If you arrange the natural numbers starting with 1 onto a hexagonal grid such that they fill in a hexagonal-shaped array of hexagons, there is only one non-trivial normal magic hexagon—that is, all of the numbers in every hexagonal row for all three directions sum up to the same number. This unique magic hexagon is shown above and the magic sum is 38. It has been proven in 1963 that this is the only normal magic hexagon (aside from the trivial solution of only 1 hexagon).

There are other “abnormal” magic hexagons of various sizes where the successive numbers don’t start with 1, but the one shown is the only normal one. Magic hexagons have only been studied relatively recently by mathematicians especially when compared with the vastly more popular magic squares which are known since ancient times.

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As I mentioned on Facebook, a micro-hobby that I picked up recently is applying perspective correction on photos of NHCP historical markers in Wikimedia Commons such that they look as if they were photographed head-on and with horizontal edges looking horizontal and vertical edges looking vertical. An example result is the corrected photo of the Fort of San Pedro historical marker shown below.

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I’ve mentioned in passing here on this blog that my favorite number is the golden ratio. If you know me, this should not be surprising at all. Two of my favorite school subjects are math and art after all, and aside from fractals (which I also really love), the golden ratio is a concept that straddles both fields, having numerous interesting mathematical properties and being used as an aesthetically pleasing proportion in the arts and architecture. I’m quite sure that I am far from alone in having the golden ratio as their favorite number.

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So far, the top highlight of 2011 for me was my recent trip to Israel where I attended Wikimania 2011, held in the beautiful seaside city of Haifa. Wikimania is the annual conference for Wikipedians (and Wikimedians) and it is held in different cities every year. Last year it was held in Gdansk, Poland and next year it will be in Washington, D.C. I applied for a scholarship to attend this year’s Wikimania and I was fortunate to be accepted. The scholarship enabled me to go to Israel with practically all-expenses paid. The only thing I needed was pocket money and some transportation fare.

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I blogged in 2008 that if ever I would get a permanent tattoo, I would get something like the one pictured above. This is a stylized Greek letter phi which represents the golden ratio. The golden ratio is my favorite number by far and I just love how it is crops up in so many places and how it provides a nice blend of mathematics and art. I love it so much that I made that logo for my amateur QuickBASIC software “company”.

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Would you believe that the missing Batanes, and the misplaced markers for the Tubbataha Reefs and the Puerto Princesa Subterranean River are not the only problems with the map of the Philippines found on the new peso banknotes?

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Occul—what? An occultation is an astronomical event wherein a heavenly body passes in front of another and hides it from view. That’s what happened earlier tonight: an occultation of the Moon and Venus. Most people saw the very close conjunction (an astronomical term signifying that two objects appear near each other in the sky) and appreciated the beauty of a “star” on top of a crescent moon. You can actually see plenty of pictures and status messages about this relatively rare Moon-Venus event and there were observations that it reflected some Islamic flags or that it looked like a one-eyed smile. What most didn’t know (and missed) was that the “star” was actually Venus and that the occultation itself is much more interesting scientifically. (In addition, the Moon and Venus are the 1st and 2nd normally brightest objects in the night sky so this occultation is actually quite special.)

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The Apache web server modules mod_gzip (or mod_deflate), mod_rewrite, and mod_include apparently don’t interact very well. Specifically, mod_gzip returns to the web browser an incorrectly compressed file when that file is constructed using includes (via mod_include) with virtual URLs rewritten using mod_rewrite. The apparent workaround is to avoid rewriting include URLs or to disable mod_gzip.

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Aside from being the tenth prime number, 29 is also the second sum (when only considering whole numbers) of three consecutive squares, namely the squares of two, three, and four. (The first such sum is 14, which is 1² + 2² + 3².) In addition, all the numbers in the sequence from 1 to 29 have at most 2 unique prime factors and that this is the longest such sequence.

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One of my managers at work knows that I love maps (she actually gave me four NAMRIA topomaps for Christmas) and so she told me a few months ago about this thousand-plus-peso atlas of Metro Manila that she saw at Fully Booked. Being the map geek that I am, I was of course quite curious. I was finally able to locate this atlas last month at Fully Booked Bonifacio High Street and discovered that it’s the first edition of the Manila Street Atlas by Periplus (see the Amazon listing).

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The solar eclipse that will occur this Wednesday, July 22, is quite remarkable in some respects. First of all, this eclipse will be the longest total solar eclipse in this century—a longer one won’t occur until 2132. The longest duration of totality will be 6′39″ and the reason why this eclipse is long is because the Earth is near aphelion and the Moon is near perigee. This means that the Sun will appear at its smallest and the Moon at its largest. (It’s very easy to imagine that a large circle moving in front of a smaller circle will cover the smaller circle longer than if the two circles were nearer to each other in size.)

