Determine the day of the week on which you were born

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In summary: No, the ## \left \lfloor \frac c 4 - 2c \right \rfloor ## term (where as in the OP ## c ## is the century number i.e. year mod 100) takes care of centuries. As I said above this is Zeller's congruence.
  • #1
Math100
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Homework Statement
Determine the day of the week on which you were born.
Relevant Equations
None.
The date with month ## m ##, day ## d ##, year ## Y=100c+y ## where ## c\geq 16 ## and ## 0\leq y<100 ##, has weekday number
## w\equiv d+[(2.6)m-0.2]-2c+y+[\frac{c}{4}]+[\frac{y}{4}]\pmod {7} ## provided that March is taken as the first month of the year and January and February are assumed to be the eleventh and twelfth months of the previous year.
To determine the day of the week on which I was born, I will use my birthday as an example.
## w\equiv 31+[(2.6)(8)-0.2]-2c+y+[\frac{c}{4}]+[\frac{y}{4}]\pmod {7} ##
 
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  • #2
What is the first day of the week?
 
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  • #3
fresh_42 said:
What is the first day of the week?
I believe it's Sunday.
 
  • #4
I entered ## c=19, y=95 ## into the equation above but I am not getting the correct answer.
 
  • #5
I got two correct answers for dates that I checked if Sunday counts as number zero (or seven).

Let's see what happens with today (9/25/2022):

\begin{align*}
w&\equiv d+[(2.6)m-0.2]-2c+y+[\frac{c}{4}]+[\frac{y}{4}]\pmod {7} \\
&=25+[2.6 \cdot 7 -0.2]-2\cdot 20 + 22+[20/4] +[22/4]\pmod{7}\\
&=25+18-40+22+5+5=35\equiv 0\pmod{7}
\end{align*}

I haven't seen that formula before. But three out of the three tests I made produced the correct result.

We had to prove by induction that the 13th of a month is more often a Friday than any other weekday.
 
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  • #6
fresh_42 said:
I got two correct answers for dates that I checked if Sunday counts as number zero (or seven).

Let's see what happens with today (9/25/2022):

\begin{align*}
w&\equiv d+[(2.6)m-0.2]-2c+y+[\frac{c}{4}]+[\frac{y}{4}]\pmod {7} \\
&=25+[2.6 \cdot 7 -0.2]-2\cdot 20 + 22+[20/4] +[22/4]\pmod{7}\\
&=25+18-40+22+5+5=35\equiv 0\pmod{7}
\end{align*}

I haven't seen that formula before. But three out of the three tests I made produced the correct result.

We had to prove by induction that the 13th of a month is more often a Friday than any other weekday.
I got ## 137.1 ##, but isn't that equal to ## 137.1\equiv 4\pmod {7} ##? Given the fact that my birthday is on October 31st, 1995.
 
  • #7
Let's see:
\begin{align*}
w&\equiv d+[(2.6)m-0.2]-2c+y+[\frac{c}{4}]+[\frac{y}{4}]\pmod {7} \\
&=31+[2.6 \cdot 8 -0.2]-2\cdot 19 + 95+[19/4] +[95/4]\pmod{7}\\
&=31+[20.6]-38+95+4+3=115\equiv 3\pmod{7}
\end{align*}

You were born on a Wednesday.
 
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  • #8
fresh_42 said:
Let's see:
\begin{align*}
w&\equiv d+[(2.6)m-0.2]-2c+y+[\frac{c}{4}]+[\frac{y}{4}]\pmod {7} \\
&=31+[2.6 \cdot 8 -0.2]-2\cdot 19 + 95+[19/4] +[95/4]\pmod{7}\\
&=31+[20.6]-38+95+4+3=115\equiv 3\pmod{7}
\end{align*}

You were born on a Wednesday.
But why did my Korean hospital says Tuesday then? That's weird.
 
