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Today's date (in America) is 12/13/14.
**NERD ALERT**
We've had sequential dates like this once every year for the past 11 years, since January 2nd of 2003. We will not see this particular date sequence type again until January 2nd of 2103. That's 89 years away, so most of us won't live to experience it.
However, in Europe the date is ordered day/month/year, so today is nothing special for them. They experienced their last sequential date like this last year on December 11th (11/12/13 in Europe) and won't see this date sequence again until February 1st of 2103. For Europe, that's a difference of 90 years.
But the Gregorian calendar is not the only calendar people use, it's just the most popular. In other calendar systems, today ain't any more special than any other day.
Sequences and series are a part of mathematics that is usually taught in calculus. But is based on the natural human ability to notice and use patterns.
Most common sequences are either arithmetic (adding the same number each time) or geometric (multiplying the same number each time), or a combination of both, and can easily be described with a function. Here is an example of an arithmetic sequence:
1, 4, 7, 10, ...
Can you guess the value being added each time?
Here is an example of a geometric sequence:
2, -6, 18, -54, ...
Can you guess the value being multiplied each time?
Here is another example of a (famous) geometric series:
1, 1/2, 1/4, 1/8, ...
Can you guess the value being multiplied each time?
Sometimes these series approach a particular value (convergent) and sometimes they do not (divergent).
If we add the values in order in a sequence, we get a series. Series can also be convergent or divergent.
One of the most famous sequences is the Fibonacci sequence, whose first few elements are: 1, 1, 2, 3, 5, 8, 13, ...
This sequence is nonstandard because to get the next element you add the two elements preceding it; so to get the next one in my list, we have 8 + 13 = 21. It is neither geometric nor arithmetic.
A related sequence is the list of each Fibonacci number divided by the one before it:
1, 2, 3/2, 5/3, 8/5, ...
Which converge to one value, an irrational number called Phi (rhymes with "tea," not "tie") or the Golden Mean, which folks used to think had some magical and divine powers. It is equal to about 1.618 ish and along with the Fibonacci sequence, is found throughout nature.
It is remarkable how powerful the human mind is, that we have an innate ability to notice patterns and use them. It is one of the many reasons why mathematics is a human ability.
**END NERD ALERT**