There are many mechanisms for doing arithmetic - the Japanese teach line multiplication. It works because the lines are proxies for powers of 10 and the number of intersections in each region is a product of the number of lines. You end up summing the products that are coefficients of the same power of ten ... so here you get (1 * 100) + (2 * 10 + 3 * 10) + (6 * 1)
A nice trick that will confuse people who haven't seen it
Random numbers have many uses - today they are important for solid cryptography. Most random numbers are pseudo-random ... they aren't truly random, but can be good enough. Problems arise when they aren't and that turns out to be a big issue in security these days.
There are many natural ways to produce them as many processes in nature are random. Here is a neat one that makes use of the fact that most light sources produce photons randomly (a flood of them to be sure, but random when you look closely enough). It uses a ccd array and a bit of cleverness to generate useful numbers - and it can generate radom bits at a few million per second using a software approach to the analysis. Probably good enough for most purposes.
Quantum random number generation on a mobile phone
Bruno Sanguinetti, Anthony Martin, Hugo Zbinden, and Nicolas Gisin
Group of Applied Physics, University of Geneva, Switzerland
Quantum random number generators (QRNGs) can significantly improve the security of crypto- graphic protocols, by ensuring that generated keys cannot be predicted. However, the cost, size, and power requirements of current QRNGs has prevented them from becoming widespread. In the meantime, the quality of the cameras integrated in mobile telephones has improved significantly, so that now they are sensitive to light at the few-photon level. We demonstrate how these can be used to generate random numbers of a quantum origin.
Some fields refer to false positives as type I errors and false negatives as type II .. I don't know why the more descriptive false positive/false negative terms aren't used, but historical labeling is often messy ..
anyway someone sent this visual way to easily remember the difference:-)
A googol is 10100 - 101 digits the inspiration for a mispelling that names a search company and sometimes taught to kids as a really big number. Beyond that is 10googol - the googolplex with about 17 million digits. But this is tiny - very tiny - compared with the scale of Graham's Number:
Change ringing refers to the playing of long sequences of permutations of the order of the ringing of bells - usually church bells. The Simons Foundation has a nice video explanation. An interesting combination of stamina, mathematics and art dating back about four centuries.
Neil deGrasse Tyson talks about the history of scientific progress and what happens when figures like the 12th century figure Hamid al-Ghazali can hit the brakes. It makes you wonder about the modern House in America with the sharia house rules of a party aiming itself at the distant past.
At least where people write a calendar as month.day and where biblical precision is all that s necessary (unless you get into hours, minutes and seconds as some do). But celebrations are often fun and an excuse to eat pie is welcome (note that e is another great irrational number).
Something curious is to look for interesting strings in pi. It is not known if the digits of irrational numbers are random, but pi gives the appearance. One of the first interesting strings comes at the 762nd decimal place where there are six 9s in a row. Richard Feynman noted if you are memorzing pi, to it to that level and then you can end by saying "... two, one, one, three, four, nine, nine, nine, nine, nine, and so on ..." suggesting pi is rational:)
For short strings it is easy to calculate pi to a few million digits and then find the string. So you can represent your initials by numbers (ascii for example) and find where they first occur in the number..
In the spirit of fun there is this video. Someone sent it yesterday and asked what it was - it is a joke .. see if you can figure it out:-)