It’s that time of year again and we can play the 2020 Year Game in our January lessons. You can preview the 2020 game now, full rules are here. Can your students use the digits in the year 2020 and the operations +, -, x, ÷, sqrt (square root),^ (raise to a power), ! (factorial), and !! (double factorial) along with grouping symbols, to write expressions for the counting numbers 1 through 100?
My students have always been curious about the double factorial function.
Excel has a function for computing double factorials, illustrated here.
I like to show my students a few examples and see if they can work out what is going on!
A great idea for a starter on return to school from Alex Bellos’s Monday Puzzle, note the end of the solutions post here where Alex Bellos describes a new New Year challenge from Inder J Taneja, a retired maths professor from Brazil; can your students write 2020 using only single digits? Solutions are provided for the digits 1 to 9.
Once again, Manan Shah has provided us with some puzzles to keep us busy, 20 in fact to keep us all busy!
I always read Transum’s Newsletter with interest, the newsletter published today notes some ideas on the number 2020 including an unusual property, something that last happened in 1210!
See also Weisstein, Eric W. “Self-Descriptive Number.”
From MathWorld–A Wolfram Web resource. http://mathworld.wolfram.com/Self-DescriptiveNumber.html
I see MEI has also noted this property in their January item of the month, Autobiographical numbers. A little further research led me to Tanya Khovanova’s 2008 paper on Autobiographical Numbers. Whilst mentioning Tanya Khovanova, we should of course check her Number Gossip site for properties of 2020 and from her paper we have a reminder of the Online Encyclopedia of Integer Sequences.
We can also look at WolframAlpha which provides further information on the number properties of 2020 including what 2020 looks like in historical numeral forms. We could use the various WolframAlpha queries to learn how Babylonian, for example, numerals work. I have successfully used this as an interesting starter for January lessons.
The Babylonian system was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.
For more on the Babylonian system including how fractions were represented see History of Fractions from Nrich.
We could look back and use the excellent MacTutor History of Mathematics Archive from the University of St Andrews, Scotland. We could check today or any day for Mathematicians who were born or died on that day.
The site is searchable in several ways, including the comprehensive index of History Topics.
Wishing educators and students everywhere a very Happy New Year.