Some of the items are taken from my old web page (2002), University of Zimbabwe in Harare.
You can downoad an Excel file with different variants for 2022!
Minimized Perpetual Julian and Gregorian calendar with visual instrctions and an example for October 2019.
Check that K!=FR for January in the leap year 2024 and that the first row in the middle part is valid - Year 2024 starts on Monday!
It is convenient to mark the row for the current month by a paper clip on a printed calendar.
Year 2020 is somehow "special". There is no need to remember K! since the year in the centry is in the same column as the full century new style and you can use directy the rows containing the months! (Such years are also 1964, 1970, 1981, 1987, 1992, 2009, 2015, 2026, 2037, 2043, 2048, etc.)
This is a modified extended version of a calendar by Leonardo Diez
for 2021 and better looking variant
of my paper for the ZIMaths
magazine with easy explanations (original
paper) (HTML format)
UNIVERSAL CALENDAR Valentin Hristov (Bulgaria) E-mail: email@example.com http://www.math.bas.bg/complan/valhrist/index.htm +-----------------------------+ | YEAR IN CENTURY | Initial transition +-----------------------------+ OLD STYLE -> NEW STYLE | 00? 01 02 03 04* 05 | Oct 4, 1582 -> Oct 15, 1582 | 06 07 08* 09 10 11 | (Thursday) -> (Friday) | 12* 13 14 15 16* | | 17 18 19 20* 21 22 | In Bulgaria 1. Intersect | 23 24* 25 26 27 | OLD STYLE -> NEW STYLE YEAR IN | 28* 29 30 31 32* 33 | Mar 31, 1916 -> Apr 14, 1916 CENTURY | 34 35 36* 37 38 39 | (Thursday) -> (Friday) and MONTH ! | 40* 41 42 43 44* | | 45 46 47 48* 49 50 | Remember K! | 51 52* 53 54 55 | 2. In the row with the FULL (Key day!) | 56* 57 58 59 60* 61 | CENTURY find the COLUMN | 68* 69 70 71 72* | with the Key day K! | 73 74 75 76* 77 78 | | 79 80* 81 82 83 +---------------- ---------------+ | 84* 85 86 87 88* 89 | FULL CENTURY | +-------------+ 90 91 92* 93 94 95 +---------------+----------------+ | MONTH | 96* 97 98 99 | OLD STYLE | NEW STYLE | +-------------+-----------------------------+---------------+----------------+ | Jun | Mon Tue Wed Thu Fri SAT|SUN|| 1 8 15 22 29 | | | Dec Sep | Tue Wed Thu Fri SAT|SUN|Mon | 2 9 16 23 30 | 18 22 26 30 | | Jul Apr JA* | Wed Thu Fri SAT|SUN|Mon Tue | 3 10 17 24 31 | | | Oct Jan | Thu Fri SAT|SUN|Mon Tue Wed | 4 11 18 25 | 15 19 23 27 31 | | May | Fri SAT|SUN|Mon Tue Wed Thu | 5 12 19 26+---+ 16*20*24*28*32*| | Aug FE* | SAT|SUN|Mon Tue Wed Thu Fri | 6 13 20 27|All| | | Nov Mar Feb ||SUN|Mon Tue Wed Thu Fri SAT | 7 14 21 28| * | 17 21 25 29 33 | +-------------+-----------------------------+-----------+---+----------------+ | DAY OF WEEK | DATE IN MONTH | +-----------------------------+---------------+ 3. Use the remembered COLUMN with the DAYS OF WEEK and the DATES IN MONTH to have a MONTH CALENDAR !!! D E T A I L E D I N S T R U C T I O N All steps use the central rectangle with the names of the days of the week. 1. Intersect the horizontal row containing the month (left) and the vertical column containing the year in the century (above) to find the key day K! Remember K! just as a symbol to used in Step 2. (Be careful if the month is January or February. For leap years use JA* and FE*. See the Note: below.) 2. Find the full centuries (right) in one of the rectangles in accordance with the style - OLD (JULIAN) or NEW (GREGORIAN). In the horizontal row with the centuries find the key day K! from Step 1. Remember the column (in the central rectangle) which contains K! for Step 3. 3. The rectangle, used in Step 2 for old style centuries, is now used for the dates in the month. Together with the column remembered in Step 2 it gives the month calendar, so, to find the day of the week, intersect the horizontal row with the date in the month and the remembered column. Note: LEAP YEARS (denoted by *) in the old as well in the new style are those, which can be divided by 4 without remainder. EXCEPTIONS exist only in the NEW STYLE: EXACT CENTURIES (years ending 00), which cannot be devided by 400 without remainder, are NOT LEAP.
