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PhotoMath uses your phone's camera to solve equations
Need a little help getting through your next big math exam? MicroBlink has an app that could help you study more effectively -- perhaps too effectively. Its newly unveiled PhotoMath for iOS and Windows Phone (Android is due in early 2015) uses your smartphone's camera to scan math equations and not only solve them, but show the steps involved. Officially, it's meant to save you time flipping through a textbook to check answers when you're doing homework or cramming for a test. However, there's a concern that this could trivialize learning -- just because it shows you how to solve a problem doesn't mean that the knowledge will actually sink in. And if teachers don't confiscate smartphones at the door, unscrupulous students could cheat when no one is looking. The chances of that happening aren't very high at this stage, but apps like this suggest that schools might have to be vigilant in the future.
Daily iPhone App: Quento is a spelling game, but with math
Quento was recommended to me just recently by someone I met at Macworld or 360iDev, and unfortunately, I don't remember who told me about it. But the recommendation was great, and now I'm passing it on to you. As you can see above, Quento is a math-based puzzle game, where you use a grid of numbers and symbols to try and put them together into a target number. The game's interface is actually half the fun -- like the popular word game Letterpress, Quento is very stylishly designed, and as you complete each target number in the puzzle, it gets replaced in the menu above. You can swipe the little menu right or left to go up to harder difficulty modes, or down to a "free play" mode (where you just get a number to make, and you can use any combination to make it). The game is casual, obviously, but it's not necessarily easy -- at times, I found myself racking my brain to try and line the numbers up right. But there's always an answer in there, and no matter what your math knowledge is like, Quento does a great job of rewarding concentration and smart gameplay. You can pick it up now as a free, universal app.
Physicist uses math to get out of a traffic ticket, publishes findings
When most folks get ticketed for running a stop sign, most people wind up writing the court a check. UC San Diego physicist Dmitri Krioukov wrote a mathematical paper instead. Rather than throw his fallible human opinion on the mercy of the court, Krioukov uses a series of equations and graphs to prove that the accusing officer confused his car's real space-time trajectory "for a trajectory of a hypothetical object moving at approximately constant linear speed without stopping at the stop sign." In other words, the officer was wrong, but Krioukov stresses that it isn't the officer's fault. "This mistake is fully justified," he writes, pointing to the math. "As a result of this unfortunate coincidence, the O's perception of reality did not properly reflect reality." And to think, you probably never thought you'd use this kind of math in the real world.
Using LaTeXiT to display math formulas
TeX is a typesetting standard that, among other things, allows you to typeset complex math formulas. One flavor of Tex is LaTeX, for which LaTeXiT serves as a front-end for on Mac OS X. Using LaTeXiT, one can drag and drop complex math formulas to a number of apps -- Pages, Keynote and TextEdit, to name a few. While the LaTeXiT workflow is fairly simple and straightforward, getting it setup and running may not prove to be the most clear-cut and easy process.
Solving the mathmatical tangles of ArPen
Armor penetration is probably one of the most misunderstood stats in the game, for a number of reasons. First of all, it's only become popular lately -- while it's been in the game since 1.10, it's only started showing up regularly on items in Wrath. And even then it's really only a meta-meta stat: the core abilities like Strength and Agility are easy to understand, the next level of abilities are things like hit rating and crit rating, and then armor penetration, you could argue, goes another level after that: it's a stat that affects a stat affected by a stat. It's for that reason, then, that Xanthan argues we need a more elegant solution.Armor penetration basically allows you to hit an opponent as if they're wearing less armor than they really are. That's not to hard to understand -- if you have a certain amount of armor penetration, then the opponent armor number in the equation that determines damage done is lower (edit: by a percentage, not a number) than it would usually be. But the confusion comes in when you see how armor penetration scales. It actually scales exponentially, not linearly -- if you have no ArP and you increase it by a little bit, you only get a little extra damage increase. But if you have a lot, and you add a little more onto that, then you'll get a bigger damage increase, due to the way the math works (I'm bad at math, but Xanthan has an excellent, clear description of the calculations in the forum thread, and we've posted some explanations before as well). Blizzard recently capped ArP at 100% (so you could never get into a place where you're reducing armor below the amount of armor that's there), but it's still possible to have the amount of armor reduced equal the amount of armor on a target, causing the equation of armor vs. armor penetration to divide by 0, and at that point, things get wacky, and terms like "infinite damage" come into play.
