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Archive of posts filed under the Numbers category.

10/26/2016 — Happy Permutation Day!

Today we celebrate a Permutation Day!  I call days like today permutation days because the digits of the day and the month can be rearranged to form the year.

10262016

We can also consider today a Transposition Day, as we need only a single transposition (an exchange of two numbers) to turn the year into the day and date.

Celebrate Permutation Day by mixing things up!  Try doing things in a different order today.  Just remember, for some operations, order definitely matters!

9/25/16 — Happy Pythagorean Square Day!

Happy Pythagorean Perfect Square Day!

9-25-16

We’ve had a lot of fun dates this year:  several Geometric Mean Days, several Square Days, and even a Power of 2 Day!  But I’m pretty sure that the numbers of dates all being perfect squares and satisfying the Pythagorean Theorem is the rarest of them all!

9/12/16 — Happy Geometric Mean Day!

Happy Geometric Mean Day!  The geometric mean of two numbers and b is

\sqrt{ab}

which makes today a Geometric Mean Day!

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A consequence of this is that the numbers in today’s date form a geometric progression

9 *\frac{4}{3} = 12 and 12 * \frac{4}{3} = 16

and here is one way to visualize that relationship

20160912-geometric-mean-day

 

06/21/2016 — Happy Derangement Day!

Today we celebrate a Derangement Day!  Usually I call a day like today a Permutation Day because the digits of the day and month can be rearranged to form the year, but there’s something extra special about today’s date:

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The numbers of the month and day are a derangement of the year:  that is, they are a permutation of the digits of the year in which no digit remains in its original place!

Derangements pop up in some interesting places, and are connected to many rich mathematical ideas.   The question “How many derangements of n objects are there?” is a fun and classic application of the principle of inclusion-exclusion.  Derangements also figure in to some calculations of e and rook polynomials.

So enjoy Derangement Day!  Today, it’s ok to be totally out of order.

06/12/2016 — Happy Permutation Day!

Today we celebrate a Permutation Day!  I call days like today permutation days because the digits of the day and the month can be rearranged to form the year.

06122016

This is our third Permutation Day of the year, and we’ve got a few more coming up.

Celebrate Permutation Day by mixing things up!  Try doing things in a different order today.  Just remember, for some operations, order definitely matters!