## Tuesday, March 31, 2009

### Pi up to...100

Okay, call me a crazy mum but I got Sean to memorise pi up to 100 decimal places. I know this is all useless, but at least he can look back and know that once upon a time, he knew pi up to 100 dp, how many people can say that? :P (I know there are lots of people who can, but just humour me okay?)

On Sunday, we turned the clock forward one hour, and Sean decides he will not go to school on Monday cos he might not be able to wake up (that's how kiasu he is). He did wake up at 7am, earlier than everyone else, but once he's decided, he's not changing his mind. I told him to be prepared to work at home. Work means doing Singapore Math assessment books.

By 2pm, all we had done the entire day was...nothing. I was in bed, clicking on the computer aimlessly all day, instead of working with him or at least starting to pack for our trip back to Singapore.

Feeling guilty about doing nothing, yet not willing to get off my butt to get the Singapore math workbook, I decided to get him to memorise pi bit by bit. By evening, he had memorised up to 95 decimal places. When Eddie was having dinner, I told him about what Sean could do. He immediately told Sean, "No need Sean, no need to memorise, don't stress your brain okay?"...sheesh...*rolls eyes*...as if this bit of brainwork was gonna fry his son's brains.

And Sean was having fun anyway, jumping around and laughing whenever he got further and further...I know, I know, I'm justifying this craziness.

This morning, I was using the computer near the dining area when he woke up. He climbed on me and sat on me while hugging me. Not a word. Then he suddenly smiled at me, and said, "I was saying pi up to 95 decimal places in my head."

So what is a crazy mum to do; I told him the next 5 digits lah (70679, see?, even I can remember) and video-ed him after he had changed and eaten breakfast.

And here is pi up to 100 decimal places, source:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

## Friday, March 27, 2009

### Parenting: Natural or Learned?

This NY Times article asks, "Are parenting skills something you are born with? (And if so, what are all those shelves of parenting books for?)"

I have not read a single parenting book in the last two years. Not that I don't find them useful, but anything I've learned from these books I end up not putting into practice after the initial couple of weeks. And while learning from friends about how they parent their kids is useful during the toddler years, I'm finding that as my kids grow older and develop their own distinct personalities, it's often easier to just trust my instincts.

So I'd have to say my style of parenting is probably in-born and then fine-tuned according to the child's temperament. As with so many things in my life, I really go with the flow. I do not subscribe to any particular parenting philosophy nor am I bound by advice from the more religious amongst my friends.

Not that it's gonna be useful to anyone other than myself, but here are a few underlying principles in the way I parent:

I don't want to be my mother

Now, I love my mum and I know she loves me. She's always been there for me, and she has many positive traits. But her authoritarian (as opposed to authoritative) parenting style compounded by an irrational temper she says she can't control, would probably had marred me for life if it had not been for the kind, generous, gentle and loving ally I had in my late father, the funniest person I know. Because of my wonderful childhood memories, I strive to be like my dad, but often I hear my mother's voice coming out of me when I lose it with the kids (...when this happens, I shudder). So while I try not to parent like my mum did, my natural parenting style is actually a mix between my mum's and my dad's, tilting more towards my dad's.

No blaming the bogeyman

My sister and mum used to like distracting little kids who hurt themselves by pointing somewhere and going "Oh, oh, look at the cat!" when there's no bloody cat around. Or they'll beat the floor after a kid's fallen down and say, "don't cry don't cry, we beat the floor, naughty floor." Ridiculous! When Brian was just a baby, I told them, NEVER, EVER, EVER do that. If they fall, they fall, it's no one's fault but their own. It's most definitely not the naughty floor's fault! This applies to other things in life, look to yourself first and ask if the fault lies with you, instead of always looking for someone to blame. And when they're old enough and able to pick themselves up, I'm not gonna hover over them making sure they never hurt themselves. Of course, if the child is truly hurt and need your help, your maternal instinct will let you know. Which brings me to...

