Ismael Tabuñar Fortunado, ECE Maker 20 25 Days of the Week Months Days of the Month Saturday 0 January & October 7 14 21 28 Sunday 1 May 1 8 15 22 29 Monday 2 August 2 9 16 23 30 Tuesday 3 February, March & November 3 10 17 24 31 Wednesday 4 June 4 11 18 25 Thursday 5 September & December 5 12 19 26 Friday 6 April & July 6 13 20 27 Years Thousands’ Place Hundreds’ Place Tens’ Place Ones’ Place Saturday 0 7000 700 70 7 Sunday 1 6000 400 50 1 8 Monday 2 5000 100 800 30 2 9 Tuesday 3 4000 500 10 80 3 Wednesday 4 3000 200 900 60 4 Thursday 5 2000 9000 600 40 5 Friday 6 1000 8000 300 20 90 6 Leap Years Leap Years Before a Centennial Centennials Millenniums Saturday 0 28 56 84 Sunday 1 4 32 60 88 700 900 5000 8000 Monday 2 8 36 64 92 300 500 2000 Tuesday 3 12 40 68 96 100 7000 Wednesday 4 16 44 72 1000 4000 Thursday 5 20 48 76 600 800 9000 Friday 6 24 52 80 200 400 3000 6000 Perpetual Calendar For the Gregorian Calendar Engr. Ismael Tabuñar Fortunado, ECE Utility Model No. Maker 18