A compact variant of the above calendar.
1. Remember the letter (A to G) to the left of the month. Find it in the row with the year in the century. Remember the column! (Presented are only the years from 00 to 27, but you can add 28, 56, or 84, to have any of the other years from 28 to 99.)
2. The remembered column contains the days of week and together with the dates (right down) they give directly the month calendar for years between 2000 and 2099.
3. For other full centuries use left down part for Gregorian style or right down part for Julian style. A Key day K! is at the intersection of the remembered column with the boxed row (with 16,20,24,28,32 on the left).
In the row with the full century (old or new style) the Key day K! determines the desired column with days of week for the month calendar.
The same compact perpetual calendar with graphical instructions
An "exotic" minimized variant of the previous calendar (PDF). It is more complicated in use since at one place are gathered the dates in the month, the years in the century, and the full centuries old style. This forces using colors and more steps which are not so obvious. Therefore, if you need some help with the graphically presented algorithm, please, contact me via the above e-mail addresses.
I made this calendar after I accidentally spotted a similar calendar at Al Stanger's page and I decided to improve it with the possibility a whole month calendar to be seen at once instead of finding the day of week for a single date only.
caltex.zip (Plain TEX
format) - unzip in a separate directory. You can run two .bat files
and view other two .dvi files.
Other calendar variants and experiments (in bulk - zip) (DOS, Excel, Basic)
There are many web pages related to calendars, but I decided to give here only one link as a suitable starting point for calendars:
All possible year
tables on one folded sheet for your pocket (PDF-A4 variant as
fold). The week in it starts on Monday and each row contains 3
months. There is also a PDF-Letter
variant. The Excel
source contains all four variants without PocketMod on one sheet - 1)
the week could start on Sunday or Monday and 2) the rows could have 3
or 4 months. If you want to make a PocketMod booklet, you have to
prepare first a pre-PocketMod worksheet with 8 pages as the second
worksheet in the .xls file. Then use printing with some kind of PDF
creator to have a file like this
one. The final step is to use the PDF to PocketMod convertor to
produce only one A4 or Letter format sheet for cutting and folding.
(Note that to be able to run "PDFtoPocketMod.exe" you
need to download Microsoft
Net Framework !!!)
Using "division by 5.6" with a calculator:
Here some modifications of Al Stanger's algorithms for finding the DayOfWeek are presented. You can search on the archive of a Calendar Mailing List (search "Al Stanger"). The algorithms use only the first two decimal digits of "division by 5.6".
My favorite files for downloading: DAY ( DDAYYYY/5.6, see some explanations and an easy way to memorize the key values), also a variant as DAY-Box for pens.
Simplified 4-years calendar table - (Excel
variants - card size + 1912-2083 calendars)
The idea from the above table is used for a suitably minimized variant of a perpetual calendar - (Excel variants - card size + full pages)
A combination of four years calendars for 2012-2039 plus compact 1916-2083 calendar ( PDF variant for printing and Excel variant for editing)
(December 2017) Unusual diagonal construction of a calendar (Excel variants)
You can subscribe to the Sundial
Mailig List or at least to visit its archive
Quadrant sundial (PostScript format) Find new variants (2017) for DeltaCad at the bottom of the page!!!
Analemma - Equation of Time vs. Declination of the Sun (PostScript format) - renewed version of my old file with average data for 2000-2047 (due to Gianni Ferrari).
(2009) You can print this data as month tables and also as approximation formulae in PocketMod variant (explaned in the calendar section above) in two formats: A4 and Letter.
The files to the end of this section are written as macro files for DeltaCad (CAD extension of BASIC). You have to download the program from www.deltacad.com. There is a DEMO version on it.
One of the active members of the Sundial Mailing List - Carl Sabanski - put in November 2007 on his web site a few pages with existing DeltaCad macro files related to sundials written by different people and, in particular, MY MACRO FILES from this page. You will find screen shots, instructions, comments and other useful information on these pages and therefore I highly recommend visiting them !!! I am very grateful to Carl for our fruitful joint work and for popularizing DeltaCad as a suitable drawing tool for sundials !!! (Below "CS" indicates links to pages on Carl Sabanski's site.)
Spider Polar Sundial (details CS). My friends Todor and Daniela helped me to convert this macro to a real dial. A better view of the dial face is included in this zip file.
Spider Sundial with perpendicular gnomon (details CS). In particular it can be Azimuthal Dial (if the plane is horizontal).
