## Posts tagged ‘calendar’

### Mathiest Fortnight of 2016

Monday, April 4, 2016, was Square Root Day, because the date is abbreviated 4/4/16, and 4 × 4 = 16. But if you’re a faithful reader of this blog, then you already knew that, because you read all about it in Monday’s post, Guess the Graph on Square Root Day.

But it doesn’t end there. It ain’t just one day. Oh, no, friends… this is a banner week. Or, really, a banner *two weeks*.

Tomorrow, April 8, 2016, is a **geometric sequence day**, because the date is 4/8/16, and 4 × 2 = 8, and 8 × 2 = 16.

And Saturday, April 9, 2016, is a **consecutive square number day**, because the month, day, and year are consecutive square numbers. Square number days, in which each of the month, day, and year are all square numbers — not necessarily consecutive — are less rare; there are 15 of them this year. But among them is 1/4/16, which rocks the intersection of square number days *and* geometric sequence days. (That’s right — I said “rocks the intersection.”)

And then Sunday, April 10, 2016, is an **arithmetic sequence day**, because 4, 10, and 16 have a common difference of 6. Though honestly, arithmetic sequence days are a dime a half-dozen; there are six of them this year.

Next Monday, April 12, 2016, is a **sum day**, because 4 + 12 = 16. Again, ho-hum. There are a dozen sum days this year, and there will be a dozen sum days *every year* through 2031.

And just a little further in the future is Friday, April 16, 2016, whose abbreviation is 4/16/16, and if you remove those unsightly slashes, you get 41,616 = 204^{2}. I’m not sure what you’d call such a day, other than *awesome*.

Admittedly, some of those things are fairly common occurrences. But, still. That’s six calendar-related phenomena in a thirteen-day period, which may be enough mathematic-temporal mayhem to unseat the previously unrivaled Mathiest Week of 2013.

Partially, this blog post was meant to enlighten and entertain you. But mostly, it was meant to send numerologists off the deep end. Mission. Accomplished.

You’ve endured enough. Here are some calendar-related jokes for you…

Did you hear about the two grad students who stole a calendar?

They each got six months!I was going to look for my missing calendar, but I just couldn’t find the time.

What do calendars eat?

Dates.

### The Math of Thanksgivukkah

Oish. Enough already.

I know it’s rare that Hanukkah and Thanksgiving coincide. But if one more person tells me that it’ll be another 70,000 years before this happens again, I’m gonna scream.

This may be the single dumbest statistic I’ve ever heard. Here’s why.

Consider some of the reasons that cause Hanukkah and Thanksgiving to coincide this year.

- Jews rely on the Shmuelian calendar for religious holidays, which is why Hanukkah seems to vary so greatly from year to year. It wouldn’t appear to vary quite so much if you followed the Shmuelian calendar, but if you’re like most of the world, you rely on the Gregorian calendar. (On the Shmuelian calendar, by contrast, it would seem that Thanksgiving varies a lot from year to year. For instance, Thanksgiving this year occurs on 25 Kislev, next year on 5 Kislev, in 2015 on 14 Kislev, and in 2016 on 23 Cheshvan.)
- The Shmuelian calendar has a 19-year cycle, while the Gregorian calendar has a (roughly) 7-year cycle. So you might expect that the calendars would coincide about every 133 years. And they sort of do. However, the last time that the first day of Hanukkah fell on November 28 was in 1861, two years before Abraham Lincoln declared Thanksgiving an official U.S. holiday in 1863.
- One year on Earth is approximately 365.25 days — but not exactly. In fact, it’s closer to 365.2422 days. That slight difference is about 11 minutes. Not a big deal, really, but over 400 years, the calendar would incur a discrepancy of about three days. That’s why Pope Gregory, in 1582, decreed that years divisible by 100 but not divisible by 400 would
**not**be leap years. But Rav Shmuel, who organized his calendar in the first century, didn’t have access to such specific solar measurements, so the Shmuelian calendar does not make similar accommodations.

Put all that together and — voila! — an amazing coincidence.

Because the Shmuelian calendar gains one day on the Gregorian calendar every 165 years or so — see the third bullet point above — it’ll be tens of thousands of years before they coincide again.

But here’s the thing. **It’ll never happen.** Not a chance.

