THE  RAINBOW  CALENDAR

 

SECTION 0 - INTRODUCTION.

RAINBOW INDEX

 

What abstraction stands nearer to reality than colour?

 

I like to work with colours for various reasons.

Like many before me I have come with the idea to compare the week with a rainbow.

It allows me to colour each weekday, but I am aware that colouring somehow implies numbering.

The numbering that I use places the center-of-gravity at thursday, day 4 as it is called in Chinese.

The ISO-Standard focusses on thursdays to determine to which year a given week belongs.

Examining the occurence of week number 53 I have "discovered" 2 series of dates:

1.  8 dates that retain allways the same weeknumber , the Particular Dates :

    4/1(=week 1);11/1(=week 2);18/1(=week 3);25/1(=week 4);1/2(=week 5);8/2(=week 6);15/2(=week 7);22/2(=week 8).

2. 44 dates that nearly allways retain the same weeknumber, the Departure dates.

    1/3(=week 9);8/3(=week 10);.........................................;20/12(=week 51);27/12(=week 52);

    Exception:  when 29/2=sunday then: mondays 1/3(=week 10);8/3(=week 11);..........;27/12(=week 53). 

0.b CALENDAR. INDEX

 

From day to day I make use of a short (!) range perpetual calendar that is memory-based.

Anyone could master this, so take notice!

 

Usually we know the date of a birthday and every year we struggle to find out the day-of-the-week.

How to reverse that?

 

Step 1.

Learn all departure dates (mentioned above) as if it were birthdays.

 

Step 2.

For the purpose of short term I give you to learn several years.

Their special weekday fits to the departure dates in that year.

So: 2000-WE(wednesday) ; 2001-TH; 2002-FR; 2003-SA.

For example : departure date 8/3 is TH in 2001, but WE in 2000 and SA in 2003.

 

Step 3.

Any date can be reached from the departure dates.

In order to reach January/February some knowledge of leap-years is needed.

See for more in the index below.

 

R.A. van Putten,

Rotterdam,

15/08/2001.

 

 

0.c I N D E X 

In the first 2 sections  the notion of leap-years is avoided.

That's the reason why the months of January, February  and the year "00" are left out.  

Section 3 will fill out this gap; see  this index:

Please Click on the subject requested

SECTION:

SUBJECT:

SECTION 0 - INTRODUCTION.  
  0.a RAINBOW.
  0.b CALENDAR.
  0.c INDEX
SECTION 1 - COLOUR AND WEEKPOSITION.  
  1.a  Central sunday.
  1.b Any chosen central day.
SECTION 2 - THE TRANSLATION INTO COLOUR.  
  2.a The colour of day.
  2.b The colour of month
  2.c The colour of century.
  2.d The colour of year.
  2.e The colour of year calculated directly.
  2.f The colour of year from tables.
SECTION 3 - WITH LEAP-YEAR.  
  3.a Example year 56.
  3.b Leap-years in table of years.
  3.c Example year = 60 (a leap-year).
  3.d What are leap-years?
  3.e The colours of Jan and Feb?
  3.f The year "00".
  3.g The advantage of transparency.
  3.h Calendar 1999-2004.
  3.i Extended table of centuries.
SECTION 4 - RAINBOW PAGES.
4.a Looking for order.
4.b Clickcalendar.
4.c Rainbow old page.

SECTION 1 - COLOUR AND WEEKPOSITION.

1.a Central sunday. INDEX

 

 The central sunday ( violet ) determines the position.
DAY WEEKPOSITION about  0. Date
SU 7 14/06/2009
SA 6 13/06/2009
FR 5 12/06/2009
TH 4 11/06/2009
WE 3 10/06/2009
TU 2 09/06/2009
MO 1 08/06/2009
SU 0 07/06/2009
SA -1 06/06/2009
FR -2 05/06/2009
TH -3 04/06/2009
WE -4 03/06/2009
TU -5 02/06/2009
MO -6 01/06/2009
SU -7 31/05/2009

 

The calculations for a weekday with respect to the central sunday are:

MO

= +1 or -6

TU

=+2 or -5

WE

=+3 or -4

TH

= +4 or -3

FR

= +5 or -2

SA

=+6 or -1

SU

=0,+7 or -7.