Mother knows best

The parenting guru does not know your child. They may have some good tips but not all will work with your particular child. We've gotta be flexible and trust our maternal instincts. For example, someone will say Spare the rod and spoil the child, another will say violence begets violence. My personal preference is to use a cane instead of my hand, if any physical punishment is to be meted out. A cane is detached from mummy but mummy's hand belongs to mummy, I don't know if this makes sense. What I know is I have been caned so many times when I was young but the one punishment that I always remember will the the one time (actually twice :(, once when I was 6 and another when I was 17) my mum slapped me on the face. That, somehow, left a deeper emotional scar than all the canings which left physical marks on my legs (many of my Chinese classmates had cane marks too, no biggie).

My caning (or what I call training) style goes like this, boys misbehave, they both (the musketeer rule of one for all, all for one, applied; one gets punished, both get punished) lie flat on the sofa on their stomach. I explain why they're being punished and give them each a swat. Brian takes it like a man while Sean will cry and plead even before he sees the cane. After the swat, they sit up and say, "Sorry Mummy, and Thank you for training me."...Sean says this while sobbing. Brian hasn't been caned in the past year and I've told him I won't be caning him anymore as he's old enough to reason with. I've told Sean he'll still get the cane if he misbehaves. So although I get bombarded by how we shouldn't cane our kids, I know I couldn't have done without the cane. No amount of reasoning and talking would have kept Sean from driving me crazy circa 2004/2005.

Mothers make mistakes, move on

I've done some pretty mean things to the kids, and I do look back with some regret, but who knows what worse things could have happened if I did not react that way? I might not even be here today. I've slapped Sean so hard on the face when I totally lost it (so really caning is when I'm still rational, when I use my hands, I am already out of control). When Brian was 2+, he gave me such a hard time one weekend that I just whacked him so hard, only to realise to my horror five minutes later that he had huge ulcers in his mouth and that was why he was making such a fuss before and during dinner. He actually had HFMD. I beat myself up and cry really hard whenever I did mean, insane things; and I tell the kids how sorry I am. Brian is always forgiving, Sean less so...but they always know how sorry I am. A friend told me once parents shouldn't ever say sorry...but I don't buy that. So regrets there have been more than a few, but we move on; the kids know I'm human and I make mistakes, while I pray I haven't scarred them for life.

Season speech with grace

I take a laissez-faire approach to lots of things and allowed my mum pretty much free rein over the way she parented the kids when I was still working, but one thing I insisted on was that she must not use negative words such as Stupid, Idiot, Naughty on them. Of course when I lose it, I have used these words, maybe even worse words. But because I hardly use these words, when I do, it really pierces the boys and you can see the hurt immediately on their faces, it's like a shock to their system. I can't help it, that's what I do when I'm incensed (it doesn't happen often, maybe once or twice a year). So later, when I've cooled down, I'll say "Sorry, I didn't mean it, I was just sooooo angry. Of course you're not stupid, and you know that."

However, for the most part, I am always praising the boys, telling them they are the best, the smartest, the cutest, the most gorgeous and so on. They know I'm exaggerating of course. If Sean climbs into my bed as he does almost every morning, the first thing I say to him while we cuddle is, "Seanie, you're the best." or "You're perfect." or "You're gorgeous." in a sing-song voice. He immediately goes, "No, I'm not." and I pretend to cry...and he goes, "Fine, I am." in mock exasperation. This is our standard joke which goes on throughout the day...he sometimes says "No, I'm not" in barely a whisper and I'll still bawl and he goes, "Fine, I am."  We giggle at our private joke.

Make sure they know how much I love them

If nothing else, I want the boys to know that I love them so much. I'm always hugging them and grabbing them and kissing them. This isn't really a conscious effort, it's just something I need to do, for myself, yes, I am that needy :). I'm always telling them how happy they make me, how perfect they are. Cos to me, they are! To others, they may be annoying little punks, but to me, they're my perfect sweethearts (except when they're annoying melah). So whatever others might think of them, they know they are No1 in at least one person's eyes, Mummy's!

Pray over them

Now I'm the last person to look to when it comes to spirituality/Christianity. I don't read the bible and I dislike organised religion and preachy people in general. I find many Christian acquaintances very judgmental, though my good friend Irene, a staunch Christian, likes to point out that I'm being jugdmental too by saying they are judgmental. Touche!

