A Mathematical Investigation

Submitted as a Project for

Linear Algebra

Mathematical Investigation

“Pattern for THE DAY”

I. Introduction

Humans, as we are, we are fond of daydreaming and try to focus ourselves into what the future would be. We tend to think more advanced rather than make something out of the present. And with this thought mathematics will always be on our side. With all the dates of annual festivities or occasions, which we keep tract on and eventually make earlier preparations because we want to focus more on the future than face the present first, investigations on how to efficiently know which day of the week a specific annual celebration will occur without scanning piles of calendars, especially if it is a super advanced preparation like planning for your own 100th birthday party or the like will be of great use. This investigation will help daydreamers or advanced-thinkers to know which day of the week a special annual celebration will fall on with a pattern to follow without juggling a million pile of calendars. II. Statement of the Problem

This Mathematical Investigation aimed at finding out if there is a pattern on which day of the week a specific annual celebration occurs. Specifically, it aimed to answer the following questions:

1) Is there a pattern on which day of the week a specific annual celebration might fall in a series of years? 2) What is the pattern on which day of the week a specific annual celebration might fall on, in a series of years? 3) Is it applicable in any celebration that occurs annually? III. Conjectures

Let n be the number to represent the different days of a week

n=1 – Monday

2 – Tuesday

3 – Wednesday

4 – Thursday

5 – Friday

6 – Saturday

7 – Sunday

The day of the week wherein a specific annual celebration falls on follows 7 trends every four years and will continuously occur again consecutively, that is:

1

2

3

4

6

7

1

2

4

5

6

7

2

3

4

5

7

1

2

3

5

6

7

1

3

4

5

6

To use this, one must first observe the trend from the previous year then continue following the given trend.

IV. Verifying Conjectures

1) Given that a barangay’s fiesta is on February 3 anually, which day of the week will the barangay’s fiesta fall on, in the year 2050? To have a full view of the trend the investigator started on the year 2000 but it is not necessary to start with this year. | 1| 2| 3| 4| 5| 6| 7|

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