Math & Beyond

Days, Dates and Possible Combinations

12th Aug '202 views9 mins read

12  August 2020

Reading Time: 8 minutes

This article will help you to familiarize yourself with days in a week and months in a year, reading the calendar to find a particular day and date.

Introduction

The measurement of time began with the invention of sundials in ancient Egypt. However, the time the Egyptians measured was not the same as the time today's clocks measure. For the Egyptians, and indeed for a further three millennia, the basic unit of time was the period of daylight.

The Egyptians broke the period from sunrise to sunset into twelve equal parts, giving us the forerunner of today's hours. As a result, the Egyptian hour was not a constant length of time, as is the case today; rather, as one-twelfth of the daylight period, it varied with the length of the day, and hence with the seasons.

It also varied from place to place on the surface of the Earth. And of course, time as a measurable concept effectively ceased as Math took control of the logic and parameters used in the age of darkness.


Day

What is a day?
To know what a day is, a little bit of science behind the concept is required. This very clearly proves that Math plays a major role in science too. Let us see how. Take a deep look at the below picture.


 Earth and sun

What do we learn from the above image?

  • Sun stands enormous in front of the Earth
  • Sun stands as a source of light to the planet Earth
  • Earth’s one half is in light and the other half is dark in shade

Let us focus on the 3rd point - Earth’s one half is in light and the other half is dark in shade.

Earth is spherical as you can see the structure in the video below.
Earth is spherical.

Facts about spherical shaped Earth

  • Earth revolves around the Sun – This causes the formation of YEARs.
  • Earth rotates around itself – This causes the formation of DAYs.

Watch the below video to see how Earth rotates to itself and revolves around the Sun.
Earth rotates and revolves around the sun.

Let us try to understand the rotation of Earth as this is what causes the formation of DAY.

 day and night


Earth - Daytime and Nighttime

Earth is always half exposed to the Sun due to its spherical structure. The exposed half receives the Sun rays and hence light, while the other half that is not exposed remains in darkness. The Sun’s rays light the Earth’s surface uniformly as the Earth rotates to itself thus giving rise to Sunrise and Sunset, Morning, Noon, Afternoon, Evening, and Night, based on the intensity of Sun’s rays hitting the Earth’s surface.

A day can be defined as the time taken by planet Earth to complete one whole rotation OR in other words, SUMMING a Daytime and a Nighttime gives birth to a DAY.

DAYTIME + NIGHTTIME = DAY

Daytime is the time at a place on Earth that is exposed to the Sun while Nighttime is a particular time at the same place that remains unexposed to the Sun.
Daytime can also be defined as the time from Sunrise to Sunset, while Nighttime is the time from Sunset to Sunrise.

The time taken from one Sun Rise to the following day’s Sun Rise makes a DAY.
Which includes Sunrise,  Sunset, and again Sunrise. This complete cycle makes a DAY.
The above explanation is geographic and does not exactly remain the same in every place of the Earth. Based on the seasons and climatic conditions Sunrise and Sunset vary. Hence, we cannot precisely calculate a DAY based on Sunrise and Sunset.

On a rainy day, since the Earth’s surface is not exposed to the Sun clearly, the ambiance looks dark and this does not mean its night. To have a system independent of the climate and geographic location, a better system was awaited. The story does not end here.

This is where the genius pitches into rock and that’s Math. Using MATH as a foundation for DAY, one can measure time independent of geographic and climatic conditions.

Now, let us dig into the MATH behind a DAY.
One complete rotation of Earth ie., from Sunrise to the next day’s Sunrise makes a DAY

hour glass

The above image is the picture of an hourglass. One hour is equal to the entire sand moving from the top chamber to the bottom chamber. This particular time makes 1 HOUR.
In the present-day scenario, the hourglass is no more in use for daily use. The clocks have replaced the hourglass due to its continuity in measuring time without manual interference.

What is a CLOCK?

A clock is a device used to indicate the time. The clock consists of Dial, Seconds needle, Minutes needle, and Hour needle.

clock

The Dial is the BACKGROUND of the clock that displays the MINUTES and HOURS in numbers to the user.

Seconds needle is the thinnest of all needles in the clock.
Seconds needle moves faster than other needles in the clock.

The Minutes needle is the thick and elongated needle in the clock.
The minute needle moves slower than the Seconds needle and faster than the Hour needle.
For every 60 movements of the Seconds needle, the minute needle will move once.

The Hour needle is the short needle in the clock.
This is the slowest moving needle in the clock.
For every 60 movements of the minutes’ needle, the hour needle will move to the next number in the clock.

CLOCK

The number 1 – 12 on the DIAL resembles various usage.

1 – 12 stands for HOURs

1 – 12 as multiples of 5 stands for MINUTEs and for SECONDs
1 x 5 = 5 minutes/seconds
2 x 5 = 10 minutes/seconds
3 x 5 = 15 minutes/seconds
4 x 5 = 20 minutes/seconds
5 x 5 = 25 minutes/seconds
6 x 5 = 30 minutes/seconds
7 x 5 = 35 minutes/seconds
8 x 5 = 40 minutes/seconds
9 x 5 = 45 minutes/seconds
10 x 5 = 50 minutes/seconds 
11 x 5 = 55 minutes/seconds
12 x 5 = 60 minutes/seconds

Time is displayed as HH:MM:SS
HH stands for HOURs
MM stands for MINUTEs
SS stands for SECONDs

Every day starts at 00:00:00 Hours. This will be the tentative midnight.
By around 06:00:00 Hours, the tentative time when Sunrises
By around 12:00:00 Hours, the tentative time when Sun will be at its peak
By around 18:00:00 Hours, the tentative time when Sunsets
The day ends at 23:59:59 Hours, the tentative midnight and the following day starts.

