Monthly Archives: October 2014

Halloween

Today is Halloween(in Singapore) so I thought I would say something.

I don’t celebrate Halloween.

The first time my mother convinced me to bond with her friends’ children by getting me to go trick-or-treating with them was not an enjoyable experience. I felt really awkward asking random people for candy. After all, almost nobody begs for candy of all things at the front door of strangers’ houses on any other day, so I didn’t see why Halloween should be so special. (Does this sound too condescending? I tried to phrase it in a way such that it didn’t but I think I failed.)

When I got home and ate the candy, of which only about a third I wasn’t disgusted enough by to eat, I realised that all of the candy I had collected could have been bought from a convenience store downstairs, without any of the fuss of meeting up at a certain place with other people and picking out a good costume which actually looked terrible and made it difficult to breathe. If I were my parents, I’d much rather buy me some candy.

Of course, anybody else is still perfectly welcome to participate in these festivities for whatever reason, be it following tradition, bonding friends or getting enough free candy to compensate for the amount of money spent on the costume. During Halloween I just like to stay at home, maybe change the background of my blog to black, and search the internet for interesting tidbits of information about Halloween.

Such as this! According to Wikipedia(which isn’t really much less credible than other websites) is supposed to be the start of a triduum(three day celebration?) called Allhallowtide, and Halloween is merely a contraction of All Hallow’s Evening. Which is probably why the festivities take place in the evening.

Halloween is apparently meant to use “humor and ridicule to confront the power of death“. It makes sense, although you’re not so much confronting death than trying to pretend that you don’t care about it whereas if you were actually about to die right now, you probably wouldn’t be dressing up as a ghost or a mummy and asking someone for candy. Or maybe some people would! I don’t really know.

One problem with Halloween is that sometimes people aren’t sure whether something is a prank or not. Two days ago, in Long Island in the U.S., Patricia Ward was beheaded by her son, her headless corpse being dragged into the middle of the street. The body left a trail of blood coming from Patricia’s house. Passers-by thought it was a Halloween prank, albeit a very macabre and realistic one. After trying to lift the body they realised that it was a real dead body. Her son was seen to have kicked his mother’s detached head across the street before committing suicide by jumping in front of a train.

Happy Halloween!

Headless_Horseman

Last Real Break

I’m currently 12 and next year I have to go to secondary school.

I’m a bit worried about what I’m going to do there. Will there be a lot of projects there? I think that if so, this is going to be my last real break before I die.

In secondary school, during our ‘breaks’ I’m going to have to complete all our projects so we won’t have real breaks. I might also have to have a sort of part-time job when I’m 16 or something, and have all these internships. I also have to arrange my own interviews which sounds like it would be really awkward or something.

Then after secondary school, I have to go and do national service because I’m a second generation Singaporean permanent resident, and then I have to look for a job(arranging my own interviews seems awkward) and then I have to do the job for the rest of my life, and I can’t retire because I’m not going to get married and have children, so I have to keep doing the job until I die.

That’s why I have to enjoy this while it lasts!(for about 2 more months)

Hexaflexagons

Now that the PSLE is over, I can finally do more interesting things! Like making hexaflexagons.

Hexaflexagons look like this.

Hexaflexagon

J. Nathan Matias

The difference between this and a normal paper hexagon is that it can flex. If you make one of these and push down every other crease(there should be three of these creases) as far down as you can, the inside will open up and reveal a new face. You can do this again and again infinity times, although flexing the simplest type of hexaflexagon three times will cause it to go back to the first face. Note that this only works one way for the simplest type of hexaflexagon(the trihexaflexagon, named because of its three faces); if the three creases you choose do not cause the inside to open up, the other three creases will.

To make the trihexaflexagon, you need to make a strip of nine equilateral triangles and some tape, or ten if you want to use glue. It’s a bit difficult to explain in words, so here are the instructions. You can draw designs on them too.

There are instructions online on how to make a double trihexaflexagon as well, also known as a hexahexaflexagon because it has six faces. You need twice as many triangles though. I also made a quadruple trihexaflexagon(a dodecahexaflexagon?) but when I was flexing it, it somehow turned into two square pyramids without a bottom, which also happens with the hexahexaflexagon. I tried to get it back to a hexagon but I couldn’t so I kept flexing it into weird polyhedra made of equilateral triangles, such as square pyramids stuck to a tetrahedron, until it finally turned back into a hexagon! Success!

Or so I thought until I realised that two of the triangles had somehow flipped over and now showed a different design! Aargh! It also happened to many other ‘sides’ of the quadruple trihexaflexagon but with different numbers of triangles switched. Some of them had 3 triangles switched, some had only 1, and lucky sides escaped this horrible mutilation of hexagons with their designs still all on one face. I had to find the point where I glued the quadruple trihexaflexagon together and carefully peel it apart, then re-fold the whole thing. So be careful with these things!

If you’ve read the instructions for the hexahexaflexagon you might know that it’s pretty easy to make this family of hexaflexagons by just doubling the number of triangles for each new hexaflexagon. I have not, however, tried making a triple trihexaflexagon. Maybe I should, but I can see some problems with it. Oh well.

For more about the history of hexaflexagons, see Vi Hart’s video on hexaflexagons and the sequel, and also the safety guide.

The Only Even Prime Number!

2 is the only even prime number! It’s so amazing!

I’ve heard statements similar to the above in many places but I was always confused by why so many people consider it amazing. Even just means divisible by 2, and of course 2 is divisible by itself. It must also be the only even prime number because if any other prime number was divisible by 2, it would have to be 2 or be composite, in which case it is not a prime number.

Why is this so amazing? 3 is the only prime divisible by 3, 5 is the only number divisible by 5, etc. I wouldn’t even be convinced that 5 is special for being the only prime number that ends in a 5, because it only retains that property in base 10, the base that we use.

You could argue that 2 is the smallest number that has this property, but since all prime numbers have this property the most you can say is that it is the smallest prime number, which it actually shouldn’t be(due to negative prime numbers) but for some reason is considered to be.

So while 2 is the only even prime number, that property isn’t as special as you might think. A more suitable ‘special property’ is that 2 is the smallest prime number that is also a positive integer.

That’s so amazing!