There are lots of reasons why not.

**First,** Thanksgiving has been around for 150 years, but there’s no reason to think it’ll last another 70,000 years any more than the Romans should have thought we’d still be celebrating Saturnalia today. Countries and empires come and go, and so do their traditions.

**Second,** smart money says that when the Shmuelian calendar gets far enough out of whack that Passover no longer occurs in spring, there will be an adjustment. Or maybe there’ll be an adjustment to the Gregorian calendar first, for as yet unknown reasons. Or perhaps an entirely new calendar will appear on the scene. Who knows?

**Third,** zombies. Just sayin’.

Dr. Joel Hoffman gives a more detailed and eloquent description of Why Hanukkah and Thanksgiving Will Never Again Coincide over at *Huffington Post*.

**co·in·cide
**

*verb*

**1.**what you should do when it starts to rain

Speaking of things that coincide…

Parallel lines meet at infinity — which must make infinity a very noisy place!

An unfortunate coincidence…

The grad student stood up in his cubicle and shouted, “Why do things that happen to dumb people keep happening to me?”

And a funny coincidence…

After a long day of teaching, grading papers, and doing research for a paper, a mathematician headed to the pub where he was supposed to meet his wife. Seeing her across the bar, he walked up behind her, spun her stool around, and kissed her on the lips. She pushed him away violently, at which point he realized the woman wasn’t his wife.

“I’m very sorry,” he said. “I thought you were my wife. You look exactly like her.”

“You rotten, good-for-nothing son-of-a-bitch,” she said, and slapped him across the face.

“Funny,” he said. “You talk like her, too.”

### Mathiest Week of 2013

Can you hear it? That’s the sound of the awesomeness approaching.

It starts this Wednesday.

5/8/13

The month, date and year are consecutive terms in the Fibonacci sequence.

It continues on Thursday.

5/9/13

The numbers form an arithmetic sequence.

And then there’s Sunday.

5/12/13

That’s a Pythagorean triple.

Arithmetic sequence dates are a dime a dozen. In fact, there are six of them in 2013 alone. Pythagorean dates and Fibonacci dates are far more rare. There are only eight Pythagorean dates and six Fibonacci dates in the entire 21st century. To have all of them occur within a six-day span is incredible.

**How will you celebrate?**

### Is It Yours? It’s Not Mayan…

It’s December 21. You’re here. I’m here. So much for the prophecy of the Mayan calendar.

So, will someone please call Ms. Angelou and tell her she had it wrong?

Actually, the Mayan calendar never predicted the apocalypse. (Nor was it developed by Maya Angelou. Or Maya Rudolph. or Maya Lin. Or anyone else named Maya.) In truth, one cycle of the Mayan calendar is ending, so a new cycle is about to begin. It’s not a like a time bomb that will explode when the cycle ends. It’s more like the odometer of a car rolling over.

While I can forgive folks who misread the Mayan calendar, I have less patience for folks who misunderstand *our* calendar.

I recently received an email that stated the following:

This year, December has five Saturdays, five Sundays, and five Mondays. This will only happen once every 824 years.

Oish. Really? I wish that folks who forward this kind of nonsense would, at a minimum, look at a calendar. (At a maximum, I wish they would lose my contact info.)

The good folks at www.timeanddate.com will gladly show you the calendar for December of any year you like. And if you look at the calendar for December in 2018, 2029, 2035, 2040, 2046, 2057, 2063, 2068, 2074, 2085, 2091, 2096, or any of 105 other years within 824 years of today, you’ll see that they all have five Saturdays, five Sundays, and five Mondays. Consequently, it doesn’t seem that December 2012 is terribly special.

The folks at www.timeanddate.com also have a nice explanation of why the math in the email that I received is all wrong (though their article is based on July 2011 which had five Fridays, five Saturdays and five Sundays, and they disprove an argument saying that such an occurrence happens once every 823 years; but, whatever).

I suspect that most folks are unaware that our calendar repeats in a 28‑year cycle. And I’d bet that even fewer realize there is a nice pattern of 6‑11‑6‑5 years when the calendar repeats… assuming you skip those nasty century years, like 1900 and 2100, that fail to include a leap day.

Still, I think most reasonably intelligent humans should recognize that a claim like “only once every 824 years” has to be an exaggeration.

