Leap Day Birthday Math

Posted on February 29, 2012 by Mr. Chase

Happy leap day!!!

Here are some leap-day birthday thoughts I discussed with my colleagues and students today:

What’s the probability of a leap year birthday?

The probability that someone is born on a leap day is $\frac{1}{365\cdot 4+1}=\frac{1}{1461}\approx 0.000684$ . Oh wait, that’s not completely true. Leap years don’t really occur every four years. Years divisible by 100 are not leap years, unless also divisible by 400. So, the actual probability is

$\frac{100-4+1}{365\cdot 400+100-4+1}= \frac{97}{146097}\approx 0.000639$ .

What’s the probability of having triplets on a leap day?

One of our RM students is a triplet, born today. What are the chances of that occurring? Well, the statistics on triplets are pretty hard to get right. But let’s say the occurrence of a triplet birth is 1 in 8000. (That’s my informal estimate based on this site and this site.) I think we can say that the probability of being a triplet is 3 times that (right?). Then, the probability of being a triplet born on a leap day is

$\left(\frac{100-4+1}{365\cdot 400+100-4+1}\right)\left(\frac{3}{8000}\right)= \frac{291}{1168776000}\approx\frac{1}{4016412} \approx 0.249 \times 10^{-7}$ .

The current US population is 311,591,917, so that means there are roughly 77 triplets in the US with leap day birthdays. Happy birthday to all of you!

Bonus thought question: Iif you have quadruplets born on a leap day, you get to celebrate 4 birthdays every four years, so doesn’t that average out to one birthday a year?

Half-birthday for those born on August 29

One of my other colleagues has a birthday on August 29th. So today is her half birthday! But it only comes around every four years (roughly). Hooray!

But then that got us thinking about half birthdays: Some people, like those born on August 30th or 31st NEVER have a half birthday. How sad!! This happens to anyone born on August 30th, August 31st, March 31st, October 31st, May 31st, or December 31st. That’s a lot of people without half birthdays.

But wait. When is your actual half birthday? Shouldn’t it be 182.5 days before/after your birthday? That’s not necessarily the same date in the month. For instance, my birthday is May 15. So my half birthday should be November 15, right? Wrong. My half birthday is (May 15 + 182.5 days), which is November 13th or November 14th, depending on if you round up or down. Even accounting for a leap year, it’s still not quite right.

Who else is miscalculating their half birthday? Unless your birthday is in June, April, October, or December, you’re half-birthday isn’t what you think it is. To calculate your half birthday, use this amazing half birthday calculator I just discovered!

Nanoseconds explained

Posted on February 28, 2012 by Mr. Chase

Hat tip to Hackaday for this one. It turns out that a nanosecond is the time it takes light to travel 11.8 inches. A very handy rule of thumb to have around as you explain large distances and small times.

Good discussions in the math blog world

Posted on February 27, 2012 by Mr. Chase

Here are two blog posts I saw a few weeks ago. I’ve been following the comments with great interest, and the conversations have been fruitful. You should go check them out and join the conversation!

Critical Thinking @ dy/dan — Once again, Dan gives deserved criticism to a contrived textbook problem. Hilarious problem, and fun discussion in the comments.
Disagreement on operator precedence for 2^3^4 @ Walking Randomly — The title says it all, but it’s the first time I had ever thought about how 2^3^4 or expressions with carets should be evaluated. Note that it’s clear how $2^{3^4}$ should be evaluated. We’re just unclear on how 2^3^4 should be evaluated.

Terrible trig humor

Posted on February 15, 2012 by Mr. Chase

*Groan*

[ht: Tim Chase]

Flipped Classroom in action

Posted on February 13, 2012 by Mr. Chase

We’ve talked about the ‘flipped classroom’ model a couple times on this blog. Here’s a nice example of a teacher doing this in real life. It looks like it’s working for him and his students!

Here’s a link to the full article, though the video does a nice job summing up the article.