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For the most part I’m a big Google fanboy (well except for some things here and there). And because I’m nominally a web developer, I certainly will try to attend as many developer-oriented Google events as I can. The first event I attended was the Google TechTalk last November 2007 and the second one was the first ever Google DevFest Manila back in November 2008. So it should not come as a surprise that I turned up at the Google-Globe Developer Workshop last June 20. This event was held at Tech Portal of the really, really, really cool U.P.-Ayala Land TechnoHub in U.P. Diliman (see a rough map at OpenStreetMap ). Did I mention that the TechnoHub is really cool?

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Google Earth 5 was released last February 2 via a much-hyped launch event at the California Academy of Sciences in San Francisco. The special feature that was unveiled (to no one’s surprise because of the many clues released prior to the event) is the arrival of Google Ocean, which lets users explore the world’s oceans in 3D. What was unexpected were the three other major features added: Google Mars, easy KML tour recording, and—the one I’m most interested in—historical imagery.

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I plurked in early January that I finished my initial draft of my personal 2009 budget. I mentioned then that I only increased my projection by 1% compared to last year’s budget due to, yes, the worldwide economic crisis. Based on the comments to that plurk, I thought it would be interesting to do a series of posts explaining how I manage my money such that I am actually able to do a year-long budget.

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There were two eclipses that were visible from the Philippines in the last four weeks. The first was a partial solar eclipse that occurred in the late afternoon of January 26 and the second was a penumbral lunar eclipse on the night of February 9. I wasn’t able to view these two eclipses since for the solar eclipse, I couldn’t go out of the office the view of the sun from my office’s windows is blocked by skyscrapers and for the lunar eclipse, I forgot all about it. Besides, since the lunar eclipse was penumbral, it wouldn’t be as spectacular as a partial or even a total lunar eclipse.

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And 6 is the first. Perfect numbers are positive integers that are equivalent to the sum of their proper divisors—that is, when you list down all the factors of a perfect number (except itself) and add them all up, you will get the number itself. The proper divisors of 28 are 1, 2, 4, 7, and 14 and their sum is 28. Neat eh? Incidentally, I expanded the Wikipedia article on perfect numbers in 2003 based on a tutorial I wrote back in 1998.

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I’ve been playing around with creating PhotoOverlays in Google Earth, and I must say, making them is hard. PhotoOverlays are a new feature in Google Earth 4.2 wherein you can place photos in 3D space such that it lines up with the underlying view in Google Earth. Note that this is different from an Image Overlay feature wherein you take a graphic (like a map) and drape it over the terrain. Shown below is how a PhotoOverlay I created looks like floating in space.

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The big news that’s rocking the physics, electrical and electronics engineering fields is the proof of the existence of the memristor. “Mem-what?” Well, that’s what my initial reaction was, too. The memristor is apparently the missing fourth fundamental basic element of electrical circuits, alongside the resistor, the capacitor, and the inductor. And the cool thing about this is that the memristor was first hypothesized in 1971 by Leon Chua, a Filipino-American professor at the University of California at Berkeley who got his degree in B.S. Electrical Engineering at the Mapúa Institute of Technology in 1959, here in the Philippines! Yay, Pinoy!

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One thing I did over the long weekend was to contribute some more to the OpenStreetMap (OSM) project, something I had been doing last year. This time around, I tackled various places in Metro Manila, not just the southern portions, and I added more types of data and not just streets.

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Found via Kottke is this absolutely geeky blog showing off science- and math-related tattoos from scientists, mathematicians, programmers, and other academics. I find it to be a wonderful blend of the rebellious and the geek.

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Did that title rattle you? Was your grammar/spelling Nazi evil twin awakened by it? If yes, then you’re not alone. Filipino Wikipedians on the English Wikipedia had a long-running debate this year regarding the name of the Philippine currency and what to name the corresponding Wikipedia article.

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Ever since I discovered that the OpenStreetMap (OSM) project expanded their coverage to the whole world, I was excited to map out my neighborhood since I saw that my area is still virgin territory yet untouched by Philippine-based OSM contributors. You can actually add data on the site itself using their Potlatch web app. It’s a slick Adobe Flash-based application that provides a rudimentary, yet powerful map data editor and can directly show Yahoo! Maps satellite imagery for tracing streets. The other popular way of adding data is via the JOSM Java-based desktop application. JOSM is intended for power users and serious OSM contributors.

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Let’s all have a slightly nerdy game this time. What is the longest chain of proper name etymology that you can think of? Here’s an example: One San Miguel Avenue (the building) is named after San Miguel Avenue in Ortigas, which is then named after San Miguel Corporation (whose headquarters is along the previously mentioned avenue), which is named after Archangel Michael. That makes a chain of four links.

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Here’s the second part of the story behind Lakbayan. You should also read the first part or the launch blog entry if you haven’t done so.