Anyway, one thing I do, though not as regularly as I should, is to pray over the boys. I pray over them when they're sick. I also pray over them when they're in bed and I make sure they hear my prayers. Eg, when Brian was going through a very rude and angry stage (which still resurfaces now and then), I would pray out loud while laying my hand on him, "Lord, Thank You for healing Brian of any hurt in his heart. Help him know that he is loved by all of us so much. Lord, I know he is a good boy with a good heart, and I pray for wisdom and understanding in raising Brian as he goes through the difficult adolescent years. Lord, Thank You for showing us the right way to go, and for strengthening our relationship every day. Thank You for giving us peace of mind that all will be well in the end. Thank You Lord for this wonderful and loving child. We love him so much. Amen" So far, he hasn't shown cynicism when I do this and whether it's coincidence or not, he's always much better behaved after I remember to pray over him.

No preaching; action speaks louder than words

I don't really talk to the boys much about values nor about religion. How can I talk about religion when I don't even read the bible nor go to church regularly? It would be hypocritical to do so. They know I pray and they know what I believe in; and when the time comes, they will choose for themselves what they believe.

Kids are smart; they'll know if you're faking it. When they ask me about creation and Big Bang, I tell them Christians believe this while scientists believe this. What do you think? If they say they think it was Big Bang, I tease them by going, "Whaaaat? You don't believe God created the world in 7 days??!!" Seriously, I can't pretend I know the answers to everything when I don't, least of all how the world was created.

Two words - BE KIND

I've told them they are to remember only one thing and everything else will fall into place - Be Kind. If there's just one value I want to impart to them, it's this. No long list of things to remember. Just be kind. And as it is, even with just one measly thing to remember, they often can't remember to be kind to each other, what more if I give them a long list of Dos and Don'ts.

So just as I want them to remember to Be Kind, at the crux of it all, my basic principle in parenting is also Be Kind. That and lots of prayers and faith that God will take care of everything.

************************************

I've learnt that the one thing I shouldn't do is to try to emulate my friends' parenting styles just cos I see their kids behaving so beautifully. Subconsciously, I'm trying to make my kids just like my friends' kids and it never works; cos my kids don't have the same parents and family and siblings and personalities as those kids. Trying to do this never fails to raise the stress level at home. Kids sense it when their parents think they aren't good enough.

I've accepted that my kids will never answer the phone in the cheeriest voice announcing, "Leong Residence, this is Brian/ Sean speaking, whom am I speaking to?" (I have friends whose kids do this) or say the sweetest hellos and how are yous to my friends and probably never take to brown rice and very little meat for meals.

I'm not gonna sweat the small stuff.  There is just one big stuff, BE KIND!  And while I'm sure I'll be picking up a parenting book in the near future that deals with angst-ridden teenagers, chances are I'll still fall back on BE KIND and the other principles outlined up there to guide me in this always surprising but exhilarating journey we call parenthood.

## Wednesday, March 25, 2009

### What the boys think of us

Inspired by Hsien's post, here are the answers I managed to squeeze out of the boys, not an easy task at all! Btw, they were questioned separately, without knowing what each other's answers were.

1. What is something mummy always says to you?
Sean: I love you

2. What makes mummy happy?
Sean: Me
Brian: Me

Sean: When I go to school

4. How does your mummy make you laugh?
Sean: By tickling me
Brian: She makes jokes

5. What was your mummy like as a child?
Sean: A girl
Brian: Mischievious

6. How old is your mummy?
Sean: 40 (No I'm not!...not yet anyway.)
Brian: 39

7. How tall is your mummy?
Sean: 160 something centimetres
Brian: 170 cm (woot...thanks Brian :))

8. What is her favorite thing to do?
Sean: Play with me
Brian: Surf the internet

9. What does your mummy do when you’re not around?
Sean: Play computer games
Brian: Surf the internet

10. If your mummy becomes famous, what will it be for?
Sean: Playing computer games
Brian: Setting a record on a computer game

11. What is your mummy really good at?
Sean: Playing computer games
Brian: Cooking

12. What is your mummy not very good at?
Sean: Playing tortoise talk
Brian: Teaching Sean

13. What does your mummy do for her job?
Sean: Cook
Brian: She's a wife and mother

14. What is your mummy’s favorite food?
Sean: Chilli
Brian: Peking Duck

15. What makes you proud of your mummy?
Sean: Loving me
Brian: She's a very funny mother

16. If your mummy were a cartoon character, who would she be?
Sean: Bloo (from Foster's Home for Imaginary Friends)
Brian: Frankie from Foster's Home for Imaginary Friends cos she takes care of everyone in the house