The rainbowcalendar uses colours to illustrate those calculations.

RED

= +1 or -6

ORANGE

= +2 or -5

YELLOW

= +3 or -4

GREEN

= +4 or -3

BLUE

= +5 or -2

INDIGO

= +6 or -1

VIOLET

= 0,+7 or -7.

The violet colour shows clearly that the day of the week does not change by adding or subtracting 7

 ( going forward or backward by weeks). 

 

1.b Any chosen central day. INDEX

Example with "central day " 11/6/2009 (green).

DAY WEEKPOSITION

about 0.

 

COLOUR =

POSITION relative

with respect to 4.

Date
SU 7 SU= +3. 14/06/2009
SA 6 SA= +2. 13/06/2009
FR 5 FR= +1. 12/06/2009
TH 4 TH=   0. 11/06/2009
WE 3 WE=  -1 10/06/2009
TU 2 TU=   -2 09/06/2009
MO 1 MO=  -3 08/06/2009
SU 0 SU=  -4 07/06/2009
SA -1 SA=  -5 06/06/2009
FR -2 FR=  -6. 05/06/2009
TH -3 TH=  -7. 04/06/2009
WE -4   03/06/2009
TU -5   02/06/2009
MO -6   01/06/2009
SU -7   31/05/2009

The relative positions (colours) for each weekday with respect to central day ( TH in this example) :

FR=

= +1 of -6

SA=

= +2 of -5

SU=

= +3 of -4

MO=

=  -3

TU=

=  -2

WE=

=  -1

TH=

= 0 of -7.

 

Central day is TH.

Weekposition of a TH (=4) +Colour (every weekday with respect to TH) = Weekposition every weekday:

(TH=4);

FR=(4)+1=5.

(TH=4);

SA= (4)+2 =6.

(TH=4);

SU= (4)+3 =7.

(TH=4);

MO= (4)-3 =1.

(TH=4);

TU= (4) -2 =2.

(TH=4);

WE= (4)-1 =3

(TH=4);

TH= (4)+0 =4.

FR

 12/6/2009

SA

 13/9/2009

SU

 14/06/2009

MO

 08/06/2009

TU

 09/06/2009

WE

 10/06/2009

TH

 11/06/2009

Een Colour by itself can be broken down again into several separate colours.

For example green:

Green= red+red +red +red= red +yellow= orange +orange= red +red +orange, etc.

In this way the weekposition can broken down into 4 colours ( provided that central day =central sunday).

In that case the day-of-the-week is expressable by 4 colours with respect to the central sunday. 

The Rainbow Calendar works with DAY-, MONTH-, CENTURY-, and YEAR-colour.

The combined sum of these colours is the appropiate colour of the day-of-the-week. 

 

SECTION 2 - THE TRANSLATION INTO COLOUR.

2.a The colour of day. INDEX

Examples:

07/06/2009 ( Central Sunday  ).
DAY 0
MONTH 0
CENTURY 0
YEAR 0
SUM 0=SU

 

11/06/2009.
DAY 4
MONTH 0
CENTURY 0
YEAR 0
SUM 4=TH

A difference of a number of complete weeks does not count: 25-14=11.

