– “News Republic” is a free smart-phone and iPad app that offers 10,000 stories a day from 180 news providers. The nice thing here is that you can click headlines and read complete articles in the same window, without having to follow a link to some other website. The app is available for all the major smart phones and tablets.

– “APPY Geek” is a news app for Geeks. “Glam life” focuses on celebrity and lifestyle news.

Type in a function like “sin(x)” and Google will instantly chart it. As you move your cursor along the curve, you’ll see where you would be for different values of “x.” We put in “y= x*x,” the formula for a parabola, which is what you need for beam focus. Another site that does graphs for you is WolframAlpha.com, but we found Google’s easier to read.

Users of either site can also find answers to word problems with numerical answers, such as the number of seconds in a year or the number of miles equal to 50 kilometers.

Google Maps has had indoor maps before, but they were a bit fuzzy on details. The maps still don’t have a search function, so if you’re looking for a restroom, say, you have to zoom around. Not every store has uploaded indoor maps yet, but there’s a long list of those that have: Chicago’s O’Hare Airport, Macy’s, Home Depot, IKEA, Bloomingdales, etc.

If you use the Chrome web browser instead of Firefox, Safari or Internet Explorer, you probably saw an on-screen notice for the Chrome web store. It has thousands of free apps. We did a little shopping (can’t beat the price) and here are three we liked.

Having a large number of browser extensions can slow down your web surfing. But apps only use your computer memory while you’re using them. We just installed the free Marvel Comics app, for instance, which puts an icon on the screen but doesn’t add itself to your browser. After installation, we clicked “Free” and got an “Avengers” comic book and could have gotten dozens of others, including X-Men, Wolverine and Captain America.

The other apps we installed were a calculator and “RemindMe,” which plays a little tune and delivers a pop-up note when it’s time to do something. The calculator is just a regular on-screen calculator. But it’s free and handy to have. (There are many free calculators you can install, including some that do scientific and interest rate calculations.)

There are currently two kinds of Google TV boxes, one made by Sony and the other by Logitech. We have Sony’s combination Blu-ray DVD player/Google TV box and connected it to a $300 Vizio TV. After the system updated itself recently, the whole interface got simpler and gave us access to hundreds of Android apps.

The first app we played with (just for fun) was “Classy Fire.” It put a big fireplace on the TV screen with options to hear a crackling fire, a thunderstorm, jazz or all three at the same time. We turned down the crackles and jazz and turned up the thunderstorm. It’s the best recorded thunderstorm we’ve heard. If you have a compatible Android device, you can get it for free in the Android marketplace.

We also tried some other free apps, including the “Wall Street Journal Live,” “Flixter,” for movie news and trailers, “All Recipes,” and “The Big Picture,” which gives you nice photos with news captions, including several of the recent flooding inThailand. “Podcasts” (audio programs) on Google TV include favorites such as The Prairie Home Companion and many others, some of which aren’t updated very often. Some author interviews, for example, were eight months old. But others are right up to the minute. Netflix, Pandora and Twitter apps are pre-installed.

The Sony Blu-ray player with Google TV is $180 at BestBuy.com. The Sony HDTV with Google TV built in starts at $400.

Update: CEO Eric Schmidt predicts Google TV will be on the majority of TVs by summer of 2012.

It’s “Zoner Photo Studio,” a free Windows program from free.zoner.com. (There are a lot of links to other programs, so confine your click to this one.) It’s superb at organizing photos. It keeps the familiar Windows file structure off to the left of your screen, making it much easier to find stuff. By contrast, Picasa annoyingly lists photos by date, and for some reason, it doesn’t even list a 2011 folder on our laptop, making it difficult to find our recent shots, except by going to the “File” menu and choosing “Add file to Picasa.”

Like Picasa, Zoner Photo Studio has a “quick fix” photo editing button, which produces great results. It easily corrects red eye, blurring, and other picture defects. A “tutorials” link shows you how to create photo name tags for gifts, make a photo calendar, show off stuff on eBay, create panoramas and other projects. Type “3D” in the help menu to learn how to make three-dimensional photos. All in all, big thanks to our reader and a nice find for the rest of us.

– Posterous, formerly a blogging site, has reinvented itself as a social network called Posterous Spaces. Here you can share audio, video and photos just with certain circles of friends without worrying that anything travels beyond that circle. It’s at Posterous.com.

– Another way to go is “Elixio.net” which claims to be a site for movers and shakers. We were a little shaken by event listings: like “International Workshop on Folk Dances of India” and a “VIP party in Abu Dhabi.” There are hundreds of special interest groups in such categories as “Finance,” “Art” “Luxury” and “Film Industry.” There were also unusual (to say the least) ads in the classified section, such as one looking for an investor to open a punk rock club. If you want an invitation to this  send us an email. We have 24 of them.

– Back to Facebook. (Who can ever get away?)Their new “smart lists” automatically groups friends from high school with you in one list, friends from work in another, and so on. You can do this manually but it saves a lot of time if you have hundreds of “friends.” This feature hasn’t rolled out to everyone yet. Another one is “subscriptions.” Decide if you want all of a friend’s updates, just the important ones, or just the ones in certain categories. Or follow a celebrity’s posts, without having to befriend them.

–Back to GooglePlus. (Apparently, a lot of people aren’t going back.) After huge publicity, public posts are down 41 percent since August, though some people are as prolific as ever. Guy Kawasaki can drive you nuts, for instance, because he does about a dozen posts a day. But they’re great.  Update: Since opening itself to the public last week, Google Plus has soared to 50 million users. No more invitations required.

We remember when people who weren’t paying cash, wrote checks at the grocery store. Some still write checks and hold up everybody in line. Most use credit or debit cards. Next step: smart phones.

“Google Wallet” is expected to arrive this summer. It will start out on the “Nexus S 4G” phone offered by Sprint, but will expand to more phones soon after.

They’ll be used with what are called “paypass.” These will be smart phone readers at merchant checkout counters. You would tap your phone on the reader itself. No, we’re not kidding. You hit the reader with your phone lightly, please and your credit identification number is recognized and the proper amount deducted from your balance. (Law suits to follow.)

We went to Google.com/wallet to see who will be participating in this new payment method and saw that McDonalds, 7 Eleven, Home Depot, CVS, and many others have already signed up. It is Google’s eventual aim to make Google Wallet a kind of digital bank, able to store thousands of credit cards, loyalty cards, gift cards, receipts, boarding passes, tickets, coded keys, etc. There will be discounts for users.

In  three days, there’s a hangout to teach you about Google Plus.

Evan Bailyn’s websites have been visited by more than 50 million people, but that’s not what impressed us. It’s the nuts and bolts info on how to boost your site’s “trust rank,” a measure he says is far more important than its “page rank” a different measure of your site’s importance, named after Google founder Larry Page.

How do you get your business to show up on the first page of search results when people are looking for your products? It turns out there’s a lot more to it than you’d think.

Here’s one example from the book. The author once owned a game site that was listed in the top five listings on Google’s results page if you searched on the word “games.” According to the Google keyword tool, this should have made his site one of the most popular in the world. Four hundred million searches for “games” take place each month. But, Bailyn got only 56,000 hits that month. He explains the problems and suggests ways to build a site that attracts new customers.