It's been too long since I've talked about the performing of actual math and memory feats!

Over at Madsen Blog, you can learn how to memorize the periodic table of the elements. This does need some qualifying. First, this technique focuses on only the most common 72 elements, neglecting the elements that have only been created briefly and viewed only in particle accelerators. Second, it only helps you remember in which column a particular element falls. If you are familiar with the peg system, you can memorize the periodic table of the elements in greater detail using this approach.

Moving from memory to math, Lindz's Blog shows you 6 ways to become a human calculator! Many of these feats have appeared here at one time or another, but both new and old readers will still enjoy these amazing math feats.

Yes, Carnival of Mathematics fans, it's that time again!

Over at Polymathematics, we have the 13th Carnival of Mathematics. Grey Matters readers will especially be interested in the posts called Students at the Zoo and Puzzle: Random Blocks.

The next carnival will be at Vlorbik on August 10th!

It's time again to have some fun with your grey matter!

I'll start out with Proximity (Flash required). This is similar to Reversi/Othello, but with a mathematical twist. Each piece placed on the board can be either red or blue, and will have a number on it. If the number is the largest among the adjacent pieces, it will change all the adjacent pieces to its color. If any adjacent piece has a larger number, it will change to the color of that piece. The challenge is to wind up with more pieces of your color than your opponent's.

If you enjoyed my post on the states, you might want to challenge yourself with Statetris (Flash required). Statetris, as the name suggests, is similar to the now-classic Tetris, but you're using US states instead of tetrominoes. You can play on 3 levels: Easy, in which the states are labeled and correctly oriented, Medium, in which the states are labeled but not necessarily oriented correctly, and Hard, in which the states aren't labeled and aren't always oriented correctly.

The most addicting and challenging game of the group is Gravity Pods (Flash required). Using your arrow keys and space bar, you have to aim to shoot the purple orb, with only a limited arsenal. Initially, this is very simple and straightforward. Starting at level 4, however, you have to start taking the physics of the Gravity Pods into account, which pull your missile off course. As you progress, you have to learn how to shoot around walls, use movable and multiple Gravity Pods and much, much more! Try working your way through all 50 levels.

Finally, we have a memory game for iPhone and Safari users. This version of the classic Simon game is called Lumina. The graphics are gorgeous, and also amusing. When you fail to remember the sequence of light correctly, the button shatters very realistically. I can imagine an iPhone user being quite easily shocked the first time they experience this.

That's all for now, so go and have fun!

Having talked about when businesses can't do math, let's turn our attention to businesses that can do math.

It's always good when the math is done properly, unless the business is counting on you not doing the math.

The most common place to find this practice is among businesses that are loaning you money. If you have credit cards, there's two money traps you may already be in without realizing it. First, there's the minimum payment trap. JLP at AllFinancialMatters runs the numbers on a $5,000 debt, on making the minimum payment versus paying $100 every month. The results are startling!

The other trap is two-cycle billing. This is when your average daily balance is calculated over the past two months. This is less common, but it is out there. JLP explains this is greater detail, but it all boils down to the fact that you're effectively paying interest on money you've already paid back.

Probably the most eye-opening case of a business hoping you don't do the math are the payday loan places, such as CashCall.com. Have you ever seen this ad or this ad for CashCall? Watch them again, and look harder at the fine print at the end of the ad.

Get Rich Slowly took a closer look at these outrageous interest rates, and discovers some troubling facts.

Another way to draw your attention away from the math is to focus on features other than the costs. With environmentalism being such a hot topic right now, this has become a popular way to get a mathematical advantage.

For example, which is a better deal: The gas-powered Toyota Corolla that gets 33 MPG, or the Toyota Prius hybrid that gets 55 MPG? Most people would say that the environmentally-correct Prius, but when the numbers are run, the Corolla proves to be the better financial value!

Over at the Motley Fool's UK branch, they discuss environmentally-friendly financial products. A close examination of the numbers find that these products often cost so much more extra money that you can often do better by putting your money into a non-environmental alternative. With the money you save, you can put the extra money into environmental alternatives over which you have more direct control.

Lest these numbers discourage environmentalists, the UK Motley Fool reminds us that it is possible to save money while being green.

Neither this post nor the previous one were meant to scare you away from businesses. The entire point is to give you an idea of how easily the numbers can work against you, and to help remind you to be aware that extra time investigating the costs of your purchases may be the best thing you can spend.

Late last year, I discussed Verizon's math difficulty. Verizon is far from a unique case, however.

To be fair, before moving on to other businesses, I should mention that Verizon has now fully refunded the customer.

