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From the page: "25 years ago today, Square One TV debuted on PBS! As a budding math geek, this show was a must-watch for me.

If you're not familiar with Square One TV, it was a show teaching math using comedy skits, music videos, guest stars, and whatever else to teach mathematical concepts. Everything from basic arithmetic to geometry to somewhat-advanaced algebra was covered in a way that was fun and interesting.

My favorite music video they ever did is a great example of this. It was called �oeChange Your Point of View.” Although largely about solving math problems by looking at the problem from different perspectives, it's also great advice for any type of problem:



To give you an idea of the comedy skits they used, here's a skit called The Adventures of Spade Parade, in which they have to figure out which consultant is which:



Magician Harry Blackstone, Jr. even had his own recurring segment, in which he would perform and teach mathematically-based magic:



Like many PBS shows, Square One TV was 30 minutes long (no commercials meant 30 minutes of content), and broadcast 5 episodes a week. The show itself had a rather unusual format, however. The first 20 minutes would consist of skits, songs, and other segments like the ones above.

The last 10 minutes of the show would always be an episode of Mathnet, a sort of Dragnet parody following the adventures of detectives Kate Monday (later replaced by Pat Tuesday) and George Frankly. A new adventure would start on Monday, and would be continued on each day, winding up on the following Friday.

To get a better idea, you can actually find full episodes online. Here's the very first episode of Square One TV. The very first skit, a song about the concept of infinity, recurs throughout the episode, as if it continued forever. The show's producers even convinced PBS to continue the gag even after that first show was over.

The Mathnet episode, �oeThe Case of the Missing Monkey,” guest stars a young Yeardley Smith, better known today as the voice of Lisa Simpson. This adventure continues in the second episode, and the third episode. I can't find the fourth and fifth episodes online yet, but you can see the rest of the same case in the 39th episode and the 40th episode, when it was re-run.

The show had a good long run, and broadcast its last new show on May 6, 1994, seven years later. Happy 25th birthday, Square One TV!"

From the page: "I've talked about the modular arithmetic before, especially as it related to the day for any date feat.

In this post, we're going to take it out of the calendar feat's shadow, and give it a starring role in its own feat!

If you remember doing division before you learned about fractions, you remember doing problems such as 21 ÷ 4 = 5 remainder 1. Modular arithmetic is simply focusing on the remainder exclusively. 21 modulo 4, for example, just equals 1, because when you divide 21 by 4, 1 is the remainder.

If we're talking at 10 AM, and I agree to call you in 5 hours, then you know to expect a call from at 3 PM. You did 10 + 5 = 15, but you know that hours aren't numbered any higher than 12, so you just subtracted 15 - 12 to get 3. This is modular arithmetic, and is also why it has the nickname �oeclock arithmetic.”

Let's try comparing the modular arithmetic patterns of two numbers, say, 2 and 4. Since 2 times 4 = 8, we'll compare the remainders as they run from 0 to 8:

[\begin{matrix} num&mod\2&mod\4 \\ 0 & 0 & 0\\ 1 & 1 & 1\\ 2 & 0 & 2\\ 3 & 1 & 3\\ 4 & 0 & 0\\ 5 & 1 & 1\\ 6 & 0 & 2\\ 7 & 1 & 3\\ 8 & 0 & 0 \end{matrix}]

What if I were to tell you that I was thinking of a number from 0 to 8. I then gave you a further clue that, when divided by 2, it has a remainder of 1, and when divided by 4, it has a remainder of 3, we run into a problem. Look at the chart. That description fits both 3 and 7, and there's no way to work out which of the two. The problem is that the pattern of remainders, when divided by 2 and 4, repeats 2 times from 0 to 8.

If we try this with, say, 3 and 6, and ran up to 18 (3 �-- 6) you can see in this chart that there are 3 times where a pattern of 3 remainders repeats.

If we want to identify a number by its remainders alone, is there some way to make sure that no repeating pattern emerges? Notice that, when we used 2 and 4 (and went up to 2 �-- 4, the remainder patterns repeated 2 times, and that 2 is the largest common factor of 2 and 4. Similarly, when we used 3 and 6 (and went up to 3 �-- 6), the remainder patterns repeated 3 times, and that 3 is the largest common factor of both 3 and 6.

If we want no repeating patterns, then what we're really saying is that, when performing modulo a and b, running from 0 up to a �-- b, we would like each number combination to only show up 1 time. For this to be true, we simply have to make sure that the greatest common factor of the numbers involved is 1!

This is the basic idea of the Chinese Remainder Theorem. Martin Gardner discusses this idea in more detail in his book Aha!: Aha! Insight and Aha! Gotcha (Spectrum). You can find the relevant pages online here and here, thanks to Google Books.