25/06/2009.
DAY 4
MONTH 0
CENTURY 0
YEAR 0
SUM 4=TH

In general:

The days of June 2009.
DAY 7 14 21 28   30 days; 

7 colours

6 13 20 27  
5 12 19 26  
4 11 18 25  
3 10 17 24  
2 9 16 23 30
1 8 15 22 29
MONTH 0
CENTURY 0
YEAR 0
SUM COLOUR=DAY

 

2.b The colour of month. INDEX

 

Every month brings in its own colour:

In General.
DAY 0
MONTH MARCH 6 10 months; 

7 colours

 

APRIL 2
MAY 4
JUNE 7
JULY 2
AUGUST 5
SEPTEMBER 1
OCTOBER 3
NOVEMBER 6
DECEMBER 1
CENTURY 0
YEAR 0
SUM COLOUR=MONTH 

 

24/07/2009.
DAY 3(24)
MONTH 2 (JULY)
CENTURY 0(20..)
YEAR 0(09)
SUM 5=FR

In general:

The days of van July 2009.
DAY 7 14 21 28   31 days; 

7 colours

6 13 20 27  
5 12 19 26  
4 11 18 25  
3 10 17 24 31
2 9 16 23 30
1 8 15 22 29
MONTH 2
CENTURY 0(20..)
YEAR 0(09)
SUM =2+DAY

 

2.c The colour of century. INDEX

It's important by what numbers the century begins.

The 21-st century  begins with "20".

In general.
DAY 0
MONTH 0
CENTURY 16.., 20.., 24.. 12 centuries; 

4 colours.

 

 
17.., 21.., 25..
 
18.., 22.., 26..
 
19.., 23.., 27..
YEAR 0
SUM COLOUR=CENTURY 

 

24/07/1809.
DAY 3(24)
MONTH 2 (JULY)
CENTURY 3(18..)
YEAR 0(09)
SUM 1=MO

 

2.d The colour of year. INDEX

It's important by what numbers the year ends; colour of year is based on the last 2 numbers of a given year.

In this table only the first 9 years are given.

The remaining years will be dealt with separately.

DAY 0
MONTH 0
CENTURY 0
YEAR - 09 9 out of 99 years; 

7 colours.

 

03 08
02 -
01 07
  06
  05
  04
SUM COLOUR=YEAR

 

24/07/1807.
DAY 3(24)
MONTH 2 (JULY)
CENTURY 3(18..)
YEAR 4(07)
SUM 5=FR 

 

As follows from this last example the Rainbow Calendar is been seen in action with 4 colours.

Now there remains still an extension of colour of year for each year....

2.e The colour of year calculated directly. INDEX

Example year = 57  

#0#  SUBTRACT AS MANY TIMES AS POSSIBLE 28.

57 -28(1 time 28)  =29.

#1#  DIVIDE BY 4 AND ADD THIS DIVISION TRUNCATED.

29 + 7 (29/4 truncated)  = 36.

#2# CANCELLED  (  depends on leap-year yes/no ).

Not applicable in this section.

#3# ADD 3.

36 + 3 = 39.

#4# SUBTRACT AS MANY TIMES AS POSSIBLE 7.

39 - 35 (5 times 7) = 4 (=GREEN).

#5# RESULT :  (YEARCOLOUR=GREEN=)4.

 

2.e The colour of year from tables. INDEX

 

The yearcolour is calculated as the sum of: (X + Y).

Yeartable based on repeating 28 years.

X 1 2 3 Y
  12;40;68;96 24;52;80   3
      2
  11;39;67;95 23;51;79   1
  10;38;66;94 22;50;78   7
  09;37;65;93 21;49;77   6
  08;36;64;92 20;48;76   5
        4
  07;35;63;91 19;47;75   3
  06;34;62;90 18;46;74   2
  05;33;61;89 17;45;73   1
X 1 2 3 0
  04;32;60;88 16;44;72 28;56;84 7
        6
  03;31;59;87 15;43;71;99 27;55;83 5
  02;30;58;86 14;42;70;98 26;54;82 4
  01;29;57;85 13;41;69;97 25;53;81 3
    12;40;68;96 24;52;80 2
      8
  11;39;67;95 23;51;79 0

X

1 2 3 Y

 

The yearcolour can also be found in the complete  YEARTABLE.

