Lattice points visible from the origin « The Lumber Room [A test of LaTeX-to-Wordpress conversion. Bugs remain, point them out. Original PDF] Here is a problem I love. It is simple to state, and it has a solution that is not trivial, but is easy to understand. The solution also goes through some beautiful parts, so I can promise it’s worth reading :-) [The solution is not mine. Question. Let us first imagine that we are standing at the origin, and that the grid is that of the lattice (integer) points. The blue points are visible; the grey points are not We now want to examine the question of which pairs are visible from the origin. not visible? is not visible because the point is "in the way", and the point obscures it. is not visible precisely when there is another lattice point blocking it, which is when there is an integer pair such that . is not visible precisely when there is an integer dividing both and , and is visible when there is no such integer, i.e. when have no common factor. For this to happen, it must be the case that no prime number . is .
Unassuming Entrances Hide the Planet's Hippest Hangouts | Magazine Parallel CityPhoto: Fulvio Salvi/Napoliunderground Bad Robot ProductionsPhoto: Cricket Alexander Milk & HoneyPhoto: Daniel Salo Safe HousePhoto: Christopher ZaborskyClub 33Photo: David Johnson Parallel CityPhoto: Fulvio Salvi/NapoliundergroundBad Robot ProductionsPhoto: Cricket AlexanderMilk & HoneyPhoto: Daniel SaloSafe HousePhoto: Christopher ZaborskyClub 33Photo: David Johnson Club 33 Where it is 1313 S. Why you want in The Magic Kingdom is dry. How to get in Good luck. Safe House Where it is 779 N. Milk & Honey Where it is 134 Eldridge Street, New York, behind what appears to be a sewing shop Why you want in This is one very highbrow cocktail joint that keeps a very low profile. Bad Robot ProductionsWhere it is Somewhere in Santa Monica, CaliforniaWhy you want in If you dream of personally delivering some fan mail to the production shop responsible for Fringe, Alias, and the Star Trek reboot, you have your work cut out for you. Parallel City Where it is 140 Piazza Cavour, Naples, Italy
10 Futuristic Materials Lifeboat Foundation Safeguarding Humanity Skip to content Switch to White Special Report 10 Futuristic Materials by Lifeboat Foundation Scientific Advisory Board member Michael Anissimov. 1. Aerogel protecting crayons from a blowtorch. This tiny block of transparent aerogel is supporting a brick weighing 2.5 kg. Aerogel holds 15 entries in the Guinness Book of Records, more than any other material. Carbon nanotubes are long chains of carbon held together by the strongest bond in all chemistry, the sacred sp2 bond, even stronger than the sp3 bonds that hold together diamond. “Metamaterial” refers to any material that gains its properties from structure rather than composition. We’re starting to lay down thick layers of diamond in CVD machines, hinting towards a future of bulk diamond machinery. Diamonds may be strong, but aggregated diamond nanorods (what I call amorphous fullerene) are stronger. Transparent alumina is three times stronger than steel and transparent. inShare28 Materials
HP printer Display Hack Article at HellBound Hackers Ok, this is my first article/tutorial, so don\'t expect it to be super great. I was just googling random stuff the other day and i found a very interesting hack that is GREAT for a little Urban Defacement in your school\'s computer lab. OBJECTIVE... Change the display of the network printer in the computer lab. How It is Done. Step One.... Go to START.CONTROL PANEL.PRINTERS AND FAXES. right click the printer you want to hack, and select properties. Step Two... Run cmd and type \"Telnet [printer ip address] 9100\" you should then get a telnet prompt. type in @PJL RDYMSG DISPLAY=\"some text here\" press enter then ^] (the escape character) Do not worry if you cant see anything when you type in the @PJL... part: Remember that you are using telnet. I did this little trick at my school and made the printer say \"REMOTE ERROR: SYSTEM HACKED\" and when the teacher saw it, she really freaked out. This will not change the actual performance of the printer, it will only change the display message.
Nice mind boggling stuff there by giajubo Dec 10