Archive for the 'mathematix' Category

Gifted

gifted.jpgWe haven’t done one of these “flix” category reviews for a long time. We both watched the “Gifted” DVD and enjoyed it very much.

While this flick has all the ingredients intended for a family audience, it also targets those of us who have experienced higher levels of mathematics associated with our jobs or avocations. The latter subject matter doesn’t bog down the family aspect of the story as it keeps moving. There is also some brief comedy in the characters banter and actions.

The presentation of a gifted seven-year old girl’s complete grasp of differential equations and the Calculus was well done. I wonder if it is actually possible for an individual of that age to “get” differential or transcendental equations? Regardless, it was an entertaining movie to watch.

The IMDB Storyline follows:

Frank Adler (Chris Evans) is a single man raising a child prodigy - his spirited young niece Mary (McKenna Grace) in a coastal town in Florida. Frank’s plans for a normal school life for Mary are foiled when the seven-year-old’s mathematical abilities come to the attention of Frank’s formidable mother Evelyn (Lindsay Duncan) whose plans for her granddaughter threaten to separate Frank and Mary. Octavia Spencer plays Roberta, Frank and Mary’s landlady and best friend. Jenny Slate is Mary’s teacher, Bonnie, a young woman whose concern for her student develops into a connection with her uncle as well.

Happy PI Day

pi.pngToday is March 14, 2015. This day, 3/14, is celebrated internationally as PI DAY. The transcendental and irrational constant of PI is the ratio of the circumference of a circle to its diameter, or 3.14 and a bunch of digits thereafter.

When I was a kid, back when computers were housed in buildings rather than handheld devices, we roughly calculated PI by using the fraction 22/7, or 3.142857142857, a rational approximation accurate to only two decimal places. Later, in the early days of four-function handheld calculators, we, as engineers, used the fraction of 355/113, or 3.141592920354, accurate to six decimal places. Or, we would use the memorized figure of 3.14159265 for eight decimal place accuracy. That was good enough for most government work, literally.

Nowadays, with supercomputers, the transcendental ratio can be calculated to billions of decimal places which is necessary for modern applications like calculation of orbits or ICBM trajectories to the required accuracy. In modern culture, March 14 has become a nerd holiday.

From the PI day Website:

Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.

Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits.

Pendulum Waves

The explanation for this is at Harvard.edu

Universal Triangle Solver

Several years ago, the project I was working on required me to become proficient with Perl, the programming language commonly used to implement Common Gateway Interface applications. I signed up for a Perl class that my employer offered. One of the requirements of the class was to develop a project using Perl. I chose to develop a universal triangle solutions application, which I now share with you.

The instructions are below the fold . . . Continue Reading »

Mouse Gun

I was looking for a miniature gun and this image of a gun-shaped computer mouse came up in the search results. I thought it was kind of funny.

I found what I was looking for, though, in a site called mouseguns.com. There, you can find a link to a catalog of diminutive weapons. The guns are listed with details as to their attributes:

gun-mouse.png

  • Lethality
  • Volume
  • Manufacturer
  • Model
  • Caliber
  • Capacity
  • Type
  • Action
  • Length
  • Height
  • Width
  • Weight

According to the website, “Lethality” is derived from capacity and power:

Lethality = log (capacity) * power

I had not seen a lethality index before, but I found it very intriguing. A table on the page lists ammunition power from 1 for .22 short to 14 for 12 gauge. I attempted to work up lethality for a couple of our favorite guns, but ran into problems when I tried the above equation and got different results. I could get into the same order of magnitude by substituting natural log (initially assumed log base 10) but the results are still off.

Example: The listing for a Glock 26 lethality is 32.26; when using natural log, I calculate 21.58. The capacity is 11 rounds (10+1) and the power listed in the table for 9mm is 9.

Ln(11) = 2.397 * 9 = 21.58

The error between my calculation and that listed is off by about 30 percent. I may try and email the author of the table to see where I’m going wrong (or where he did). I’ll post any findings if and when I get feedback.

I saw an abstract of a study that listed body armor threat level for various firearms, but was not interested in paying to see it. Has anyone else seen a firearms lethality index?

At any rate, I would be inclined to change “Lethality Index” to “Self Defense Potential Index” when it comes to scoring firearms with regard to caliber and capacity. I would also score the projectile type (HP vs. ball, shot vs. slug).

‘Tis the Season . . .

taxcaster.jpg . . . either to be jolly, or to get a head start on your taxes - which currently is canceling out any jolliness the holidays might have generated for me.

I set out this morning to do a budget forecast for 2010. This is important since it will be my first full year of retirement and I need to set up distributions and withholding.

Throughout the day, I studied our spending habits, our real estate holdings, our potential income and all the little things that might happen to us that cost money. I used an Excel spreadsheet to analyze our special circumstances.

The odious task of how much I should withhold for the clowns in Washington and Sacramento to waste on their nonsensical pork projects depends on a forecast of next year’s tax liabilities. I found an on-line 2009 tax estimator at the TurboTax website, so I used it to forecast how much 2010 tax I should withhold. No problem, it did that just fine.

Then I opened Pandora’s Box - I doodled in the numbers for our 2009 return which I haven’t started.

OH SHIT!

Nothing like seeing a preview of the tax bite to blow away any holiday spirit I might have had. Oh well, I’ll just re-watch Bad Santa - some gratuitous blue humor dressed as the holiday spirit should lift mine.

By the way, the little TaxCaster® thingy is handy and easy to use. The image above is clickable for a close-up.

Cranking the Numbers

rpn-planner.jpgI’ve been doing a lot of financial planning over the last several years, for obvious reasons (retirement). It pays to “do the math,” to invoke a trite expression.

There are a number of on-line sorts of tools provided by your favorite financial institutions, but sometimes it is necessary to do some more personal budgeting and planning. That’s when the old fashioned calculator comes in handy.

It seems funny to call a calculator “old fashioned,” but, it’s true. After the first “Bomar Brain” calculators appeared in the early 1970s the technology skyrocketed. Everything “hot” quickly became “not.” The best part of it was the prices kept dropping even as the technology improved.

I got hooked on Hewlett-Packard “Reverse Polish Notation” calculators. I don’t have a dedicated calculator anymore, but I have a dead-ringer for an HP for my PDA called Math-U, from Creative Creek. On the desktop or laptop, I use “Excalibur,” a functional equivalent, although not a look-alike to the HP series.

OK - so what am I budgeting with all these fancy tools? Our guns and ammo habit, of course. Like how many rounds per month we can afford to keep in practice or how much can we set aside for the shiny new pistol, AR or who knows what else? I’ll keep cranking the numbers and get the job done.

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