The yearcolour is calculated as the sum of: (X + Y).

X

1 2 3 4 5 6

Y

7 8

9

  12 24 36 48 60 72

3

84 96
            2    
  11 23 35 47 59 71 1 83 95  
  10 22 34 46 58 70 7 82 94  
  9 21 33 45 57 69 6 81 93  
  8 20 32 44 56 68 5 80 92  
              4      
  7 19 31 43 55 67 3 79 91  
  6 18 30 42 54 66 2 78 90  
  5 17 29 41 53 65 1 77 89  
X 1 2 3 4 5 6

0

7 8 9
  4 16 28 40 52 64 7 76 88
              6      
  3 15 27 39 51 63 5 75 87 99
  2 14 26 38 50 62 4 74 86 98
  1 13 25 37 49 61 3 73 85 97
    12 24 36 48 60 2 72 84 96
            8      
  11 23 35 47 59 0 71 83 95

X

1 2 3 4 5 6 Y 7 8 9

The yearcolour is calculated as the sum of: (X + Y).

Example:

Year 1957 ends with "57" .
(X=)5 + (Y=)6  =  11 (=green); yearcolour=green=4.

 

SECTION 3 - WITH LEAP-YEAR.

 

3.a Example year 56. INDEX

It's important by what numbers the year ends; colour of year is based on the last 2 numbers.

In general the years follow each other in the way as days-of-the-week.

A leap-year though is being divided into 2 parts; for example year 56.

Part 1 contains the months of January and February which receive yearcolour orange that follows red of year 55.

 

Part  2 contains the months of March to December; because of 29/2 the yearcolour has shifted to yelllow.

Januari until December year 57 

regular

March until December  year 56

 (part 2, official yearcolour)

Januari until Februari  year 56 

(part 1, without numbers in yeartable but with "id.J/F")

Januari  until December  year 55

regular

 

 

3.b Leap-years in table of years. INDEX

 

Rows of Leap-years indicated in the X-axis by an " L" ( exceptions: year "00" and "100" ).

Jan./Feb. of leap-year in box straight above is marked by "id.J/F". 

X

1 2 3 4 5 6

Y

7 8

9

L

12

24

36 48 60 72

3

84 96 L
L id. J/F id.J/F id.J/F id.J/F id.J/F id.J/F 2 id.J/F id.J/F L
  11 23 35 47 59 71 1 83 95  
  10 22 34 46 58 70 7 82 94  
  9 21 33 45 57 69 6 81 93  
L 8 20 32 44 56 68 5 80 92 L
L id.J/F id.J/F id.J/F id.J/F id.J/F id.J/F 4 id.J/F id.J/F L
  7 19 31 43 55 67 3 79 91  
  6 18 30 42 54 66 2 78 90  
  5 17 29 41 53 65 1 77 89  
X 1 2 3 4 5 6

0

7 8 9
L 4 16 28 40 52 64 7 76 88
L id.J/F id.J/F id.J/F id.J/F id.J/F id.J/F 6 id.J/F id.J/F L??
  3 15 27 39 51 63 5 75 87 99
  2 14 26 38 50 62 4 74 86 98
  1 13 25 37 49 61 3 73 85 97
L 0 L?? 12 24 36 48 60 2 72 84 96
L L?? id.J/F id.J/F id.J/F id.J/F id.J/F 8 id.J/F id.J/F id.J/F
  11 23 35 47 59 0 71 83 95

X

1 2 3 4 5 6 Y 7 8 9

 

3.c  Example year = 60 (a leap-year). INDEX

 

#0#  SUBTRACT AS MANY TIMES AS POSSIBLE 28.

60 -56(2 times 28)  =4.

#1#  DIVIDE BY 4 AND ADD THIS DIVISION TRUNCATED.

4 + 1 (4/4 truncated)  = 5.

