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  1. TOPIC The Doomsday Algorithm (世界末日算法)

  2. LESSON Doomsday Algorithm The Doomsday Algorithm (世界末日算法) tells us whether a specific date was a Monday, Tuesday, etc. For example, what day was it on : 1 July 4th, 1776 May 1st, 1895 August 4th, 1962 Thursday 2 Wednesday 3 Saturday

  3. LESSON Doomsday Algorithm The Doomsday Algorithm (世界末日算法) is very easy to learn and we’ll do few quick examples. It was invented by the renowned British mathematician John Conway. Tell me your birthday and I will tell you what day you were born using Conway’s algorithm.

  4. TOPIC 8:00 minute I am going to show you a video of Arthur Benjamin. He can tell you the day of the week (Monday, Tuesday, etc.) of any date in under 3 seconds. He also uses The Doomsday Algorithm (世界末日算法). We’ll be using English mathematical terms for the Doomsday Algorithm, so pay attention carefully.

  5. TOPIC Fast forward to 8:00

  6. LESSON Doomsday Algorithm The Doomsday Algorithm uses very simple math to get the day of the week. You just have to remember a few numbers. The type of Doomsday Algorithm we are going to learn is called the “First Sunday” or “Odd + 11” Doomsday. If we have time, we will learn the original Doomsday algorithm. The “First Sunday” Doomsday Algorithm is by Bob Goddard and is found at http://firstsundaydoomsday.blogspot.com/. The first two examples are from his website.

  7. LESSON Doomsday Algorithm You will need the following tables for reference. These are also on the sheet of paper provided. January 3 or 4 February 0 or 1 March 0 April 4 May 9 June 6 July 11 August 8 September 5 October 10 November 7 December 12 1700s 0 1800s 2 1900s 4 2000s 5 Sunday 0 Monday 1 Tuesday 2 Wednesday 3 Thursday 4 Friday 5 Saturday 6

  8. LESSON Doomsday Algorithm July 4th, 1776 (7/4/1776) 1 Take the last 2 numbers of the year: 76 If this number is odd, add 11 and divide by 2 T = T + 11 / 2 75 = 75 + 11 / 2 = 43 43 = 43 + 11 = 54 If it is odd again, add 11 If this number is even, do not add 11, but divide by 2. T = 76 / 2 = 38 Subtract 7’s from the number: T = 38 – 35 = 3

  9. LESSON Doomsday Algorithm July 4th, 1776 (7/4/1776) 2 Add the value of the first 2 numbers of the year: 17 1700s 0 1800s 2 1900s 4 2000s 5 The first two numbers of the year 1776are 17, so the value is 0. T = 3 + 0 = 3

  10. LESSON Doomsday Algorithm July 4th, 1776 (7/4/1776) 3 Add the value of the month: 7 January 3 or 4 February 0 or 1 March 0 April 4 May 9 June 6 July 11 August 8 September 5 October 10 November 7 December 12 The value for July (7) is 11, so we add this number to the total. T = 3 + 11 = 14 Subtract 7’s from the number: T = 14 – 14 = 0

  11. LESSON Doomsday Algorithm July 4th, 1776 (7/4/1776) 4 Subtract the value of the day from the total : 4 Sunday 0 Monday 1 Tuesday 2 Wednesday 3 Thursday 4 Friday 5 Saturday 6 Take the day of the date (4) and subtract from the total (0). T = 4 – 0 = 4 Thursday = 4 July 4th, 1776 was on a Thursday!

  12. LESSON Doomsday Algorithm May 1st, 1895 (5/1/1895) 1 Take the last 2 numbers of the year: 95 This number is odd, so we must add 11 and divide by 2. T = 95 + 11 / 106 = 53 It’s odd again! Add 11 one more time. T = 53 + 11 = 64 Subtract 7’s from the number: T = 64 – 63 = 1 T = 1

  13. LESSON Doomsday Algorithm May 1st, 1895 (5/1/1895) 2 Add the value of the first 2 numbers of the year: 18 1700s 0 1800s 2 1900s 4 2000s 5 The first two numbers of the year 1895are 18, so the value is 2. T = 1 + 2 = 3 T = 3

  14. LESSON Doomsday Algorithm May 1st, 1895 (5/1/1895) 3 Add the value of the month: 5 January 3 or 4 February 0 or 1 March 0 April 4 May 9 June 6 July 11 August 8 September 5 October 10 November 7 December 12 The value for May (5) is 9, so we add this number to the total. T = 3 + 9 = 12 Subtract 7’s from the number: T = 12 – 7 = 5 T = 5

  15. LESSON Doomsday Algorithm May 1st, 1895 (5/1/1895) 4 Subtract the value of the day from the total : 4 Sunday 0 Monday 1 Tuesday 2 Wednesday 3 Thursday 4 Friday 5 Saturday 6 Take the day of the date (1) and subtract the total (5) T = 1 – 5 = -4????? Instead, take the absolute value (绝对值) of | -4| and subtract from 7 T = 7 – 4 = 3 May 1st, 1895 was on a Wednesday!