But perhaps that’s the problem: I’m assuming that people who forward emails like this are reasonably intelligent.

Along similar lines, here’s a math trick that I’ve received several times via email:

- Take the last two digits of the year in which you were born.
- Now add the age you will be this year. (That is, if you’ve already had your birthday this year, add your current age. If you haven’t, add the age you’ll turn on your birthday this year.)
- The result will be 112 for
*everyone in the whole, wide world*.

There’s only one problem with this trick: It doesn’t work.

For someone like Besse Cooper, who was born in 1896, the result will be 212.

For someone like my twin five-year-old sons, who were born in 2007, the result will be 12.

In fact, the trick won’t work for anyone born before 1900 or after 2000. Based on data about age distribution, the result will not be 112 for approximately 15% of the U.S. population. The yellow bars in the graph below indicate the ages for which this trick does not work.

A better statement of this “trick” might be…

- Take the year in which you were born.
- Now add the age that you will be this year.
- The result will be 2012 for everyone in the whole, wide world.

Completely correct! But not much of a trick anymore, is it?

### The Ides Have It

When my sons woke up today, I told them, “Beware the Ides of March.”

To which Alex responded, “What are ides?”

I explained that the ides are roughly the middle day of the month. But then Alex asked why the ides was the 15th of March instead of the 16th, since March has 31 days.

“I don’t know.”

Nor do I know why the word *ides* is used to refer to this date. It comes from the Latin word *idus*, which can be translated to — yep, you guessed it — the English word *ides*. Nor do I know why *ides* is singular.

I also don’t know why the ides of March, May, July and October occur on the 15th day, but the ides of every month occur on the 13th day. But it does lead to a fun math problem for a four-year-old to figure out:

What is the maximum number of days between the ides in consecutive months?

The following calendar may help you figure this out.

Here are some math jokes related to things in the middle:

A circle is a round straight line with a hole in the middle.

What was Zeno of Elea’s middle name?

Of.

And all this talk of ides made me think of a really stupid joke from a really stupid joke book that I read when I was in elementary school. (That was a long time ago, hence the dated references, but maybe some of my older readers will appreciate it.)

If a woman named Ida married Dan Rather, got divorced, then took Bill Knott as her second husband… she’d be Ida Rather Knott.

### What Dates are Mathier than Pi Day?

While I am grateful that Pi Day gives some much-needed publicity to math, it’s a contrivance like textbook problems about two trains approaching from opposite directions. (Honestly, rather than spend your time determining how long until two trains on the same track collide, why not use that time to inform someone about the imminent collision?) Other than containing the same digits that appear in 3.14, there’s nothing terribly special about 3/14. And it propagates the widely held belief that π is only known to two decimal places.

That said, the cultural significance of Pi Day cannot be overstated. (Or maybe it just was?) Consequently, there are **six cool Pi Day cards at Illuminations** for you to share with friends via Facebook, Twitter, and Pinterest, or download them and include them in an email, on your website, or in a blog post. This one is my favorite:

Recently, there has been a movement to replace π with τ = 2π. (See The Tau Manifesto.) That would suit me just fine, and then we could celebrate Tau Day, which occurs on the more mathematical date 6/28. In addition to 6.28 representing the value of 2π (to two decimal places, anyway), it is also the case that both 6 and 28 are perfect numbers (the sum of their proper factors is equal to the number itself), and this year the value of the month, date and year of 6/28/12 are all even.

Please understand, my disdain for 3/14/12 is not personal. It’s just that other dates this year are, well, *mathier*.

Christmas Eve is one of those mathier dates…

- When written as 12/24/12, all of
*mm*,*dd*and*yy*are even. *mm*+*yy*=*dd*- Each of the digits within the date (1, 2, and 4) are powers of 2.
- The sum of the digits is 1 + 2 + 2 + 4 + 1 + 2 = 12, and 122412 ÷ 12 = 10,201 = 101
^{2}.

…as is the ninth of June…

- The numbers 6, 9, 12 form an arithmetic sequence.
- All three numbers are multiples of 3.
- The month (6) is a perfect number, the date (9) is a square number, and the year (12) is the smallest abundant number.

What do you think is the mathiest date of 2012? And what criteria do you use to determine if a date is mathy?