17. What do you and your mummy do together?
Sean: Hug each other
Brian: Play computer games

18. How are you and your mummy the same?
Sean: We both play computer games
Brian: We both know how to take care of ourselves

19. How are you and your mummy different?
Sean: Mummy likes surfing the internet and I don't
Brian: She's funnier.

20. How do you know your mummy loves you?
Sean: She hugs me
Brian: She always hugs me and tells me she loves me

21. Where is your mummy’s favorite place to go?
Sean: China Dreams (a chinese restaurant in Moscow)
Brian: Japan

_____________________________________

1. What is something daddy always says to you?
Sean: I don't think daddy ever says the same things to me.
Brian: Ze boys....(Eddie's standard greeting to the boys when he gets back from work)

Sean: Fruit plus (a sweet)
Brian: Prawn crackers and dvds

Sean: By farting
Brian: He makes jokes about himself

Sean: A boy
Brian: Mischievious and funny

Sean: 40
Brian: 39

Sean: Maybe about the same height as my mummy
Brian: 165 cm (LOL!)

8. What is his favorite thing to do?
Sean: Watch TV
Brian: Watch TV

Sean: Watch TV
Brian: He works

Sean: For being the fattest person
Brian: Most hardworking at work

Sean: Eating Fruit Plus
Brian: Working

Sean: Being thin
Brian: Taking care of himself

Sean: Work at Singapore Airlines
Brian: He works at Singapore Airlines

Sean: Fruit Plus
Brian: Charsiew

Sean: Peeling me oranges
Brian: He works very hard

16. If your daddy were a cartoon character, who would he be?
Sean: I don't think he would be a cartoon character
Brian: Mr Herriman cos he's always ordering Frankie around

Sean: Eat sweets and watch TV
Brian: Watch movies

Sean: We both like oranges
Brian: We both like eating raisins

Sean: Daddy eats peanuts and I don't
Brian: He's always eating tidbits and not taking care of his body.

Sean: He gives me oranges
Brian: He does many things for us

Sean: I don't know
Brian: Kota Kinabalu

### Pi in the sky

Nowhere near any record of any kind but pretty good for a boy who's always saying he doesn't have a good memory. Sean recites pi up to 31 decimal places.

I've never been able to make Sean memorise anything, not spelling, not poems, not multiplications; he always goes, "I can't...I don't have a good memory..." so who knew he'd remember a 32-digit number. I'm not sure when he started memorising this, I did hear him mumbling 3.142...blah blah blah for some time now from wherever he was reading his book, but didn't think very much of it.

And why 31 decimal places? Well, he showed me the page where he got the numbers from, Murderous Math's The Perfect Sausage.

And there it was, pi at 31 decimal places :)

Who knows how much more he would have remembered if the book had more digits? But this is at least one thing Sean has over his korkor, whom he is always saying is very clever...cos Brian, the brother with the good memory, can only remember pi up till 16 decimal places.

Go Sean, who says you don't have a good memory!

ps. When Sean heard himself on the video, he said to Brian, "You're right...I do have a whiny voice." LOL! At least no one can say he isn't self-aware.

pps. And yes, I know my boys need to get out of the house more often.

### Tabloid Junkie No2

I'm a tabloid junkie, no doubt about that. London was heaven for me, so much rubbish to read, and most at only 99p. These magazines cost many times more in Singapore. Well, Eddie came back from London with 4 magazines for me, most were about Jade Goody, who sadly, lost her battle with cancer a couple of days ago.

But someone else has been reading the magazines more than I have, Sean! 6-year old tabloid junkie.

He spent most of the weekend reading these magazines quietly. I don't know what he finds so fascinating actually, since he doesn't even know the celebrities, but he'd ask me why Jade was bald, what happened to her, and he'd read the real life stories section too.

Of all the things to take after me!

### Farewell to the Laws, farewell to mahjong :(

This Ghzel Porcelain plate holds 8 eggs, the chicken in the middle can be lifted up, maybe meant to contain condiments, we're not quite sure. It's a farewell gift for our mahjong kakis Eugene (SQ Station Manager) and May who left Moscow last Friday. They will take up their new posting in Paris soon.

