A colleague of mine recently mentioned something to me about an article that circulates every year during the holiday season, entitled “The Physics of Santa Claus”. This was news to me, so I ran a few Google searches to find out what she was talking about.

It seemed that some enterprising person had taken the time to go through and explain just what is involved in Santa’s Christmas Eve trip around the world delivering presents. How many households does he have to visit? How much do all those presents really weigh? How fast do the reindeer need to fly in order to get it all done in a finite amount of time? There is much speculation as to the origins of this piece; the general consensus seems to be that it began life published in SPY magazine in the early 1990s. Whatever the true story, it’s still an entertaining read in 2008.

I’ve taken some time to update the original with more current data – for instance, it seems the world’s population has grown a bit in the last 20 years. According to the Population Reference Bureau, the world population in 2008 was approximately 6,705 billion; 28% of these are children (defined as being under 15):

In fact, making some assumptions about the percentage of these children that celebrate Christmas and the number of children per household, it turns out that Santa needs to visit close to 200 million homes in one night.

We assume he distributes gifts from 5 pm to midnight, or for 7 hours. Due to the Earth's rotation, there is an overall time difference of 24 hours between different time zones, so we can therefore say that Santa has 31 hours to finish his work (assuming he logically travels east to west). Visiting 200 million homes in 31 hours means that Santa has to visit approximately 1586 homes per second:

This gives him about 1/1600th of a second to do everything at each home, such as parking his sleigh, looking for the right gifts, climbing down the sleigh and chimney, binge on snacks, fill the stockings, come up again and rush to his next stop!

For the complete details of his annual trip, visit the Applications Center where I’ve posted the Maple document in which I’ve recreated the Santa calculations. Happy Holidays!!

We are happy to announce Maplesoft's latest solution for modeling and simulation is now available!  For those of you who are not familiar with the product, it is a high-performance multi-domain modeling and simulation tool which will revolutionize how you bring products to market.

To learn more about MapleSim follow this link.

Recently, I was reading about random.org again.  It is an online random number generating service that uses atmospheric noise gathered from radios tuned between stations as a source of randomness.  It has been running more or less continuously for about ten years.   On their analysis page there is a nice pair of bitmaps (scroll down past the Dilbert comic) that contrast their random bits with those from one version of the PHP rand() function. Basically this demonstrates how easy it is to create a pseudo-random number generator that is periodic with too small of a period.

I decided to take a look at Maple's random number generator in comparison.

The attached work sheet teaches you the fundamental concepts behind the antiderivative.

The examples in this worksheet are entirely done in an interactive video tutorial - follow the link below:

 (Ctrl+Click on the link to view the video)

Antiderivatives - Video Tutorial

Enjoy!

The attached worksheet is a wonderful introduction to the concept of obtaining the area under a curve.

You'll see how easy it is to learn how to find the limit of the sum of a series using Maple.

An interactive video tutorial that shows you how to do Riemann sums really fast is linked below:

(Ctrl+Click on the link to view the video)

Riemann Sums...

In this previous post, an example is shown that demonstrates the potential problems that can arise following symbolic conversions such as from sqrt(x^2)  to x^(1/2).

Here x is an unknown symbol. The difficulties include the fact that, while `sqrt` can be smart about simplifying numeric values (eg. integers, rationals) the `^` operator has no such opportunity. Once the conversion from `sqrt`...

The attached Maple worksheet gives an outline of the basics of Concavity, Points of Inflection and the Second Derivative Test, commonly encountered problems, and how to use Maple to solve them.

The attached Maple worksheet gives an outline of the basics of increasing and decreasing functions, commonly encountered problems, and how to use Maple to solve them.

Download Attached File

The attached Maple worksheet gives an outline of the basics of limits, commonly encountered problems, and how to use Maple to solve your limit problems.

Download Attached File

Everybody is invited to Maple Wiki .

It is hosted on Maple Advisor, a Maple community site independent of Maplesoft and/or Mapleprimes.

The site has started just a couple of days ago and doesn't have much of a content yet.

Suppose you want to solve a large dense linear system AX=B over the rationals - what should you do? Well, one thing you should probably not do is directly apply Gaussian elimination. It does O(n^3) arithmetic operations, but the size of the numbers blow up, leading to an exponential bit complexity. Don't believe me? Try it:

with(LinearAlgebra):
for N from 5 to 9 do
  A := RandomMatrix(2^N, 2^N+1,generator=-10^5..10^5):
  TIMER := time(GaussianElimination(A...

We are pleased to announce that Maple 12 is now available.  It has some very cool new features - my personal favorites include the addition of polar plots, nifty new dials and gauges, a start-up code region, and the ability to use colour in table cells.  Check out our website to find out what’s new, to watch Maple 12 movies in the new , for full details on upgrade specials and more.

We are pleased to announce that Maple 12 is now available.  It has some very cool new features - my personal favorites include the addition of polar plots, nifty new dials and gauges, a start-up code region, and the ability to use colour in table cells.  Check out our website to find out what’s new, to watch Maple 12 movies in the new , for full details on upgrade specials and more.

Because of John's answer to my last comment about a Maple wiki, I have searched first for antecedents in Maple Primes. From the many posts found in this search, I put together here what I consider the main points stated so far.

Oficial plans + technology:

http://www.mapleprimes.com/forum/how_do_we_grow_this_site

As Demmel and others have noted, SVD is both more reliable and more expensive than QR as a method of solving rank-deficient least squares problems.

SVD is the method that LinearAlgebra:-LeastSquares will choose when the Matrix has more columns than rows (n>m), unless instructed otherwise using the optional 'method' parameter.

LinearAlgebra:-SingularValues always computes a full U and Vt. But for least squares computations, such as when n>m, this is not necessary. Including the smaller singular values may just be (re-)introducing noise. See here for more detail.

Here's a 20x2000 example, using wrapperless external calling and the SVD routine dgesvd in the CLAPACK library. The effective speedup by using the Thin SVD for that 20x2000 least squares example is about a factor of 100 (ie, 2000/20), with a similar reduction in additional memory allocation.