#2# EXAMINE IF WE HAVE GOT TO DO WITH JANUARY OR FEBRUARY OF A LEAP-YEAR.

IF THE ANSWER IS YES THAN WE SUBTRACT 1.

YES: Part 1 of year jaar 60 (January until February): 5 -1 = 4.

NO:  Part 2 of year 60 (March until December): 5.

#3# ADD 3.

36 + 3 = 39.

Part 1 of year jaar 60 (January until February): 4 + 3 = 7.

Part 2 of year 60 (March until December): 5 +3 =8.

 

#4# SUBTRACT AS MANY TIMES AS POSSIBLE 7.

39 - 35 (5 times 7) = 4 (=GREEN).

Part 1 of year jaar 60 (January until February): 7 - 7= 0.

Part 2 of year 60 (March until December): 8 -7= 1.

 

#5# RESULT :  (YEARCOLOUR=GREEN=)4.

Part 1 of year jaar 60 (January until February): (violet=)0.

Part 2 of year 60 (March until December): (red =)1.

 

3.d  What are leap-years? INDEX

In the Gregorian Calender:

Years non-zero, multiple of 4, like: 4,8,12,16,.....,96.
Years ending with "00" but beginning with: 16, 20, 24, etc.:

 1600, 2000, 2400, 2800,..  .

In the  Julian Calender:
The year 4 AD.
Years that are positive multiples of 4 like:

 8,12,16,.....,96,100,104,....until 1580. 
The years  BC  (Before Christ):

  1 BC, 5 BC, 9 BC, 13 BC, 17 BC,....., 97 BC, 101 BC, 105 BC,....,1581 BC. 

 

3.e The colours of Jan and Feb? INDEX

Seemingly there is added the leap-colour  indigo.

By each leap-year this will be shown because in part 1 locally the yearcolour is 1 dayposition behind at the official yearcolour of part 2 ( see above).

Example with (day,year and century) =0.

Regular or leap-year.

DAY 0
regular:

MONTH

and YEAR.

 

JANUARY 3 2 more months; 

2 colours

 

FEBRUARY 6
leap-year:

MONTH

and YEAR.

JANUARY 2

 

after adding

indigo.

 

FEBRUARY 5
CENTURY 0
YEAR 0
SUM COLOUR=MONTH AND YEAR.

 

3.f  The year "00". INDEX

The year "00"  turns out not allways to be a leap-year.

In the Gregorian Calender only years ending with "00" but beginning with: 16, 20, 24, etc.:

are leapyears ( so: 1600, 2000, 2400, 2800,.. ) .

This is especially important for part 1, namely to determinate the leap-yearcolour of Jan./Feb. 

That colour being red can be deducted from yearcolour 99 violet, provided we consider the right century.

At least part 2 of the year "00" is yellow as shown in the yeartable ( see "00").

This because the official yearcolours ( part 2) are incorporated in the table.

 

3.g The advantage of transparency. INDEX

We have already noticed that a lot of days can be brought down to one shift within a week after leaving out complete weeks.

The data of Day, Month, Century and Year which are each separately converted into colour may turn out to be transparent.

That could eliminate a separate calculation.

Examples.

a). Transparent centuries.

The 21st century has got the transparent centurycolour.

That's why the year  2057 is green like the yearcolour of  57.

The year 1957 is blue, because centurycolour red ( ..19) is added to the green of 57.

Only the years of the 21 st century retain the yearcolours  .

 

b). Departure dates

Those dates conform to the colour of year and century combined.

In leapyears that (official) colour is only valid for part 2.

In order to find the colour of Jan./Feb. of a leap-year we add indigo.

Departure dates.

(Day + month) = 0; for example 19/07 : 5(19) + 2(07) = 7;7 -7=0.

Jan./Feb. Leap-year? 04/01 11/01 18/01 25/01  
01/02 08/02 15/02 22/02 (29/02)?
DAY & MONTH=

Departure date

(TRANSPARENT).

