By Candice McKenna - Director of Sport
Well done to students and staff on Season 2 of APS sport. The effort contributed by all to weekly practise, and the energy committed to Friday sport is appreciated.
Andrew Wrigley, Senior School Mathematics Teacher
Over the Easter break there was a special date with a numerical significance that all mathematicians (well, perhaps some) celebrated (well, perhaps acknowledged). It is known as ‘Square Root Day’ where the day and month in the calendar are the square root of the year – and it works in either the US or European format.
The date, naturally, was 4 April 2016 or 4/4/16 and there are only nine occurrences of Square Root Day each century. We have already seen 1 January 2001 (1/1/01), 2 February 2004 (2/2/04), 3 March 2009 (3/3/09) and there are five more to look forward to; 5/5/25, 6/6/36, 7/7/49, 8/8/64 and 9/9/81.
The naming of the day was proposed by Californian Maths teacher Ron Gordon who noticed the connection when writing the date on a cheque on 9 September 1981 (9/9/81). There are a number of other noteworthy days each century named by Gordon like the ‘Odd Days’; 1/3/05, 3/5/07, 5/7/09, 7/9/11, 9/11/13 and most recently 11/13/15; the ‘Once Upon a Days’ 11/1/11, 11/11/11 and the ‘Tic Tac Toe’ days (three in a row) like 11/12/13. 13 December 2014 (12/13/14) fell on a Saturday and being the last sequential date for 20 years until 2 January 2034 (1/2/34), there was a big surge in the number of weddings, as couples sought to lock in a date they would never forget.
Gordon even offers special awards to those who celebrate these days in a creative manner. It should come as no surprise that the prizes are based on the numbers. For 12/13/14, he offered $1,213.14 to be shared between 12+13+14 winners - that works out at about $10π each. Speaking of π, that is celebrated on 14 March each year (3/14) and this year was Rounded π Day (3/14/16) - correct to four decimal places.
Ron Gordon has also introduced two other mathematical holidays, 'Trumpet Day' (2/2/22), "two-two-two-two", and 'Romeo and Juliet Day'. That will be on 1/2/35. “Where ‘four’ art thou, Romeo?”
Tic Tac Toe days are otherwise known as Sequential Days and but it should be noted that Finland had a calculated countdown to the end of prohibition in the country. The banning of alcohol finished on 5 April 1932 at 10.00am (5/4/32, 10 o'clock).
Pythagorean Triple days also occur occasionally and most recently we had 9/12/15, although for purists this does not really count as it is a multiple of the primitive triple, 3/4/5. A Pythagorean triple relates to the lengths of the sides (a, b and c) of a right angled triangle where a2 + b2 = c2, for example 32 + 42 = 52. The next non-primitive Pythagorean triple day will be 8/15/17 (15 August 2017) as 82 + 152 = 172. Dates can also be logged as ‘Indices Days’ and this year, in particular, created a base for two such occasions. There was 2/4/16 and 4/2/16 representing both 2 April and 4 February whichever notation you use (24 = 42 = 16). In 2064 there will be the three possibilities of 2/6/64, 4/3/64 and 8/2/64 as 26 = 43 = 82 = 64.
Felix Klein, the German mathematician best remembered for the Klein bottle, a non-orientable surface, was born on 25 April 1849 which is 22/52/432 and therefore a ‘Perfect Square Day’. He knew his destiny was to become a mathematician when he discovered the powers of his birthdate numbers. Now 442 = 1936 so anyone celebrating their 80th birthday this year could qualify as a perfect square with the next square birth year being 2025, or 452.
If you are wondering when a ‘Cubic Triple Day’ might occur, that is when the month cubed plus the day cubed equals the year cubed and we write that out algebraically, it would be similar to a Pythagorean Triple but with a power of three, a3 + b3 = c3. The short answer is that it never occurs (nor does it occur with higher powers). The long answer is the proof of Fermat’s Last Theorem, a mathematical problem that remained unsolved for over 350 years and was famously solved in 1995 by Andrew Wiles. It was announced last month that Wiles will now receive the 2016 Abel prize for Mathematics, a Norwegian government award similar to the Nobel prize.
Of course, there are always the special ‘Triple Digits Days’ like 12 December 2012 (12/12/12), which was the precursor to a more sinister looking date on 21 December 2012 (12/21/12). That was supposedly the last day in the Mayan calendar and therefore the end of the world. It wasn’t.« Back to IndexNext article in this edition »