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Oh. My. God. This has got to be the coolest thing I have ever seen on Google Maps by far. Google has now integrated street-level panoramic views of practically every street in 5 U.S. cities: New York, San Francisco, Miami, Denver, and Las Vegas. The photos only require a flash player, is zoomable, pannable 360°, and it’s interactive! You could practically do a virtual drive around these cities! It’s almost as good as being there.

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If you understand the title, then it sounds intuitive doesn’t it? If you have a plurality elections (like what we have here in the Philippines), then the more candidates there are, the lower the probability of the winner getting the majority votes. To interpret that in another way and to put it into statistical terms, there is an inverse correlation between the number of candidates and the percentage of votes that the winning candidate gets.

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Not bad. I was able to name 115 UN member countries out of a total of 192 in 10 minutes. That’s almost 60%. Try to see if you can beat me via this cool online quiz. Tip: you don’t have to press the return key if you typed an unidentified country correctly. I would’ve listed my results here but that would spoil the fun! (Via Kottke.)

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Last weekend, I played around with the public domain data obtained by the Shuttle Radar Topography Mission or SRTM. I wanted to use this data to create topographic maps that I can contribute to Wikipedia.

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I read an interesting business article yesterday saying that an Australian bank has developed a new purchasing power parity index called the iPod Index. We all know about foreign exchange rates. But we also know that just because the U.S. dollar is equivalent to 49 Philippine pesos, does not mean that an apple that sells for 50 cents in California will go for 24.50 pesos in Cebu.

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I believe I have created the first Philippine-related Google Maps mashup that is more than just placing points on a map. I remembered recently that I have scanned before an aerial photography plate of the University of the Philippines, Diliman area from the early 90s. (These plates are used by U.P. Geodetic Engineering students in their courses.) So last night, I had this brilliant idea to create a custom map in Google Maps with the aerial photography as a new map type. So now I’m proud to present my University of the Philippines, Diliman Map Mashup located at my dormant U.P. community site ASwalk.net (which I plan on reviving soon). Please select the “Aerial” map type to view the “new” imagery.

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I’ve added a beta Map page to my second blog, Tanawing Pinoy, (now named Vista Pinas). Like the original Google Sightseeing, I plan this page to be an interactive embedded map pointing to all or a subset of the featured sights from the blog.

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Before reading on, visit this puzzle post by Jason Kottke about a plane on a conveyor belt. Read it? Thought about it? Or are you as confused as many of the commenters on his post?

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Tim Berners-Lee has a blog! If you don’t know who he is, then you either probably haven’t read Dan Brown’s Angels & Demons, or you haven’t carefully read Dan Brown’s Angels & Demons. For the still clueless, he’s the reason you’re reading this blog entry now; he’s the inventor of the World Wide Web.

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Being a person with good spatial intelligence, some talent for visual arts, and technical inclinations, it’s not a surprise that I’m a map freak. I love maps; I probably wouldn’t mind a job in the field of cartography or geographical information systems (GIS). And don’t be surprised if you find me poring over those you-are-here maps longer than the average person.

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Since I’ve now done my part in passing the baton, I’ll blog about the meme itself. I first saw this meme on this post by Stuart Langridge, one of the geek bloggers that I read. Then I noticed it entered the Philippines (as far as I can tell) through Markku Seguerra’s post. From there, it took several more blogs and weeks before it got passed on to me.

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You learn something new everyday. While exploring the website of silverfilter, a local electronica act I saw at last Saturday’s Fête, I came across this tutorial explaining how to make a dance track. It’s interesting to say the least, and it might’ve ruined the way I listen to music (at least for a while).

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I’ve owned my Nokia 6610 for almost a year now, but I only discovered two of its nice hotkey features only recently. You’re welcome to skip this post if you’re not interested in techie minutiae. (I’m a self-confessed geek. So sue me.)

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An officemate of mine, Joanne, gave everyone in our division Rubik’s Cube for Christmas. These are not the official versions, but are imitation versions with maddeningly weird cartoon figures on the stickers. (Solving the Cube with these figures is actually more difficult since not only do you have to have the correct colors, you have to have the center cubes rotated correctly.)

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I opened Winamp a while ago and set it to play my playlist consisting of 75 songs in shuffle (random) mode. Imagine my surprise (and delight) when I heard it play my three currently most tripped songs one after the other within the first five songs! What are the chances of that happening? I would’ve believed it’s a sign from God except that I don’t know what it is a sign of.

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Several weeks ago, my officemates and I had a discussion on the question, “do you get wetter walking or running in the rain?” My guess is that the walker gets more wet, primarily because he spends more time in the rain. But intuitively, you could also say that the runner gets more wet because he is running into rain, rain that would not hit you if you were walking more slowly.

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