 

01/03 08/03 15/03 22/03 29/03
05/04 12/04 19/04 26/04  
03/05 10/05 17/05 24/05 31/05
07/06 14/06 21/06 28/06  
05/07 12/07 19/07 26/07  
02/08 09/08 16/08 23/08 30/08
06/09 13/09 20/09 27/09  
04/10 11/10 18/10 25/10  
01/11 08/11 15/11 22/11 29/11
06/12 13/12 20/12 27/12  
CENTURY CENTURY
YEAR YEAR
SUM (regular) COLOUR=YEAR

YEAR =(CENTURY + YEAR).

 

SUM

 If Leap-year :

 

COLOUR=YEAR+6.

YEAR =(CENTURY+YEAR).

 

 

Departure dates retain almost every year the same weeknumber (ISO-standard).

Exception.

Exception is formed by leap-years with (official)  yearcolour red.

In those years  29/2 just occupies SU in week 9, while next day week 10 begins with MO 1/3.  

The year 2057 is green, so all dates below are TH.

 ()* 

The date 29/2 exists only within leap-years; in that case the following date 1/3 makes the shift toward the next (official) colour.

MONTH

DATES  

[3]JANUARY  4 11 18 25   [3]
[6]FEBRUARY 1 8 15 22 (29)* [6]
[6]MARCH 1 8 15 22 29 [6]
[2]APRIL 5 12 19 26 [2]
[4]MAY 3 10 17 24 31 [4]
[7]JUNE 7 14 21 28 [7]
[2]JULY 5 12 19 26 [2]
[5]AUGUST 2 9 16 23 30 [5]
[1]SEPTEMBER 6 13 20 27 [1]
[3]OCTOBER 4 11 18 25 [3]
[6]NOVEMBER 1 8 15 22 29 [6]
[1]DECEMBER 6 13 20 27 [1]

 

3.h  Calendar 1999-2004. INDEX

If one knows to handle the departure dates this calendar will do.

CALENDAR 1999-2004.     

mnemonics

 

leap-year

     

leap-year

PART 1

 

1999

mo

part 1

2000

tu

 

2001

th

2002

fr

 

 

2003

sa

part 1

2004

su

[3] [3]JANUARY 11/1
[6] [6]FEBRUARY 22/2
PART 2 part 2

2000

we

part 2

2004

mo

[6] [6]MARCH 1^3
[2] [2]APRIL 5>4
[4] [4]MAY 3^5
[7] [7]JUNE 7>6
[2] [2]JULY 5^7
[5] [5]AUGUST 9>8
[1] [1]SEPTEMBER 6<9
[3] [3]OCTOBER 11>10
[6] [6]NOVEMBER 8<11
[1] [1]DECEMBER 13>12 

3.h Extended table of centuries. INDEX

 

TABLE OF CENTURIES

The 20 st century  is displayed as: "19.." .

Years BC + 101  comparable with years AD.

For example the  period -13 BC until +1 AD is comparable with the period +88 AD until +101 AD one century later.

 

 

Centurycolour

JULIAN CENTURIES

last day:

TH 4/10/1582

GREGORIAN  CENTURIES

first day:

FR 15/10/1582 that follows the Julian TH 4/10/1582.

B.C.

(before Chr.)

A.D.

Anno Domini

A.D.

Anno Domini

-8 -1 - 5 12 16,20,24,28,...< +4 > 7
-7 -0 - 6 13   6
-13 -6 0 7 14 17,21,25,29,...< +4 > 5
-12 -5 1 8 15   4
-11 -4 2 9 .. 18,22,26,30,.. < +4 > 3
-10 -3 3 10 ..   2
-9 -2 4 11 .. 15,19,23,27,.. < +4 > 1
-8 -1 5 12 .. 16,20,24,28,...< +4 > 0