Yet Again Still More Quick Snippets

Published on Thursday, February 16, 2012 in , , , , , , , ,

Luc Viator's plasma lamp pictureFebruary's snippets are here, and it's time to have a bit of fun with math!

• Let's start off with the founder of recreational mathematics, Martin Gardner. The January 2012 issue of The College Mathematics Journal is available for free online, and is dedicated to the work and memory of Martin Gardner! Being a math journal, it does get into some heavy math, but even if you don't care for that, there's still plenty of fun math-related experiments and puzzles you can try and enjoy. You can also access each article individually, if you prefer.

• There's a magic tumblr blog called 366 effects. The magic tricks posted there are largely classic effects, many of them math-based. You can even find a nod to Martin Gardner there! The author is very good about giving proper credit, as well.

• Over at Mind Your Decisions, there have been several interesting posts recently. The first one dealt with a puzzle about page numbers: A book has N pages, numbered the usual way, from 1 to N. The total number of digits in the page numbers is 2,808. How many pages does the book have? Back in 2000, this same puzzle was featured on Numericana, too. It's amazing how challenging such a simple problem quickly becomes.

• What's a better value for your money, a 12-inch diameter pizza, or two 8-inch diameter pizzas? One blogger was faced with that decision, did some mental math, and opted for the choice with more surface area, even winding up with a bonus! The Presh at the Mind Your Decisions blog had a similar experience, used a calculator and was beaten by someone using some quick mental math!

The latter version's mental math is especially impressive, as there are several layered mental math tricks used. The first trick is the elimination of constants. Pi, of course, is constant, and we can also assume the thickness is, as well, but those only matter when going for an exact answer, not a comparison. Next, notice that even though the formula for a circular area is Pi × radius2, the mental math genius squared the diameters of the pizza. Again, because we're making a comparison, this is merely a scaled-up version of comparing the same circle's radius. Being able to work out problems such 14/9 in your head was taught here on Grey Matters back in 2009, and figuring out 1.5 squared is just a minor variation of squaring numbers that end in 5. Sometimes, in mental math, it's not just knowing what to do, but knowing what you don't need to do, as well.

• While we're focused on pizza and the Mind Your Decisions blog, here's how to play Nim with an unevenly-divided pizza, and ensure you wind up with the most pizza! If you like this game, make sure to check out my Nim posts. If it's tasty versions of Nim you're after, you'll particularly enjoy Chocolate Nim.

• I'll close with an answer, instead of a question. A poster over at Quora wondered what it was like to have an understanding of very advanced mathematics. An anonymous user provided a wonderfully clear and sincere answer that is a must-read. This is one of those posts that make you want to stand up in front of your monitor and clap, even though you know the author will never hear you.

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