Monday, December 08, 2008

Almost prime numbers

Sean has been entertaining himself all afternoon, writing little stories, drawing 3-dimensional shapes, imagined 4-D and other-D shapes; while Brian and I worked on some Singapore Math. Oh, he also watched Sound of Music alone. Eddie flew off to Athens for a meeting this morning, that's why I could get Brian to do some work on a weekend. Otherwise, we'd be vegetating in front of the tv watching dvds.

Right before bedtime, I found a piece of paper with the scribblings above. It's a mathematical term concocted by Sean called "Almost Prime Number".

Just to refresh, remember the definition of Prime Numbers? ie Numbers that have only 2 factors; 1 and itself.

Well, Almost Prime Numbers are numbers with only 3 factors, Sean says. He squares prime numbers, and discovers they only have 3 factors.

He goes on to explain:
"As you can see here, a prime number times itself equals an almost prime number. And there's also something special about it. Every almost prime number always has 3 factors. 1, itself, and its square root. The square root is the thing that makes the number not prime."

When I tucked him into bed just now, he asked this, "Mummy, are square roots of prime numbers always irrational numbers?"

Brian says, "Of course."

I said, "I'm not sure."

Brian goes, "Look Mummy, prime numbers only have two factors, 1 and itself, so obviously it cannot have any square roots that are rational numbers or that number would be be its factor."

I then wondered if all square roots of integers have to be either integers or irrational numbers. Brian says that is so and when I googled, Wikipedia says, "Square roots of integers that are not perfect squares are always irrational numbers."

Interesting stuff.


monlim said...

My head is spinning... Sean can come up with his own number systems? And you say your kids are not math geniuses??

Lilian said...

He's just had too much time on his own.

Math genius is like this 10 year old boy lah.

Anonymous said...

My head is spinning too...LOL.

Lilian, your kids are super lah!


Domestic Goddess said...

My jaws are on the floor now. Wah! Your boys got to be math geniuses! Sean is just 6, isn't it? OMG!

What do you feed them on daily basis, huh? :P

Lilian said...

They just like talking and reading about number patterns and such, that's all. They definitely don't have lightning-speed calculation prowess or very deep understanding of mathematical concepts that math prodigies do.

Again, it's the availability of wonderful books written for children these days that make such knowledge accessible to kids at a younger age than during our time. These books save me a tonne of effort man, don't need to teach factors (and relatedly division), squaring, roots, fractions and lots more.

BUT I still need to teach Singapore Math escaping that...

monlim said...

There are different levels and types of geniuses. Just because Beethoven doesn't compose the same type of music as Mozart doesn't mean they're both gifted musicians. Don't deny the talent in your kids, embrace it.

Lilian said...

Ha! You throwing that back at me. Okaylah, embrace embrace, even though your analogy using Beethoven & Mozart, both maestros, is really bad!

monlim said...

How about Paul Theroux and Charles Dickens?

Lilian said...

Maybe something I can relate to...Jack Neo and Adam Sandler :P

monlim said...

also can lah :D