It’s the Carnival of Mathematics, here to brighten your weekend and chase any winter blues or summer sadness away. There are forty-nine eleven great posts, which we’ve interspersed with facts about the number 49.
Our very first post is Ethnicity, Religion, and War, courtesy of Fëanor at Jost a Mon, in which a statistical approach to history aims to show that if an Ottoman sultan’s mother was of European origin, the likelihood of him attacking Europe dropped by several percent. Since “Religion” is part of the title, it might be worth mentioning that the period of “49 days” is significant in many religions: the Buddha, for example, meditated for 49 days and in Christianity the Pentecost is 49 days after Easter. [The 50 implied in the word Pentecost comes from inclusive counting.]
Next up, Rod Carvalho presents Distance between two words at Reasonable Deviations, which shows how to measure the distance between two words of the same length. He introduces a graphical approach to make things more intuitive, and includes Python source code so readers can generate word graphs. We can trust Rod to be truthful about his Python (code), unlike the people who spread the story five years ago that an almost-49 foot Python snake was captured in Indonesia. That would have been the largest snake ever found, but the python turned out to be only half that length.
It’s now time for a reading break. If you were curious about the book Is God a Mathematician? by Mario Livio, you’ll be delighted to know that Arj reviews it over at Science on Tap! Driving, like reading, is a leisurely activity and if you’re ever in San Francisco (maybe for the Joint Mathematics Meetings next January!) you might use 49 Mile Drive, a scenic route that winds its way through the city.
Break’s over! Rémy Oudompheng now treats us to a post on computer assisted computations in algebraic geometry with Experimental Algebraic Geometry I: the Grassmanian over at Embûches tissues. Speaking of computations, the fraction 1/49 can be written as 0.02+0.0004+0.000008+… . For that matter, the number 49 can be written as the geometric series 0.98+0.982+0.983+…
Next, David asks the question, “Is it possible to make a toroidal polyhedron in which all faces are equilateral triangles and all vertices have six incident edges?” The answer appears to be no, but in Flat equilateral tori? at 0xDE he shows a colorful model that comes close. These might look good in a motion picture — perhaps one put at by Dreamworks Animation, the company founded by the 49th richest American (David Geffen).
Mike Croucher now presents Quadraflakes, Pentaflakes, Hexaflakes and more from Walking Randomly, which shows lots of different fractal flakes. These flakes won’t make you cold like the snowflakes that have been covering a lot of the northern hemisphere lately, including Alaska, the 49th state in the US.
The fractal flakes above aren’t the only thing that blend the familiar with the unusual. The calculus of finite differences has remarkable similarities to ordinary calculus, but yields a few surprises itself, as illustrated by John Cook in Finite differences at The Endeavour. The number 49 is (4+3)2, a familiar fact, but it’s also the 4th smallest number with 3 factors.
Le’ts move on to games! Burak Bilgin shows how game theory applies to economics, and how you can benefit from a simple rule derived from it, in The Simple Rule of the Economics Game from Distiller’s Corner. A simple fact about 49 is that it is 23 base 23.
Next there’s Math: A Different Perspective at Foxmaths! 2.0, in which Foxy derives some nice approximations for a complicated summation; these prove to be rather nice approximations indeed. The moral is to really stop and think about the math, do the math, rather than treating math as an abstract object. With sums in mind, it’s pretty simple to verify that 49 can be written as 1/24+2/24+3/24+…+49/24.
Now we hit a snag: this next post was submitted by Dave Richeson, but it’s on the blog bit-player that seems to be by Brian Hayes. Are secret identities being revealed? Whatever the case, the post Long division has lots of neat division. Not the “4 goes into 12″ kind, but the kind that divides an entire continent — in this case, North America. There are pictures included that look like they were based on photos taken from out in space. Space is where the space shuttle Endeavor might be in mid-May; its first flight was STS-49.
Finally, we end with vlorbik’s Section 5.5: A Manifesto, which he refers to as a “lengthy rant about pre-calc text” on Vlorbik on Math Ed. And we’ll end the 49 trivia by noting that 49 has an interesting connection with the numbers π and e:
The sum of the first ten decimals of πe is 49.
The sum of the first ten decimals of ln(π) is 49.
With that, our Carnival comes to a close. Thanks to all who submitted!
Balloon photo by wwskies.