  16. LESSON Doomsday Algorithm January 3 or 4 February 0 or 1 March 0 April 4 May 9 June 6 July 11 August 8 September 5 October 10 November 7 December 12 If the year is a leap year (闰年), use 3. If it is not a leap year, use 4 If the year is a leap year, use 0. If it is not a leap year, use 1

  17. LESSON Doomsday Algorithm February 21st, 1996 (2/21/1996) 1 Take the last 2 numbers of the year: 96 This number is even, so we do not add 11 but we must divide by 2. T = 96 / 2 = ? Subtract 7’s from the number: T = ? – 42 = ? T = ?

  18. LESSON Doomsday Algorithm February 21st, 1996 (2/21/1996) 2 Add the value of the first 2 numbers of the year: 19 1700s 0 1800s 2 1900s 4 2000s 5 The first two numbers of the year 1996are 19, so the value is 4. T = ? + 4 = ? Subtract 7’s from the number: T = ? – 7 = ? T = ?

  19. LESSON Doomsday Algorithm February 21st, 1996 (2/21/1996) 3 Add the value of the month: 2 January 3 or 4 February 0 or 1 March 0 April 4 May 9 June 6 July 11 August 8 September 5 October 10 November 7 December 12 The value for February (2) is 1, so we add this number to the total. T = ? + 1 = ? T = ?

  20. LESSON Doomsday Algorithm February 21st, 1996 (2/21/1996) 4 Subtract the value of the day from the total : 21 Sunday 0 Monday 1 Tuesday 2 Wednesday 3 Thursday 4 Friday 5 Saturday 6 Take the day of the date (21) and subtract the total (?) T = 21 – ? = ????? Subtract 7’s from the number: T = ? – ? = ? So February 21st, 1996 was on a ??????????

  21. LESSON Doomsday Algorithm PRACTICE – Your Turn Tell me the days for the following dates 1 September 10th, 1856 2 January 22nd, 2001 3 Your Birthday

  22. LESSON Doomsday Algorithm Can you do it in your head?

  23. LESSON Doomsday Algorithm The original Doomsday Algorithm There is an easier to get the day of the week but it requires memorizing several days of the year and a special doomsday for the year. For example, the doomsday for 2013 is Thursday. All the dates below always fall on Doomsday. April 4th(4/4) =Thursday June 6th (6/6) =Thursday August 8th(8/8) =Thursday October 10th(10/10) =Thursday December 12th(12/12) =Thursday May 9th(5/9) =Thursday September 5th (9/5) =Thursday July 11th(7/11) =Thursday November 7th(11/7) =Thursday “I work 9 to 5 at the 7-11”

  24. LESSON Doomsday Algorithm Example: July 22nd, 2013 We already know the doomsday for 2013 is Thursday, and thus we know that July 11th is also Thursday. Since July 22nd, 2013 is 11 days or 2 weeks and 4 days after July 11th, we know that July 22nd must be a Monday. April 4th(4/4) =Thursday June 6th (6/6) =Thursday August 8th(8/8) =Thursday October 10th(10/10) =Thursday December 12th(12/12) =Thursday May 9th(5/9) =Thursday September 5th (9/5) =Thursday July 11th(7/11) =Thursday November 7th(11/7) =Thursday “I work 9 to 5 at the 7-11”

  25. LESSON Doomsday Algorithm What day was April 19th, 2013 (4/19/2013)? 1 What is the doomsday for 2013? Thursday 2 What doomsday is closest to April 19th? April 4th 3 How many weeks are between April 4th and April 19th? 2 weeks and 1 day What is Thursday plus 2 weeks and 1 day? Friday 4

  26. LESSON Doomsday Algorithm The Doomsday is not the same every year! The Doomsday for 2013 is on Thursday…but it is not on Thursday every year. It changes depending the year and whether it is a leap year (闰年). For example: 2014 Friday 2015 Saturday 2016 Monday  Every leap year, one day is skipped. It is not Sunday. 2017 Tuesday 2018 Wednesday 2019 Thursday The next page shows the Doomsday for every year between 1945 and 2100.

  27. LESSON Doomsday Algorithm The Doomsday between 1944-2100

  28. LESSON Doomsday Algorithm What day is May 1st, 2049 (5/1/2049)? 1 What is the doomsday for 2049? 2 What doomsday is closest to May 1st? 3 How many weeks are between ________ and May 1st? What is ________ plus 2 weeks and 1 day? 4

  29. LESSON Doomsday Algorithm Practice – Your Turn What day are the following dates? 1 December 25th, 2065 2 March 29th, 1948 3 October 11th, 2011

  30. LESSON Doomsday Algorithm What day are the following dates? 1 December 25th, 2065 Friday 2 March 29th, 1948 Monday 3 October 11th, 2011 Tuesday