One complete rotation of Earth forms a DAY starting with mid-night of a particular day to the mid-night of the following day.

In numbers, considering a 12 Hour clock to complete the cycle twice, the DAY starts when it is 00:00:00 Hours on the clock and ends when it is 23:59:59 Hours on the clock. Resetting to 00:00:00 Hours to start with the next DAY.

The first cycle of the clock starts from 00:00:00 Hours and ends at 11:59:59 Hours
The second cycle of the clock starts from 12:00:00 Hours and ends at 23:59:59 Hours

Calendar

As we are now aware that Earth revolves around the Sun, it takes 365 days for the Earth to complete one cycle of revolution around the Sun. In other words, 365 DAYS makes 1 YEAR.

Earth rotates and revolves around the sun.

Let us do some practical work out to evaluate our understanding of time and day so far.
If I must pick up a day in a year, for example, the 250th day of the year. It becomes difficult for me to remember what I was doing on the 250th day of a particular year. Hence, to simplify the concepts for better usage, months were invented based on the moon's rotation around the Earth.

In 1 YEAR, there will be 12 MONTHs.
1 YEAR is also EQUAL to 365 DAYs.
Which means there are 12 MONTHs in 365 DAYs.
365 (DAYs) DIVIDED by 12 (MONTHs) is TENTATIVELY EQUAL to 30 DAYs in 1 MONTH.
Hence, we have roughly around 30 DAYs in 1 MONTH.
These 30 DAYs in a MONTH is based on the phase of the moon revolving around the earth.

The months in a year are,

calendar

An easy way to remember the number of DAYs in a MONTH is illustrated in the below image.

 number of days in a month
 

To further simplify the usage of DATEs, the concept of WEEK was introduced.

SUMMARY

60 Seconds = 1 Minute
60 Minutes = 1 Hour
24 Hours = 1 Day
7 Days = 1 Week
Tentatively 4 Weeks = 1 Month
12 Months = 1 Year

Using Maths conversions can be written as below,
Instead of 12 Months = 1 Year
It can also be written as
52 Weeks = 1 Year
365 Days = 1 Year
8760 Hours = 1 Year

Calendar Exercise

Getting back to the question of what I was doing on the 250th day of a year can now be sorted using these simple conversions.


Months in the year 2020

calendar-full

 

 


Dates

As you are now aware that there are 12 months in a year, let us find out which date in a month points to which day.

For example, let us consider the month of January.

january


As you have learned before, there are 7 days in a week.
And now let us get to know what these days are?

The week starts with

  • SUNday
  • MONday
  • TUESday
  • WEDNESday
  • THURSday
  • FRIday
  • SATURday

Just because the week starts with Sunday, it does not mean that the first day of every month starts with SUNday. Days from Sunday to Saturday are for logical usage while the actual usage differs based on the practical application.

In January 2020, we have the 1st day falling on Wednesday and the last day of the month 31st falling on Friday. Which means 1st February will fall on Saturday and not on Sunday.

The month holds 1 - 31 days which are the dates for January 2020.

Day And Date Exercise

  1. Can you find the day on which the 20th of January for the year 2020 falls in?
  2. What is the date for the 2nd Thursday in January for the year 2020?

Possible Combinations

Possibility

Possibility is a thing that may be chosen or done out of several possible alternatives.

Combination

A combination is a selection of all or part of objects, without regard to the order in which objects are selected.
For example, suppose we have a set of three letters: X, Y, and Z. We might ask how many ways we can select 2 letters from that set. Each possible selection would be an example of a combination. The complete list of possible selections would be:
XY
XZ
YZ

So, 3 combinations are possible.

Combination Exercise

Let us consider there are 3 pants - RED, BLUE, and GREEN in colors and 1 Shirt - WHITE in color.
How many combinations are possible with 3 pants and 1 shirt?

Answers

Calendar Exercise 
1 Year = 365 days
½ Year = 182.5 days
½ Year = 6 Months
250th day falls in the 2nd half of the year
250th day falls between July – December
July starts with the 181st or 182nd day of the year. Let us consider 181 days completes 1st half of the year

calendar-3

 

By referring to the above image July has 31 days, August has 31 days, September has 30 days.
181 + 31 days in July = 212 days
212 + 31 days in August = 243 days
243 + 30 days in September = 273 days
250th day falls in between 243 and 273
August month ends by 243rd day
7 days after August is the 250th day.
This means the 250th day falls in the 1st week of September.
This narrow down approach is possible only with Maths when streamlined through concepts.

Day and Date Exercise 

Based on the above calendar table, the 20th of January for the year 2020 falls on Monday.

9 is the date for the 2nd Thursday of January for the year 2020.

Combination Exercise 
Combination 1 - RED pant + WHITE Shirt
Combination 2 - BLUE pant + WHITE Shirt
Combination 3 - GREEN pant + WHITE Shirt

Thus there are 3 combinations possible.


Conclusion

The effort behind this blog is to emphasize how MATH helps SCIENCE and its impact on our daily lives. Though there has been a bit of science introduced in the article, the sole purpose is to make the reader know how time evolved over a time giving birth to Days, Dates, Months, and Years. Please provide your valuable suggestions to improve the article. Thank you for your support.
 


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