In order to do this, I check a calendar of the year 2004.Ex 1.2: Results for 2004 Months ( n ) Start day 1 Thursday 2 Sunday 3 Monday 4 Thursday 5 Saturday 6 Tuesday 7 Thursday 8 Sunday 9 Wednesday 10 Friday 11 Monday 12 Wednesday Therefore, we can see that the dates are thus: 1, 4, 7 = same 2, 8 = same 3, 11 = same 5 6 9, 12 = same 10 As you can see, the dates which fall on the same day are not the same as in the study sample Ex 1.1, so there is no pattern here.
However, since the second column was n = 7n – 2 this means there is obviously not a pattern of the n = 7n – x being directly related to which column it’s in.
Conclusion of Ex 2: I have noticed that generally, all columns are n = 7n – x where x varies with the start date.
However, this is not quite right, so to get the correct expression, subtract 5.
The expression is: n = 8n – 5 This is because you increase by 1 week 1 day as you go down diagonally to the right.
The pattern is the same in examples 1 and 3, even though they are not the same year because the days of the week are different.
I think that example 2 was the odd one out because it was a leap year.I will test another two diagonals descending to the right.Ex 4.5 Starting June 6th n date 1 6 2 14 3 22 4 30 The above table gives the expression 8n – 2.Introduction: I was given a task to investigate calendars, and look for any patterns.I noticed several patterns, the first of which was the relationship between the starting days of different months, also I noticed the relationship between numbers in columns of the calendar, the relationship between numbers in the rows, Studying diagonal relationships, and Studying relationships between adjacent numbers. Days on which months start First, I explore the days on which different months start. Ex 1.1 Study Sample Calendar: Month Starting day 1 Friday 2 Monday 3 Monday 4 Thursday 5 Saturday 6 Tuesday 7 Thursday 8 Sunday 9 Wednesday 10 Friday 11 Monday 12 Wednesday From the above table, I can see that some of the months start on the same day, which means there may be a pattern when compared with other years.The formula exists in this form because the columns with which it deals represent weeks, which consist of 7 days, 7 being the all important number. Exploring the relationship between numbers in the rows Now I explore the horizontal numbers…Ex 3.1 The first row in June: n 1 1 2 2 3 3 4 4 5 5 The formula is obviously n = n here, but will it change in the next few rows?However, to make this a fair test I will check another year, 2003, to be sure of this, as it could be an anomalous result of some kind.Ex1.3 Results for 2003: Months ( n ) Start day 1 Wednesday 2 Saturday 3 Saturday 4 Tuesday 5 Thursday 6 Sunday 7 Tuesday 8 Friday 9 Monday 10 Wednesday 11 Saturday 12 Monday Thus, the months which have the same start day are: 1, 4, 7 = same 2, 8 = same 3, 11 = same 5 6 9, 12 10 These results are very important, as the dates that are grouped together are the same dates as those in the study sample, which we know is not 2003 because of the differing days.Ex 4.6 Starting July 4th n date 1 4 2 12 3 20 4 28 The above table gives a formula of 8n – 4.I have noticed that descending diagonally left is always n = 6n – x, where x depends on which date you choose to start with. Columns) is always n = 7n – x; and that descending diagonally right gives n = 8n – x. Studying relationships between adjacent numbers I drew a box around 4 numbers: Ex 5.1 Starting 2nd August 2 3 2 x 10 = 20 9 10 3 x 9 = 27 The difference is 7.