Created by Dr. Irv Bromberg, University of Toronto, Canada
[Click here to go back to the Symmetry454 / Kalendis home page]
Don’t be Anti-Symmetric!
The Gregorian calendar is deficient in the following ways:
A perpetual calendar reform is of prime importance, starting every year on the same weekday while conserving the traditional 7-day sabbatical cycle. The following recent precedents support conserving the sabbatical cycle as an absolute requirement:
"Minimal change" isn’t important for calendar reform. Although it’s possible to make the Gregorian calendar perpetual without correcting any other deficiencies, if any change is to be made then we may as well correct every deficiency, to obtain an optimal outcome and enjoy all the benefits.
The Symmetry010 or its sister Symmetry454 calendar reform will solve all of the Gregorian calendar deficiencies.
The Symmetry010 calendar is a simple perpetual solar calendar that fully conserves the traditional 7-day week (by using a leap week instead of a leap day), has symmetrical equal quarters each having 30+31+30 days, and starts every quarter on Monday. The Symmetry010 calendar arithmetic is openly documented, royalty-free.
The Symmetry010 calendar is a simple perpetual solar calendar that conserves the traditional 7-day week, has symmetrical equal quarters each having 30+31+30 days, and starts every quarter on Monday.
Holidays and special days, indicated with background yellow shading, are permanently fixed.
Hover over the day number to see the pop-up event description.
All Easter-related ecclesiastical calendar days are shown on the fixed dates that they would have if the proposed perpetually fixed Easter date of Sunday April 7th were adopted (based on the median astronomical Easter date, and the fact that Julian Sunday April 9, 30 AD was Symmetry010 Sunday April 7, 30 AD).
Provided that years always start on Monday, the Symmetry010 calendar shares the same epoch as the Gregorian calendar, starting on Monday, January 1, 1 AD. This was also the same epoch as that of the Symmetry454 calendar, the ISO calendar, and the Revised Julian calendar. The Symmetry010 year number before the epoch was year zero, to be consistent with the astronomical convention.
Non-leap (common) years have 52 weeks = 364 days. Leap years, which occur at intervals of 6 or 5 years, have a leap week appended to December, shown above as week 53 of the calendar year = 371 days.
The Symmetry010 calendar employs a superior symmetrical smoothly-spread leap rule that ensures excellent long-term astronomical accuracy:
The simple fixed arithmetic 52/293 leap rule has 52 leap years that are automatically and inherently symmetrically spread as smoothly as possible within each repeating cycle of 293 years:
It is a leap year only if the remainder of ( 52 × Year + 146 ) / 293 is less than 52
(If a leap year remainder is less than 33 then the next leap year will be 6 years later, otherwise 5 years later.)
With this simple single-step leap rule, leap year intervals occur in groups of either 6 + 6 + 5 = 17 years or 6 + 5 = 11 years,
which symmetrically group into sub-cycles of 17 + 11 + 17 = 45 years or sub-cycles of 17 + 17 + 11 + 17 + 17 = 79 years.
In each full calendar cycle these sub-cycles inherently occur symmetrically in the sequence 45 + 79 + 45 + 79 + 45 = 293 years.
With 52 leap weeks in the cycle, and 52 weeks in a regular year, the fixed cycle length equals exactly 294 regular years, and the average interval between leap weeks is exactly 294 weeks.
The Symmetry010 calendar mean year ≡ 365+71/293 days ≡ 365 days 5 hours 48 minutes 56+152/293 seconds. This is intentionally slightly shorter than the present era mean northward equinoctial year of about 365 days 5 hours 49 minutes 0 seconds, ensuring essentially drift-free performance for more than 4 future millennia.
Due to the symmetrical arrangement of leap years, the timing of the mean northward equinox moment always falls at the cycle average in the first year of every 293-year cycle. This feature simplifies astronomical performance evaluations. Click here for more information about symmetrical leap cycles.
Using this leap cycle as described, in the present era the mean northward equinox lands near midnight at the start of Symmetry010 date March 19th (reference meridian at Jerusalem, Israel).
The "Solar Calendar Leap Rules" web page at <http://individual.utoronto.ca/kalendis/leap/> explains why the 52/293 leap rule is preferred and compares it with a wide range of alternative leap rules.
Within the original 140-character limit of Twitter.com, the following "Tweet" defines the rules of the Symmetry010 calendar:
Common year 52 weeks = 30+31+30 days/quarter; append 7 days if remainder of (52×Year+146)/293 < 52; quarters start Monday; epoch Jan 1, 1 AD
nullor leap days outside of the traditional 7-day weekly cycle.
Friday the 13thnever happens.
The following documentation is in Adobe Acrobat Portable Document Format (PDF).
All Symmetry010 and Symmetry454 calendar layouts show the calendar for this year and every year, because every year is the same!
Click here to access quick reference manual date conversion sheets.
Come back for updates -- check the version numbers and revision dates, as well as the web site news.
|Short File Name and PDF Size||Description (see also the Kalendis freeware program)|
|Symmetry010 Summary 426 KB||The Symmetry010 calendar has a nearly uniform 30+31+30 days per quarter structure.
Introduction to the Symmetry010 Calendar — the Executive Summary:
|Symmetry454 Summary 428 KB||For those interested in a slightly "more radical" calendar design with significant further benefits, the Symmetry454 calendar has a 4+5+4 weeks per quarter structure.
Introduction to the Symmetry454 Calendar — the Executive Summary:
|010 Quarter Layout 137 KB||A calendar design depicting the year as a single repeating quarter, shown in portrait and landscape layouts, which could be manufactured as attractive flip calendars.|
|010 Wide Layout 163 KB||A calendar design stretching each month into a single row across a "legal" size page in landscape layout, with and without ordinal week and day numbers. These layouts are handy for planning projects and monthly meetings. (Conceptual design by Marc Elliott.)|
|FAQs 1 MB||Frequently Asked Questions (FAQs) about the Symmetry454 and Symmetry010 calendars.|
|Holidays & Events 577 KB||Explains how Symmetry010 and Symmetry454 permanently fix birthdays, anniversaries, memorials, holidays, annual events, etc.|
|Compare 152 KB||A single-page table comparing some properties of the Symmetry010 and Gregorian calendars.|
|Basic Arithmetic 898 KB||Basic Symmetry454 and Symmetry010 Calendar Arithmetic:
This document is for those who want to know how to implement these calendars in computer systems, how to do calendar calculations, how to test for leap years, or how to interconvert dates from and to other calendars.
|Convert by Hand 61 KB||Simple instructions for hand-converting any year 1900 to 2099 Gregorian date to Symmetry010, according to the policy that the ISO standard leap rule shall always be used for such conversions because it perpetually maintains a standard relationship to the Gregorian Calendar. (Concept and initial development by Shriramana Sharma of India.)|
|References 43 KB||Literature and internet references cited by the above documents.|
|What is Irvember?||A brief and hopefully amusing history of the Leap Week name.|
Designs for a new year, in the
Innovatorssection of the Toronto Star newspaper, Friday, December 24, 2004, page A3, by reporter Peter Gorrie.
Star Trek Math Inspires Calendar Reform, Discovery Channel, Thursday, December 30, 2004, by Jennifer Viegas, Discovery News.
Time and Again, the Calendar Comes Up Short: Sticklers for Symmetry Lament Imperfections in the 400-Year-Old Gregorian System; Earth’s Inconvenient Orbit, The Wall Street Journal, December 31, 2009, by Charles Forelle, The Numbers Guy.
This page updated May 5, 2020 (Symmetry454) = May 3, 2020 (Symmetry010) = May 1, 2020 (Gregorian)