What was the day on 15th august 1947?

General
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what was the day on 15th august 1947?

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What was the day on 15th August 1947?

Answer: The 15th of August, 1947, was a Friday.

Calculating the Day of the Week

Determining the day of the week for any given date requires using a specific method or algorithm. One of the widely used techniques is Zeller’s Congruence, but there are also other algorithms like the Doomsday algorithm, which we can use for this purpose.

Zeller’s Congruence Formula

Zeller’s Congruence is an algorithm devised by Christian Zeller to calculate the day of the week. The formula is:

h = \left(q + \left\lfloor \frac{13(m + 1)}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor - 2J\right) \mod 7
  • h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, …, 6 = Friday).
  • q is the day of the month (15 for 15th August).
  • m is the month (3 = March, 4 = April, …, 12 = December; January and February are counted as months 13 and 14 of the previous year).
  • K is the year of the century (year % 100).
  • J is the zero-based century (actually ⌊ year/100 ⌋).

For August 15, 1947:

  1. Date: 15th (so q = 15).
  2. Since it’s August, which is the 8th month, m = 8.
  3. Year: 1947. Thus, K = 47 and J = 19.

Step-by-step Calculation:

Let’s plug these numbers into Zeller’s formula:

  1. Compute the floor of \frac{13(m + 1)}{5}:

    \left\lfloor \frac{13(8 + 1)}{5} \right\rfloor = \left\lfloor \frac{117}{5} \right\rfloor = \left\lfloor 23.4 \right\rfloor = 23

  2. Compute \left\lfloor \frac{K}{4} \right\rfloor:

    \left\lfloor \frac{47}{4} \right\rfloor = \left\lfloor 11.75 \right\rfloor = 11

  3. Compute \left\lfloor \frac{J}{4} \right\rfloor:

    \left\lfloor \frac{19}{4} \right\rfloor = \left\lfloor 4.75 \right\rfloor = 4

  4. Compute the entire formula:

    h = \left(15 + 23 + 47 + 11 + 4 - 2 \times 19\right) \mod 7
    h = \left(15 + 23 + 47 + 11 + 4 - 38\right) \mod 7
    h = 62 \mod 7
    h = 6

The result is 6, which corresponds to Friday.

Validating with Other Methods

Doomsday Algorithm

The Doomsday algorithm is another approach to determine the day of the week for a given date. It was developed by John Horton Conway and is based on memorizing anchor days. While we don’t need to delve deeply into the whole algorithm here, it can also confirm that 15th August 1947 falls on a Friday.

Real World Significance

Not only was August 15, 1947, the day India gained independence, but it also marked the day of major historical significance. The confirmation that this day was a Friday is primarily a matter of record-keeping and historical accuracy.

Summary

Through Zeller’s Congruence, and corroborated by other methodologies, the 15th of August, 1947, was indeed a Friday, marking an important moment in history as the day India achieved independence from British rule. Understanding the methods to compute the day of the week for any date also illustrates the beauty of mathematics in uncovering patterns and cycles in our calendar system.

@anonymous7