Spider Sundial with arbitrary plane and arbitrary gnomon - shows local, civil and daylite savings time. Contains also the previous two types as options. (details CS)
Spider Polar Square Sundial (details CS)
Foster-Lambert Sundial (details CS)
Box Folding Sundials
Some of my Box Sundials can be downloaded also from the DeltaCad web page of The North American Sundial Society.
Polar Box Sundial (details CS)
Box Sundial with arbitrary orientation (read some instructions) (details CS)
Polar Nodus Box Sundial - you have to print two dials (one for 21Dec-21Jun and another for 21Jun-21Dec) (details CS)
Polar Box Sundial with gnomon - based on the previous dial, but the gnomon allows to use it during the whole year (one of the ends is used as nodus for 21Dec-21Jun and the other for 21Jun-21Dec, i.e. the analemma is splitted) (details CS)
In this picture the time is approximately 14:30 Daylight Savings Time (DST) on 8 May in the upper part. In the lower part you can see that the position of the sun will be the same at approximately 14:40 DST on 5 August.
The size of the box is 66 x 81 x 16 mm when printed landscape on A4 paper. After folding it becomes a rectangle with dimensions only 33 x 81 mm.
Horizontal Box Altitude Sundial which uses the height (altitude, elevation) of the Sun to show the time (details CS)
Modification of the Horizontal Box Altitude Sundial (January 2008) which shows only one month for better reading (details CS)
(February 2009) Double Box Altitude Sundial Another modification of the Horizontal Box Altitude Sundial (January 2008) with the edge of the middle wall between two adjacent boxes as a gnomon.
(2012) The same sundial was modified by Fabio Savian and was included in his sundialatlas.net - Gnomolab - Paper sundials - App 8 (use the slider).
Wee-Meng Lee from Singapore pointed out to an existing origami box construction which is applicable also to my box sundials. He also put on his page some of my sundials.
In the end of 2006 I made a DeltaCad macro with improvement of a design made by Wee-Meng Lee of a
Universal Ring Dial (details CS)
Now the hour scale can be adjusted for the Longitude and the Equation of Time.
Polar Cross Sundial (test variant - April 2007) (details CS)
Sundial with Parallel Gnomon and arbitrary position (test variant - May 2007) (details CS)
Classical Bifilar Sundial with two perpendicular gnomons parallel to the dial plate and with arbitrary position (test variant - December 2007) (details CS)
Bifilar Sundial WITH ARBITRARY STRAIGHT GNOMONS AND DIAL PLANE (test variant - December 2007) (details CS). THIS IS MY NEW YEAR PRESENT TO THE SUNDIAL COMMUNITY !!!
Cylinder Sundial (Type 1) with arbitrary position. A beam of light through a hole at its surface gives the time inside the cylinder (January 2008) (details CS)
Cylinder Sundial (Type 2) with arbitrary position. A beam of light through a concentric hole or a nodus point at its base gives the time. It can be read from inside the cylinder or from outside (if the cylinder is transparent). (September 2008) (details CS)
(2009) Flag Combo: Sun Compass and Sundial Allows to find first the North-South direction and then to read the Local Time. Longitude and EoT corrections are printed on it. You can download directly a PDF file with instructions.
(2009) Polar Half-Cylinder The Light-Shadow boundary indicates the Civil Time and DST.
(June 2009) Sun Position - Represents hour and date lines vs. the azimuth and the height of the sun.
(August 2009) Star and Sun Clock for the Northern Hemisphere - An essential extension of my Star Clock (below) with the pozition of the sun among the stars (the ecliptic).
(August 2009) StarSun.zip contains the previous "Star and Sun Clock" and also a file StarSunZ.bas with added drawings of the zodiacal constellations ("Z" for Zodiac). The drawing resembles an astrolabe with "overhead" view which is a standard for the star maps. Unzip all files in one directory. Read the instruction for use and printing in the beginning of the file.
(September 2009) Sundial correction is a modification a Fer de Vries' macro. It shows the total correction, i.e. the Equation of Time + the Longitude correction in both Civil and Daylight Savings Time.
(October 2017) Quadrant
sundial for the whole year. See a picture.
(October 2017) Quadrant sundial for any separate month. The reading of the time is much more easier and accurate! (picture)
Cylindrical Perpetual Calendar
with Moon Phases (download this
zip file with instructions and see a picture.)
Moon Phases Calendar (nomograph) (See the variant as a picture)
Star Clock for the Northern Hemisphere