When using two numbers, it's pretty easy to make sure their only common factor is 1. If we use, say, 4 and 5, and go up to 20, we can already know that there won't be any repetitions, because the largest factor common to 4 (factors: 1, 2, 4) and 5 (factors: 1, 5) is 1.

The Chinese Remainder Theorem also tells us we can go further, and even use 3 or more numbers, and they won't repeat (up to a �-- b �-- c �--...) as long as their largest common factor is 1! The easiest way to do this, of course, is to turn to our old friend, prime numbers.

In the Martin Gardner book linked about, he talks about a version of a trick where someone thinks of a number from 1 to 1,000, and gives you the remainders after dividing by 7, 11, and 13. Since 7 �-- 11 �-- 13 = 1,001, you'll get a unique combination of remainders for any number given. But what about the version he mentions from 1 to 100 with 3, 5, and 7? What's the formula for that?

Let's take the approach in his article and apply it. For the remainder after dividing by 3, we need a multiple of 5 �-- 7 that's 1 greater than a multiple of 3. 35 doesn't work, because 34 isn't a multiple of 3. 70, being 69 + 1, works perfectly, though. OK, we start with 70 �-- a (or 70a for short).

What about 5? Let's look at the multiples of 3 �-- 7. There's 21...perfect! It's already 1 more than a multiple of 5. OK, now we've got 70a + 21b. What about 7? 3 �-- 5 = 15, and 15 is already 1 more than a multiple of 7. For all three numbers, we now have 70a + 21b + 15c. Divide that total by 105 (3 �-- 5 �-- 7), and the remainder will be the number you're looking for!

You could do that on a calculator, but if you're familiar at all with Grey Matters, you'll know that I encourage you to do things like that in your head. However, I understand that it can be tricky.

A magician named Tom Harris, back in 1958, proposed a different approach that required no calculation. You memorize the number combinations with help from the Peg/Major system, linking the combined numbers you get to the unique answer for that combination. For example, if someone gives you the numbers 1, 0, and 3, you would recall the phonetic equivalent �oetwosome”, and remember that you linked that to the word �

From the page: "Shortly after lifehacker linked to my Day of the Week For Any Date post last fall, I was inspired to see how much further I could minimize the required work.

Even I was surprised at the results of this effort, which I just released earlier this week as Day One.

Instead of giving a day of the week for any date verbally, you ask the spectator for a meaningful year and month, and instantly create a calendar for that month from memory! You then ask for the particular day, circle it, and give the calendar to the spectator as a souvenir. Ideally, of course, this is on the back of your business card.

Other methods used usually require the performer to stop and work through 100 years of mnemonics (to cover the century), and several steps of arithmetic. This also necessitates a 10 to 15 second pause. I was never happy with that pause, which is why I wanted to improve the current method I use.

Here's the teaser ad I created for Day One:



The math in Day One involves only a single subtraction, and even that isn't always needed! No, you won't need to memorize 100 year mnemonics, or even a third of that amount.

One of the things I'm proudest of, however, is that there's no conversion of the month, date, or year into a numeric code. Yes, there's conversion into mnemonic images, but your brain will handle these more naturally than abstract numbers.

The complete package includes the PDF notes themselves, a PDF template for the calendar used in this effect, 4 videos of animated mnemonics (each available in 800 by 600 and 480 by 360 resolutions), two quiz apps (both made to run in any browser and take advantage of touchscreen mobile devices when available), and a file of several relevant links to help you explore other ideas related to this routine.

Over at the Magic Cafe, some of my early testers provide some great reviews:


�oeI will most likely use this instead of the standard feat now. It offers something new and different in that you produce an entire month and calendar you can give away. So I would reasonably assert that if you have any interest in this type of feat, Day One is probably the most accessible and easy method to get into this. I honestly believe the entire concept, approach, and delivery of Day One is brilliant.”
-Jim Wilder

�oeI especially like Scott's brilliant idea of filling in the month calendars as a presentational ploy. This not only allows a very fast start to the effect but also gives something to hand the spectator at the end - especially useful if you print these calendars on the back of your business card. Of course this presentation can easily be adapted for other DFAD methods and I will certainly use this with my own Speed Dating system....Scott's instructions are very thorough and the ebook comes with an extremely impressive set of learning tools.”
-Michael Daniels (author of Speed Dating)

�oeWhat stands out most for me is that this is not just another "show off" effect, but it connects with people because they will get a present at the end of the routine. It reminds me of my own creation "Stigma Square". They would make a perfect couple! Imagine you have a piece of thick paper, you ask for the birthday of a spectator, then you produce the calendar month of his birth, and then on the back of this paper you create the matching Stigma Square. A complete little act of a math genius, fitting inside your pocket!