Our last mahjong outing was fun, I won the most, followed closely by May. The men lost, but Eugene lost by far the most! So FUN!

Our weekends will not be the same anymore :(

### Treasure from London

Eddie was in London last week for a meeting and bought these 9 tubs of cocoa powder for me. Anyone looking for Green & Black's organic cocoa at High Street Kensington's Waitrose last Wednesday will be disappointed. They're all with ME, they're MINE, ALL MINE!

I have been missing these beauties for so long. Haven't been able to bake my favourite chocolate cake for the longest time cos I had run out of cocoa. This particular brand has been the one I've been using all the while and I didn't want to risk baking a cake no one wants to eat if I use brands like Hershey or Van Houten. I can't find Varlhona (sp?) here and I think the only place to get it in Singapore is Shermay's? That's a bit out of the way for me.

And I'm sure this is much cheaper anyway, only GBP1.65 a tub. Anyone craving for a slice of chocolate cake, come by for tea next week.

## Monday, March 16, 2009

My friend from Frankfurt, whom we all call Bao cos she's such a cute BaoBao :), is now a published author.

Her book can be found on Amazon now. So anyone going to Malaysia to work or for business, this is the book for you.

Bao, this is so exciting, can't wait for your Martha-Stewart-style book next, I know you have plenty of material for that.

BIG CONGRATULATIONS Gorgeous!

## Thursday, March 12, 2009

Sean said he told his friends this, "When my mother got addicted to the Jewel game, she stopped being addicted to the Patty Panic game, and she stopped being addicted to the Jewel game now that she's addicted to the Zuma game."

So kaypoh these boys, always monitoring what I do.

Brian gets smart-mouth by asking me the moment he reaches home, "So Mummy, how was Zuma today?" !!!

So I played Zuma non-stop for the past week. He's one to talk, he totally takes after me in game-addiction. First was the 1-hour free Monster's ball (can't remember the title, I think it's Monster's ball) that Monica recommended months ago. Brian begged me to purchase the game, he said he'll pay me back. Nope.

Then last week, he got to try Ouba, also recommended by Monica. Again, he begged me to purchase this. Again, I said no, (1) cos I don't like to make internet credit card payments and my Paypal isn't working cos the card linked to it expired; (2) the game will be downloaded onto my notebook which I need to use ALL the time; (3) even if Brian had his own notebook to download the game, it'll still be a no, cos knowing him, he'll be thinking of the game all day and night.

He likes Ouba more than Monster's Ball but his favourite is this on-line game that he learnt to play at my friend Slim's house, I forget the name, maybe it's Age of Mythology. He doesn't get to play this at home, I think you need to purchase the cd-rom first.

Anything that needs to be purchased, er, Nope. Free games will do just fine for now.

And yes, I do get a bit quiet when the addiction strikes. It's Zuma time now, see y'all later!

## Saturday, March 07, 2009

### Murderous Math Round 2

I said back in mid-September that Sean wasn't too interested in the Murderous Math books that Brian used to love so much. Right after we returned to Moscow from Singapore in mid-January, he started reading the entire series every day. He's read many, if not all, of the books at least 3 times. I'm sure he understands only bits of the books, but that's the beauty of these books, kids enjoy the comics first, and learn more and more each time they re-read the books, without ever realising that they're learning. The best kind of learning, in my opinion.

After reading the books, Sean would draw, make things (eg make shapes out of paper) or find things in real life that he feels are related to what he's learnt from the books. I don't remember Brian doing much of this in the past. I think it's Sean's way of internalising what he's read and reinforcing his understanding.

Some examples:
Pythagoras Theorem illustrated. He's just drawing what he's seen from the book, it doesn't mean he really understands how to use the formula.

And here he's tri-secting (I don't think tri-secting's the right word but that's what he said he was doing) regular polygons, from 3-sided ones to nine-sided ones. He offers this nugget, "The more number of sides the shape has, the smaller the central angle will be."

And one day, he came by with these two blocks and points to the semicircular bit and tells me it was a Reflex Angle (an angle more than 180 deg but less than 360 deg).

