**Here are just a few of the mathematically special dates in 2016. I hope you’ll have fun celebrating them – I know I will!**

**1. Pi Day 2016 !!** We might as well start with what we called *last year* the * ONCE IN A CENTURY *date! As you may remember, the common decimal approximation for

*pi*is

**3.14**. So March 14 (

**3/14**) (which also happens to be Einstein’s birthday!) is called

*Pi Day*and is actually celebrated

*every year.*But, if you carry pi’s decimal expansion (3.1415926535 . . . going on forever without repeating!) a little further for your approximation, you get

**3.1415**– which was GREAT last year!! BUT, if you

*round*the approximation above to 4 places, you would get

**3.1416.**So, on Pi Day

*this year*(3/14/16), there you could almost have just as big a celebration as last year. 🙂 Mark your calendar now! 🙂

**2.** **Days involving Powers and Exponents. **Since the last two digits this year are 16, and since 16 is equal to * both *2^4 (2 x 2 x 2 x 2)

**4^2 (4 x 4), this lends itself to lots of nice patterns with exponents. (See also 2.5) We’ve shared one of them already, namely**

*and***1/4/16**, which is 2^0/2^2/2^4 (consecutive even exponents. Another will be

**4/8/16 (2^2/2^3/2^4, consecutive exponents)**. In fact,

*any date*this year with only 1’s, 2’s, 4’s and/or 8’s for the month/day will be some kind of ‘powers of 2 day’.

**2.5 Base/Exponent Day: Feb 4 (2/4/16) and April 2 (4/2/16). ** In each case, the *month* raised to the power of the *day* equals the *year. *These are pretty rare**. **The phenomenon won’t happen again until 2025. (What day?)

**3. Perfect Square Day This is somewhat similar to #2 above. On April 4 or 4/4/16. Since 4 x 4 = 16, 16 is the perfect square of 4.**

**4. Year-Product Days: Jan 16, Feb 8, Apr 4, and Aug 2. ** Also similar. Look carefully at these four dates (1/16/16, 2/8/16, 4/4/16, and 8/2/16), and you’ll note that the *product* of the first two numbers (mo/day) is the third one (year). These are called “Year – Product Days”, and this is the first year we’ve had (at least) FOUR of them since 2012 (when there were 6!) .

**5. Consecutive Multiples of 4 Day: Aug 12. **That day – 8/12/16 – is composed of three consecutive multiples of 4. We haven’t had one of these since April 8, 2012 and we ** only have one more this century! ** (What is the day? Why is that the last one?)

**6. June 28 – The BEST mathematical day each year! ** We did this last year, but this is MY favorite numerical day *each year*. There are TWO reasons to celebrate 6/28, each one significant!

*each year*

**A. 6/28 is** **2-PI Day** (Take 3.14 or 3/14, and double each number). Note that there is no 3-PI Day or any other similar multiple. (Why?)

**B. 6/28 is the only day each year** where the month (6) and day (28) are different perfect numbers!! (For a quick review of perfect numbers, visit the **July14 Math Tidbit** and note the material in red font. Visiting this link will also remind you why July 28 is special each year as well.)

**7. Over 300 others!** I mentioned that I happen to believe *every* day is special. If you’re so inclined, send in your birthday – or any other favorite – date, and I’ll let you know why it’s special! 🙂 [I’ll respond directly and -with your permission – possibly list it in a future mailing.]

A quick comment on consecutive multiples of 4 days. The next one after 8/12/16 will, in fact, be the last one ever. In addition, it will occur on the 250 anniversary of the birth of Ludwig van Beethoven, whose Fifth Symphony (1st movement) is arguably the most famous musical motif, and that motif is a simple 4 note motif.

Wow, Cameron! what a neat juxtposition of facts!! Thanks for sharing!

Oops, the next one is not the last one ever–forgot that dates only use the last two digits of the year. But the bit about Beethoven is still true.

I was going to make a comment on that, but you beat me to it! 🙂

Thanks again, Cameron!