  • #9
Math100 said:
But why did my Korean hospital says Tuesday then? That's weird.
No, that's true. Wednesday is wrong. I made a mistake. I calculated ##[95/4]## as the remainder, not the integer part.

Correction:
\begin{align*}
w&\equiv d+[(2.6)m-0.2]-2c+y+[\frac{c}{4}]+[\frac{y}{4}]\pmod {7} \\
&=31+[2.6 \cdot 8 -0.2]-2\cdot 19 + 95+[19/4] +[95/4]\pmod{7}\\
&=31+[20.6]-38+95+4+23=135\equiv 2\pmod{7}
\end{align*}
... and ##2## is Tuesday.
 
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  • #10
fresh_42 said:
Let's see what happens with today (9/25/2022):
I can understand why an American would use that ridiculous way of writing a date, but surely you know better ? :wink:
 
  • #11
pbuk said:
I can understand why an American would use that ridiculous way of writing a date, but surely you know better ? :wink:
I would have written it 200220925175845, but communication means understanding the set-up of your dialogue partner. :wink:
 
  • #12
Is this intended to be a restatement of Zeller's congruence? Note that the roundings should be floors e.g. ## \left [ \frac y 4 \right ] ## should be ## \lfloor \frac y 4 \rfloor ##.
 
  • #13
pbuk said:
Is this intended to be a restatement of Zeller's congruence? Note that the roundings should be floors e.g. ## \left [ \frac y 4 \right ] ## should be ## \lfloor \frac y 4 \rfloor ##.
My textbook defines ##[x]=\lfloor x\rfloor## so it doesn't make a difference.
 
  • #15
I'd think we need to know this is the Gregorian Calendar and not Chinese, or otherwise, which may not be 365.25 days long. If its Gregorian, you can use that 365=52.7+1, 366=52.7+2. Then find the number of leap years and "regular" ones in-between.
 
  • #16
WWGD said:
I'd think we need to know this is the Gregorian Calendar and not Chinese, or otherwise, which may not be 365.25 days long. If its Gregorian, you can use that 365=52.7+1, 366=52.7+2. Then find the number of leap years and "regular" ones in-between.
It's not exactly 365.25. It gets complicated every 100 (no leap) and 400 (leap) years IIRC.
 
  • #17
fresh_42 said:
It's not exactly 365.25. It gets complicated every 100 (no leap) and 400 (leap) years IIRC.
I guess we use simplified assumptions. Hey, if physicists can approximate a basketball player with a cylinder, why not?
 
  • #18
WWGD said:
I guess we use simplified assumptions. Hey, if physicists can approximate a basketball player with a cylinder, why not?
Where is that d*** cylinder?

Uh! Found it!

 
  • #19
fresh_42 said:
It's not exactly 365.25. It gets complicated every 100 (no leap) and 400 (leap) years IIRC.
WWGD said:
I guess we use simplified assumptions.
No, the ## \left \lfloor \frac c 4 - 2c \right \rfloor ## term (where as in the OP ## c ## is the century number i.e. year mod 100) takes care of centuries. As I said above this is Zeller's congruence.
 
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FAQ: Determine the day of the week on which you were born

When was the concept of determining the day of the week on which you were born first introduced?

The concept of determining the day of the week on which you were born was first introduced by mathematician John Conway in his book "The Book of Numbers" in 1996.

How is the day of the week on which you were born calculated?

The day of the week on which you were born is calculated using a mathematical formula called the "Doomsday Algorithm" which takes into account the month, day, and year of your birth.

Does the day of the week on which you were born have any significance?

Some people believe that the day of the week on which you were born can influence your personality traits and characteristics. However, there is no scientific evidence to support this belief.

Can the day of the week on which you were born change?

No, the day of the week on which you were born will always remain the same. It is a fixed date and cannot be altered or changed.

Is it possible to determine the day of the week on which you were born without using a calculator or computer?

Yes, it is possible to determine the day of the week on which you were born without using a calculator or computer by memorizing the Doomsday Algorithm and using it to calculate the day of the week for any given date.

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