He spends hours using the protractor, drawing angles, folding paper, cutting out shapes (yes, he's been left alone a lot the past month, I was sick lah). For some time, he kept bugging me for a UK 50p coin cos Brian had told him it was the shape he (Sean) was looking for, a heptagon.

I couldn't find him a 50p coin and was still not sure if it was really a heptagon till I googled it 10 seconds ago. True enough, 7 sides. Not many coins with 7 sides right? Must remember to keep a 50p coin for Sean next time I'm in London.

While I was typing this, Sean came by to ask, "If each side of an equilateral triangle was 33cm, how many 3cm equilateral triangles would fit in it?" Upon drawing the big and small triangles, we then find out it's 121 triangles, ie the 11th (33/3) square number.  So if the big triangle was 48cm-sided, and the small triangles were 2cm-sided, it'll just be the 24th (48/2) square number, ie 576 small triangles would fit into the big triangle.

MM books put many mathematical concepts within the grasps of primary schoolchildren. Heck, it's useful for adults too, since we never learnt many of these in school, at least I didn't. I thought I learnt quite a lot when Brian was using the books cos he would tell me all the interesting things he had read, but this time round, I'm learning more new stuff too with Sean cos he learns in such a different way from Brian.  It probably helps that I've had 1 round of MM with Brian, so some of the basics have been covered, and I'm not as clueless as before.

Kjartan Poskitt is truly my hero, math-wise, that is. I just wish he'd write an MM book on Calculus soon.

### Undefined & Indeterminate Defined

I asked for help at the end of this post but nobody came...

Never mind...today I chanced upon an excellent explanation for zero over zero and the difference between Undefined and Indeterminate.

Here.

## Friday, March 06, 2009

### Tesselation and angles

These are a couple of Sean's messy drawings of tessellating shapes.

He told me the other night that the only regular polygons that tessellate are the triangle, the square and the hexagon. It had something to do with the interior angles of these polygons. I didn't understand what he meant and called for Brian of course.

Brian explains that only regular polygons with interior angles that are factors of 360 tessellate.

The boys watched me as I tried to find out the interior angle of each polygon, to see if it was really true that only the interior angles of the triangle, square and hexagon are factors of 360.

The interior angle of an equilateral triangle is of course 60deg, so that goes into 360deg 6 times. Tick.

The interior angle of a square is 90deg, and that goes into 360deg 4 times. Tick.

No protractor in sight, I ask Brian, er, what's the interior angle of a hexagon?

He tells me this:

So to find the angle of any regular polygon, you've gotta subtract the number of sides by 2, multiply by 180deg, and divide by the number of sides.

After my usual "are you sure?", I got hold of a calculator and started doing what Brian said. First, I checked if the formula worked for a square, it does.

So I find that the interior angle of a pentagon is 108deg, and that doesn't go into 360deg. Which means it doesn't tessellate.

Moving on to hexagon, the angle is 120deg, which goes 3 times into 360deg.  Tick.

We've got all 3 of the regular polygons that Sean tells me are the only ones that tessellate.  But do I stop?  Nooooo....I'm anal that way....I continue calculating for the rest of the whatever-gons.

I was about to calculate the interior angle of a 14-sided regular polygon when Brian asks me, "What are you doing Mummy?"

Me: The next number that will go into 360deg is 180deg, so I'm looking for the polygon with that interior angle.

Brian: You can't!  180deg is a straight line!

Me: Uh...oh...hmmm...really?

I then calculated the angle for a 1,000,000-sided polygon, and the calculator showed, "179.99964".

Ohhhhh, you're right Brian, I said, feeling really dense. Unlike me, Brian doesn't gloat.

I can't believe I was gonna go on calculating interior angles of goodness knows how many more polygons. 180deg! Of course it's a straight line, what a Duh! mummy moment. Unbelievable.

*Note: Sean's first drawing shows tessellation of an octagon, but it only works if combined with a square of equal sides to the octagon's sides.

## Thursday, March 05, 2009

### Sean's mathematical rainbow

750am.

I am watching American Idol results show on the internet in my bedroom and Sean shouts from the kitchen, "Mummy, I see a rainbow!"

I shout back: Goood! (back to AI)

Sean runs in: Don't you want to see the rainbow?

Me: Later okay? (back to AI)

Sean leaves the room, then shouts again: "Mummy, don't you want to see the rainbow?"

