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Leap Day, 2016

February 29, 2016

Today is February 29.  A day that only occurs every 4 years, or does it?

Dr. Jeffrey Boats, chair of Mathematics adds this mathematical perspective:

First of all, the rule is that a year is a leap year if it can be divided by four -- but with one exception.  If the year can be divided by 100, but not 400, then it is a regular year with no leap day. 

As a result, there are 97 leap years every four centuries. 

The year 2000 was a leap year, but 2100, 2200, and 2300 will not be.  The year 2400 will be a leap year, and the cycle will renew.

The reason for this is that the length of time it takes for the Earth to orbit the Sun, which is what a year is, is not 365 days. 

It's actually a little bit less than 365-and-a-quarter days. 

If it were exactly 365-and-a-quarter, then having a leap year every four years would be fine.  However, the Earth's orbital period is a little less, we need the exception rule -- to take back three leap years every four centuries, as a correction. 

This correction still isn't quite precise enough for the impeccable measurements necessary for astronomy, so there are occasionally "leap seconds" added to December 31st of certain years.

One weird side effect of the leap year rule is that certain days of the week are more likely to be leap days than others. 

Monday and Wednesday leap days happen 15 times every four centuries, while Friday and Saturday leap days happen 14 times per four centuries. 

The rarest leap days are Tuesday, Thursday, or Sunday leap days, each of which happen only 13 times per four centuries. 

Proving this (efficiently) requires an elementary understanding of an area of mathematics called Number Theory.

There are a lot of superstitions around the world about leap days and leap years. 

But as any mathematician will tell you, a number is just a number.  A day is just a day.  Is there really, truly, scientifically ... anything special at all about February 29th?

Only this:  the sporadic existence of this day on our calendars represents our ability to recognize scientific truths of the universe, to understand their significance, and adapt.

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