�oeBUT there is one really annoying part of "Day One": in my opinion it´s way too cheap! For this extensive work I would have taken at least the double price!”
-Nico Reuter (author of Stigma Square)


Day One is currently available as a download from Lybrary.com, and is currently only $9.99.

If you buy it and have any questions about it, please contact me through Grey Matters or the Magic Cafe, and I'll be glad to help!"

From the page: "The classic "Day For Any Date" feat has been updated!

Day One is a new approach to appearing as a human calendar. You ask for the year and month of the spectator's birthday, and instantly create that month's calendar for them on the back of your business card.

Day One is designed to be simple to learn, as well as quick and impressive to perform.

The role of math and mnemonics has been greatly simplified and minimized, and you don't need any previous experience with other mnemonic systems. Entire centuries are covered with less than a third of the mnemonics required by other approaches. The only math used is a single subtraction, and even that isn't always needed.

Even better, the mnemonics have been animated for you with the included videos, and you reinforce these vivid images with help from the included quizzes, which run in any browser. You can even quiz yourself on the go in your mobile device's browser.

Once learned, the principle is even flexible enough to be adapted to platform and stage venues.

If you want a simple, direct, and visual approach for learning the "Day For Any Date" feat, you'll like Day One."

From the page: "I've had some fun with Wolfram|Alpha in previous posts, and now they can be made even more fun.

Any Wolfram|Alpha search, without any programming, can be turned into a widget you can place on your website as easily as embedding a video!

In July of last year, I posted about a trick with Wolfram|Alpha, which the widgets make it even easier to present.

Instead of typing everything in directly, they can enter the numbers in the following widget, make sure you can't see the screen, and give you the three numbers that result:
Quadratic Equation Solver
x^2
x
constant
Submit
Computing...
Get this widget

Wolfram|Alpha has even helped make the method itself easier. Instead of performing it as Martin Gardner originally described, you can get the first number by taking the leftmost number of the group and subtract twice the middle number from that. Next, add the rightmost number. Divide that by 2, and you've got the first number you need!

For example, given the default numbers of {4, 9, 18}, you would do 4 minus 18 (twice the 9 in the middle) to get -14, and then add 18 (the rightmost number) to get 4. 4 divided by 2 = 2, so now you know the equation begins with 2x2.

To get the second number, take the middle number and subtract the leftmost number from it, such as 9 - 4 = 5 in our example. From that result, subtract the number you got in the previous step. The result of the previous step was 2, so we figure 5 - 2 = 3. That gives us 2x2 + 3x (plus 3 because the result was a positive 3).

As before, the leftmost number is the constant itself, so we get 2x2 + 3x + 4 as the original equation! You can find several good videos on adding negative numbers, as well as subtracting them, over on YouTube.

Similarly, for the Wolfram|Alpha Factorial Trick, it just becomes a simple matter of submitting a simple number as input, and noting the result:
Factorial's Trailing Zeroes
Find the number of trailing zeroes in the factorial of:
Submit
Computing...
Get this widget

Creating widgets like these can be handy for simple quizzes, too. If you're learning the Instant Magic Square for example, you could quickly develop a widget that gives you a random total from 21 to 100. Similarly, if you want an effective way to practice the Day of the Week For Any Date feat, you can start with input that generates random date on Wolfram Alpha and develop that into a widget that gives you random dates.

The following video will give you an idea of how easy it is to create a Wolfram|Alpha widget. When you're familiar with making simple widgets, check out their blog for new features as they become available."

From the page: "It's time for January's snippets.

This month, we're going to catch up with the latest round of math-related videos!

• Back in December, mathemusician Vi Hart posted the first of a 3-part video series she dubbed Doodling in Math: Spirals, Fibonacci, and Being a Plant. The second part has just been posted, with the third part expected in about 2 weeks:



While waiting for more fun from Vi, you might want to explore more fun with Phi.

• James Grime is back with another math puzzle. In this one, the answer should be simple, but it depends on an aspect of numbers that's not often considered. Watch this video, and see if you can figure out the answer before he finishes going through the entire process:



• Speaking of James Grime, he's also been busy doing videos for the NumberPhile channel. Check out their channel if you haven't already. Each video focuses on fascinating aspects of different numbers. Their newest one features James Grime on Mersenne Primes:



• I've added a new section to the Grey Matters Online Store. I've moved all my CafePress items together in one store. In the Penny Star Puzzles section, you can even try the puzzle yourself before you buy it!

In addition, I've added a new item called the Magnetic Perpetual Calendar. The basic idea is very simple, as you can see in this video:



They come as a set of 3 for less than $15, with discounts available for bulk orders."