Me: Later! (back to AI)

Sean returns: Can't you just pause it?

Me: :(

Feeling guilty, I pause AI reluctantly, walk to the kitchen window expecting to see a rainbow outside.

Instead, he points to the floor, and indeed, a rainbow is reflected from outside on to the dining area floor.

Sean: Isn't it beautiful?

Me: Yes, wow! (I'm very good at my Wows)

As I head back to my bedroom, Sean looks at his rainbow again, jumps about happily and adds, "It's like a parabola."

He laughs, "It's a Mathematical Rainbow."

### Zero over Zero

730am this morning.

Sean: If a fraction equals 1, that means the numerator is the same as the denominator right?

Me: Right.

Sean: So what if the fraction is zero over zero? Does that equal 1?

In the past, Sean has asked why can't anything be divided by zero, and I've explained that if you divide 1 by 1/2, you get 2, and the smaller the denominator, the bigger the answer, eg divide 1 by 1/1000, you get 1000, hence, as the denominator approaches zero, the answer would approach infinity.

But his question today is slightly different. He notices that when the numerator=denominator, the quotient is 1...so he's wondering if 0/0=1. Fair enough.

A professor even created a new number (he calls it "nullity") to deal with dividing by zero but he got panned by many.

"Hi, I was just wondering - if you have 0/0 (zero divided by zero), which law takes precedence - a) zero divided by any number is zero, or b) any number divided by zero is undefined, or c) any number divided by itself is one? Thanks."

Sean seems to think (c) take precedence from the way he asked his question.

This entire section is devoted to questions on dividing by zero, and includes dividing zero by zero.

What I'm getting from the site is:

(Any number other than zero)/zero = Undefined
Zero/zero = Indeterminate

There, apparently, is a difference between Undefined and Indeterminate. How the site explains it is...

Undefined: (About 1/0) "What happens if you add apples to oranges? It just doesn't make sense, so the easiest thing is just to say that it doesn't make sense, or, as a mathematician would say, "it is undefined."

Indeterminate: (About 0/0) "There's a special word for stuff like this, where you could conceivably give it any number of values. That word is "indeterminate." It's not the same as undefined. It essentially means that if it pops up somewhere, you don't know what its value will be in your case. For instance, if you have the limit as x->0 of x/x and of 7x/x, the expression will have a value of 1 in the first case and 7 in the second case. Indeterminate."

Unfortunately, I'm all alone now, the boys have gone to school, and I only understand bits of the explanations. My understanding is definitely not robust enough for me to confidently explain the difference to a 6-year old though. It seems 0/0 can be 1 and it can be any other number.

Help...?

### Platonic Love

Someone recently gave me an advice, he said, "When your young child asks you something, find an answer for him immediately. Don't tell him to come back later, cos he won't ask you again." I'm guilty of often shoo-ing Sean away when he comes to me with questions.

This evening, he asked, "Why isn't a sphere a platonic solid?". I remember shoo-ing him away weeks back when he asked me this exact question, so it's not true that they won't ask again hehe. Still, the above is good advice to take on board, and so I dutifully googled the answer.

Firstly, I asked Sean what a platonic solid was cos really, I have no idea. His reply, "A polyhedron where all the faces are regular polygons and all the corners have the same number of faces joining them and all the faces are exactly the same size and shape and they certainly don't wear trainers." Whhhhat???

So I find pictures of Platonic Solids on the internet and there are just 5 of them. I shout out to Brian asking him if he knew what Platonic Solids were. He comes over and says, "Well, the Greeks believed that these were the shapes that made the four elements and the universe."

Yeah, and he points to the 5th Platonic Solid (PS) up there and says, "This is the Universe."

Sean immediately jumps in, "No it's not. The Dodecahedron is the Universe.", pointing to the 4th PS. Brian says, "Oh...yeah."

And kiasu Sean fearing his brother would name the rest, blurts out quickly, "The tetrahedron is Fire, the cube is Earth, the Octohedron is Air and the Icosahedron is the Water. The Dodecahedron represents the entire Universe."

Brian returns to where he came from and I go back to Sean's original question. I asked him why he thought a sphere should be a platonic solid, he says, "It's a kind of solid, a regular solid. That's all."