However, that doesn't mean the same problem won't happen again. Already, over at Celebrity Cruises' Staying in Touch page, you can see a similar problem starting. Their default package for internet access aboard their cruise ships is, “$0.65cents a minute.”[sic] Saying $0.65 cents is like telling someone that a package weighs 65 grams in kilograms. It makes absolutely no sense.

Looking at the other rates for context does at least help here. You can get $40 for 75 minutes, which is a decent deal if internet access otherwise is $0.65 per minute (which would come out to $48.75 for 75 minutes). If they actually meant 0.65 cents per minute, then 75 minutes would cost less than 50 cents, and be a far better deal than $40!

Unfortunately, not every math error is so blatant. Imagine you're shopping for 2 DVDs, each of which are $29.99, and you discover the store has a “Buy 1, Get 1 Free” sale. You would expect to pay $29.99 plus tax for the two, correct? One DVD buyer got only 30% off, instead.

Did that last mistake seem too easy to catch? OK, we'll try another one.

In this one, you order a 12-inch pizza for you and your friends. The waitress comes by, explains that your 12-inch pizza was accidentally given to someone else, and apologizes. For the error, she offers the 8-inch pizza she has now, plus a second 8-inch pizza at no charge. Which is the better deal for the same money, the 12-inch pizza or the two 8-inch pizzas? If you need a hint, I'll refer you to the Pizza Theorem.

To find out the answer, I'll refer you to a post by someone who actually faced this decision, entitled, Geometry Saved Me Money.

Sometimes, the error isn't in the cost itself, but in the comparison. Both Quicken Loans and the Gerber Life Grow-Up Plan have fallen prey to this type of error.

Math errors can work both ways. In the next part of this article, I'll discuss businesses who can do the math, but hope that you cannot.

Attention, Carnival of Mathematics fans! The 12th Carnival of Mathematics is up over at the Vedic Maths Forum India Blog!

Regular Grey Matters readers will especially enjoy the entries on Sudoku and graph theory and mnemonic abbreviations.

When creating any type of performance, you need to keep in mind how you want your audience to feel. Deciding what emotions are your goal, and structuring your performance accordingly, can be a major challenge.

This time last year, I discussed Dramatica, a tool for creating logically and emotionally comprehensive stories. James Hull, a regular Dramatica user, discusses various aspects of storytelling as it relates to the software in his Daily Dramatica blog.

Before reading the following article, you may want to read the Dramatica comic book (PDF opens in a new window), in order to better follow the terminology used in the article.

Earlier this week, James posted an excellent entry entitled, Thinking of Your Audience First. This post discusses the four major ways in which audiences appreciate a performance: nature (Does your story involve a dilemma or work? Is it actual or apparent?), essence (Does the main character have a heavy or light feel?), reach (Will men and/or women empathize with the characters?) and tendency (Does the story drive the character or vice versa?).

The best thing about the article is that you can either start with the audience's point of view in mind, or work through your story and evaluate how the audience will appreciate it as a result.

If you thought the Tinkertoy Tic-Tac-Toe computer was impressive, you haven't seen anything yet!

Daniele Benedettelli has taken some LEGO Mindstorm sets, introduced them to the Rubik's Cube, added her experience with artificial intelligence.

The result was the LEGO Rubik Utopy! The unit, also known as the LRU, can look at a mixed cube and then proceed to solve it in the fewest number of moves possible!

The LRU page details all the steps that were taken in the project. The starting point was J. P. Brown's Rubik's Cube solver, and Daniele's own cube-solving software. The story is one of simplification, testing, problem-solving and design.

Two of the steps are demonstrated with videos, with the final results seen here. Some criticize it as slow, but the LRU is nonetheless impressive!

In Carnival of Mathematics XI, I began by discussing the ways in which math is commonly viewed. I thought this topic deserved further attention.

Leland McInnes highlights the problem itself by pondering what would happen if we taught English the way we teach mathematics. This article really helps you understand the problems the modern mathematics teachers face.

David Appell, in his article Math = beauty + truth / (really hard), sums up the problem quite well. The trick with math is getting them interested in the mystery, the result and the process. This can be done, as the Computer Science Unplugged videos demonstrate. Another good example is the journey taken by Andrew Wiles to solve Fermat's Last Theorem.

Often, the best way to create interest in math is to change perspective. One of the most classic examples of this approach would be Edwin Abbott's 1884 book, Flatland, about life in a 2-dimensional world. The hero, A. Square (yes, that's a proper name), learns about the nature of dimension after encountering lines, points and spheres. This great work is even being turned into Flatland: The Movie, which is now available on DVD to schools, and will be available as a home DVD later this year.

What can happen when students are properly motivated? Daniel Greenberg shows that it can take only 20 hours to teach 6 years worth of math.

This challenge is a large part of the reason I started this site. If brainy topics can be made interesting, and even entertaining, then perhaps we can get more people to take a closer look at them.