DAYS OF OUR LIVESAuthor(s): GEORGE KNILL and GEORGE FAWCETTSource: The Mathematics Teacher, Vol. 75, No. 6 (September 1982), pp. 489, 503Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27963016 .

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application

DAYS OF OUR LIVES

By GEORGE KNILL Ministry of Education

Willowdale, ON M2J 1W4

and GEORGE FAWCETT Board of Education for the

City of Hamilton Hamilton, ON L8N 3L1

Did you ever wonder what day of the

week an important event occurred? A

formula has been devised to calculate the

exact day without having to look back on

calendars that are hard to get. The formu

la is

w = d + 2m + 3(m + 1) 5

+ y

+ 100

+ 400

+ 2,

where

and

d = day of the month,

y =

year,

m = number of month.

January is regarded as the thirteenth

month of the previous year and February is regarded as the fourteenth month of the

previous year. All other months are regu lar month numbers. The numbers in the

brackets denote the greatest integer func

tion, for example, [9.6] = 9 and [19.49]

=

19. To find the day of the week for 2

February 1978, substitute d = 2, m = 14, and y

= 1977 in the formula. Once you

have a value for w, divide it by 7. The remainder is the day of the week. Sunday is the first day of the week and Saturday is the zero day.

Example 1. On what day of the week did New Year's Day fall in 1979? Using d =

1, m = 13, and y = 1978, we have

w = 1 + 2(13) + 3(14) + 1978

+ 1978 1978 100

1978 400

+ 2

= 1 + 26 + [8.4] + 1978 + [494.5] - [19.78] + [4.9] + 2

= 1 + 26 + 8 + 1978 + 494- 19 + 4 + 2 = 2494.

Since 2494 -r 7 = 356 with a remainder of

2, then the day of the week was Monday.

Example 2. Roger Bannister broke the

four-minute mile on 6 May 1954. What

day of the week was it? Using d = 6, m =

5, and y = 1954, we have

w = 6 + 2(5) + 3(6) + 1954

+ 1954 1954 100

+ 1954 400

+ 2

= 6 + 10 + 3 + 1954 + 488 - 19 + 4 + 2 = 2448.

Since 2448 -r 7 = 349 with a remainder of

5, then the day of the week was Thursday.

(Continued on page 503)

Four copies of manuscripts to be considered for inclusion in "Applications" should be sent directly to

George Knill, 164 Hillcrest Avenue, Hamilton, ON L8P 2X4. For ideas on content and format, consult the

remarks from the Editorial Panel that appeared with this section in the September 1980 issue.

September 1982 489

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(Continued from page 489)

Questions

1. Find the day of the week on which you were born.

2. On what day will your birthday fall in the year 2000?

3. Mr. Shifty was on trial for murder. The murder occurred on 30 July 1944 at 10:00 a.m. His alibi for the day in question was that he was helping a

customer in his department store at that time. Was he telling the truth?

4. Calculate the day of the week for each of the following: a) Henry Winkler's birthday?30 Oc

tober 1945 b) First telephone call?3 June 1875 c) George Washington's birthday?22

February 1732 d) Television first publicly broad

cast?30 April 1939 e) Dionne quintuplets, first to survive

infancy, born?28 May 1934

/) First Model 4T" put on the mar

ket?1 October 1908

Answers

3. No, 30 July 1944 was a Sunday. 4. a) Tuesday d) Sunday

b) Thursday e) Monday c) Friday f) Thursday

Answers to Problems of the Month

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'(* + %)0l)f = + *000l)6

sauioooq

xvHXoa * = xoaxvH 6

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= + ) so S3o8 uaqm J3UI11 3jrunui-[ \ sqi pBjsa^ "(jauni d)nuiui-{ \ sqi uo IJ9J 9JB samuiuj fr) Jjo ssoS jaiup amuiui-? aqi uaq/vv Supjooo ??a aqj jjbjs *sjauip qjoq y is

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September 1982 503

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