Some googling later, we find out, a sphere isn't even a polyhedron! So by the definition Sean gave up there, of course the sphere can't be a platonic solid, since it isn't even a polyhedron in the first place.

When I told Sean a sphere isn't a polyhedron, he asks, "Why not?" er...one can argue it is a polyhedron with infinite numbers of faces and vertices...but let's not go there.

So mathematicians say a sphere is not a polyhedron and it has no face (it does have a surface).

From Wikianswers: "A polyhedron is a 3 dimensional figure made up of polygons. We use the term 'face' to refer to these polygons. Since a sphere is not a polyhedron, we mathematicians consider it to have no faces."

Similarly, a circle isn't a polygon and has no sides. Really? Did they teach us this in school?? Was I sleeping in class??

I shout out to Brian again and asked, "Did you know that a circle isn't a polygon."

He says, "Of course. A polygon has to have straight sides so a circle isn't a polygon."

Okayyyy "So a circle is just a shape?"

"Yes, shapes include polygons but shapes aren't necessarily polygons. And polygons can't have holes in them, so a square with a hole in the middle isn't a polygon."

"So a semicircle isn't a polygon?"

"No Mummy...and neither is a ring." (rather impatiently)

"A ring?"

"Yes, a ring, a circle within a circle, a flat Torus."

"Taurus??"

"Torus...a doughnut shape, like a ring."

Now it's my turn to be sassy, "Of course it's not lah. It doesn't even have straight sides."

## Tuesday, March 03, 2009

### Square Root Day

Math nerds around the world are celebrating Square Root Day today, 3/3/09, ie 3 is the square root of 9. The last Square Root Day was 5 years ago on 2/2/04 and the next will be 7 years later on 4/4/16. Happy Square Root Day!

Sean has stopped doing this, but for a long time, he kept going around asking us, our friends, (and this is no good) his classmates, this question, "What's the square root of -1?" All the time, he'd go, "What's the square root of -1?" no matter how many times you give him the answer "i", he would still ask that question. I think he was just really intrigued by the concept of imaginary numbers. Here's a funny cartoon on imaginary and irrational numbers.

## Monday, March 02, 2009

### Scribble game

This is a 'game' we play; someone scribbles something, and the other person tries to make a face out of the scribble. I had forgotten about this until Sean recently came up to me to ask me to play. By this, it usually mean he scribbles and I've gotta draw.

So this...

...becomes this.

This...

...turns to this.

And the boys love it when I turn this...

...into drawings like this, nostril hair and all.

### Frankfurt food in Moscow

Raclette probably isn't from Germany...but when I think raclette, I think Frankfurt, which is where I first enjoyed this style of eating. Today, I took my raclette set out for the first time since leaving Frankfurt 3 years ago and had a feast.

The set's been in storage since Frankfurt days cos I couldn't find raclette cheese in London. Also, Eddie hates that it stinks up the house plus he's not a fan of raclette. Well, two weeks ago, I found raclette cheese in Metro (a supermarket), happiness! Bought more than 1kg back, thinking we could have people over for a raclette party. But I've been sick for 2 weeks, cough is gone but nose is blocked...appetite is as good as ever though.

Well, I finally decided we'll just have our own party, just the two of us, today! Two of us as in Brian and Mummy, the only two huge fans of raclette. So at exactly 11am, ie, right after Eddie stepped out the door to fly off for a business trip, we turned on the grill! Hopefully, by the time he gets back, the house will no longer stink.

When you have raclette, you've gotta use raclette cheese. Once in Germany, someone tried using other cheeses, and it didn't work out at all. While the Caucasians have their raclette with potato, gherkins, that kind of stuff; we have ours with marinated beef, prawns, mushrooms, onions, garlic...very much like Korean bbq, but combined with melted raclette cheese, it's just out of this world.

What you do is grill whatever it is that you like, for us, it's beef, prawns, mushrooms, for others, it could be sausages, capsicum, zucchini. Each diner then places a thin slice of raclette cheese into his individual cheese tray and slides it under the grill. My raclette set has 8 trays. Once the cheese has melted to your preferred consistency (some like it melty, some like it slightly burnt), scrape it with your personal wooden spatula (comes with the set) on to the grilled food you've placed on your plate. That's it, makan time.

Best downed with red wine.