Category Archives: Math

Fake stuff

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.

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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!

12. And 12 again. Then 12 and 12 and 12 and 12 and 12 and 12 and 12 and 12 and 12 and 12!

Hello!  Today is 2012/12/12.  It’ll soon be 12:12.  It’s a once in a lifetime experience!  I think today I’ll brush my teeth thoroughly 12 times.  12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12.  12 12s.  The title also has 12 12s.  8,916,100,448,256  is 12 multiplied by 12, 12 times.I’m so excited!

What are you going to do to mark this day?  You can’t do this after tomorrow!

by mortimer?

Comment/s from old blog:

Dear Sean,
Yes 12/12/12 was really cool…. I did not do any thing though. I can’t believe the next time it is some thing like that will be in 03/3/3 Probably not in our life time. Bye Sean, sorry I was not at school to say good bye.
Sincerely Molly

Statistics and Birthdays

If you have 4 people in your family there is a 70% chance that 2  people will have a birthday in the same month.  I have a family of four(only counting parents, myself, and older brother) and my birthday is in September, which is the same month as my father’s!

If you have 7 people in your family then it is likely that 2 people will have a birthday in the same week.

If you are in a group of 14 there is a 50% chance that 2 people in that group will have the same birthday.

If you are in a group of 35 there is a 85% chance that 2 people in that group will have the same birthday.

If you are in a group of 60 there is more than 99% chance that 2 people in that group will have the same birthday.

Isn’t that amazing?

Student Learning: Math

Hello! Today I will tell you what I learned in math. We learned about probability. Probability means the chance that something will happen. For example, the probability that a tooth will conquer the world is impossible. Impossible means it cannot happen any way. It is 0%, which means 0 out of 100 outcomes. Outcome means what happened or what can happen. There is also unlikely, which means it can happen but it is probably not going to happen. It is around 25%. It is unlikely a cannibalistic tortoise will be born. In the middle is maybe. That means there is an even chance, or 50%. Maybe a coin will land on heads. Likely means it is probably going to happen. It is 75%. It has been raining for many days in Thailand, so it is likely that it will rain again. Finally there is certain, which means it will definitely happen. Can you think of anything?

Pi Day

Today is World Pi Day. These are videos of me taken about 2 years ago where I recited the pi up to 200 digits. I managed to recite the pi up to almost 300 digits, I think, but I can’t do it anymore. I’m posting this video because my brother’s homeroom teacher from Moscow who is now teaching in Shenzhen wants to show this to his students. Hi Mr Robins’ students!

This is me reciting pi.

When I go so fast, the numbers may not sound clear, so here I am writing pi down.

Pi up to 200 decimal places:

3.1415926535897932384626433832795028841971693993751
05820974944592307816406286208998628034825342117067
98214808651328230664709384460955058223172535940812
84811174502841027019385211055596446229489549303819

 

Comments from old blog:

  1. Hello Sean! My 7th graders were super impressed! I of course, was already impressed when you showed me in person (the ABBREVIATED version) back in Moscow. Sounds like you and your brother continue to do great work and I’m always happy to get an update from your family.
    Tell your big brother I wish him good look on the AIME at the end of the month! He may not be able to remember 200 digits of Pi, but he’s still pretty smart! ;)

    • Hi Mr Robins! Do your 7th graders have blogs? I would like to visit their blogs if they do. Thank you for visiting my blog. Please visit again. I will let my brother know when he gets back. He just left for the weekend to build houses for Habitat for Humanity. He’s away a lot these days.
      Sincerely,
      Sean
      ps Do you miss Moscow? I miss Moscow because Thailand doesn’t have any snow.

  2. Dear Sean,
    I love World Pi Day and I was so sad to miss it this year. I didn’t realize it was that day until I got home from school. Did you do anything to celebrate this year? The blog post is a great idea! Maybe we can explain to the other kids a little bit about pi. It is such a cool number.
    Sincerely,
    Ms. Chesebro

    • Dear Ms.Chesebro,
      I think I can share pi with the class if I have time. I agree that pi is an extroardinary number. After all, where else can you find such an irrational number?
      Actually, there’s also phi and e but I don’t know what they are used for. Pi, on the other hand, is useful for finding the area or volume of circular objects, such as pies!
      Sincerely,
      Sean

  3. Hi Aunty Tsu Lin, thank you for commenting on my blog. As for my technique, I just looked and memorised and then when I’ve memorised a string of numbers, I memorised more and more and more. Some strings have a certain pattern in them. Too bad I can’t do this anymore. Maybe I’ll try again over summer holidays. Bye!

  4. Hi Brett, I like your blog. It’s very nice and it’s very interesting. I will visit again soon. Thank you for visiting my blog.

  5. Hi Sean,
    I am Brett and I am from the USA. I found you through the blogging challenge. I thought it was really cool that you could memorize pi! At our school we celebrated pi day, and we had a lot of fun. If you want to see my blog click here:http://www.brettm18.edublogs.org
    From,
    Brett