A Note on a Theorem of Euler

By Diogenes

NB: Euler is pronounced "oiler". 

We found this wonderful piece of literature a few years ago via Prof John Webb - thanks Prof!!

Brilliant Mathematical Thinking (or is that brilliant daydreaming??)

Transcript:
In algebric equation if 1+y is the sum you cannot add 1 and y together for example 1 would be a man and y would be a crocodile. But 1 [times] y can be possible because for example 1 would be a man and y would be a crocodile but [times] would be the fairy that change 1 and y into a frog so they can stay together then the answer is 1y.

Smiley face but no mark...

Beware the Ides of November (for the Southern Hemisphere)

These days it seems like I turn around and two weeks have just GONE. FOREVER.

For example, I am nearing the end of my first year as a full time teacher. So since I have been in a listing mood recently it seems appropriate to list some of the things I have learnt this year.

1. Be bossier!

Let's face it: being bossy is basically part of my job. Diffidence might be charming but it doesn't help kids learn. And frankly, some times its more important to be confident than right. At least forging confidently ahead despite uncertainty demonstrates where the potholes are (though sacrificing a party member or two is not ideal; not even in the interests of making an accurate map of the terrain).

 
Some of the arenas in which I need to be bossier are discipline, record keeping, note taking and time keeping. I particularly sometimes need to be bossier with my colleagues. When I know what I'm talking about (which I do, occasionally), then I need to insist.




2. Plan more.


A planned week is 100% better than an unplanned week. Don't get the wrong impression - I don't actually FOLLOW my plan. But having lessons ready and resources printed and schedules created and all that jazz still makes a huge difference.

The difficulty is that planning is never as urgent as a thousand other bits and pieces. It tends to feel like procrastination. 

IT ISN'T.

At the moment I'm sacrificing loads of other more urgent work (like admin, marking etc.) in order to plan for next year. And I'm sure that this is the right decision. Not only does planning help me to teach better, it also helps me to teach with a higher level of confidence and fluency. It helps to decrease stress levels and exhaustion levels. It is also easier to be creative in advance. So if you plan, you're more likely to be creative. See points 1, 4 and 5 if you're still not sure why planning more is a good idea!


3. Live closer to work.

This just isn't worth it:

The stress, the time, the petrol money, the stress, the time, the petrol money, the stress, the time, the petrol money, the stress, the time the petrol money, the stress, the time, the petrol money....








 You get the picture. Why choose inefficiency when you could have... THIS:



Hmm, yes, being a glorious 50s housewife has always been a dream of mine...


But seriously, moving to live within ten minutes walking distance from work has probably been the single most life-enhancing decision of the year. 
 We have so much more time to enjoy life. It's the ultimate way of slowing everything down a notch or two.


Our kitties also love our new place (though that's probably more to do with the garden than its proximity to work).


And yes, it has made more time for creativity in the kitchen...

4. Stress less.


I am a champion stresser. I could probably win a medal if they had medals for stressing. NEWS FLASH: stressing doesn't help. The work will get done faster and better if you don't stress about it. Stress is supremely inefficient.

Of course, not stressing is easier said than done (duh). In fact, I have been known to be stressed about stressing. And I have yet to actually succeed in not stressing. But I'm studying to improve. Points 2, 3, and 5 in this list have helped me to stress less. 


But these are some of my anti-stress mantras:

• It doesn't matter that much anyway.
• In two weeks time I won't even remember this.
• Who gives a %#@*!$#? [no matter what they say, profanity always helps in times of trouble]
• It'll get done eventually.
• I shall run away and join the circus.

Saying these repeatedly in any order you choose and with increasing levels of hysteria has been know to not help at all... But they're good to remember anyway.


5. Be more creative.

Being more creative is difficult. It requires proficiency in time management and planning OR a general ability to tell the world to go hang while you get on with your creative project.

BUT it builds your soul. It relaxes you. It gives your "serious" work fresh flair and imagination.

Now the ideal application of creativity is to your work. Because then you can hit time-management/planning/creativity/work buttons all at once and STILL reap the rewards of creativity.

image source

Mwahaha!

Make new, nice resources and share them (this also garners praise which is always nice). Write reflective marathon blog entries (who cares if no one reads them). Dream up new ways of organising the universe. Rearrange your admin under colour coded headings. Invent a new curriculum. Play (*educational*) games in class.

After all, why not?

Woeful Wednesday - Energising Efforts

It's woeful wednesday again and despite not having taught a lesson yet today I am CAPUT out of energy. So I'm drinking a huge cup of very sweet coffee and trying to hype myself up to start a new and extremely challenging chapter with my grade 11s..

Energising Efforts:

more awesome coffee piccies

1. Get the caffiene flowing in my veins (feel the heartbeat skyrocket!)
2. Music: soundtrack mix (preferably lots of vibey Disney stuff - think Hercules and so on...)
3. Work - preferably something completely non-essential and non-urgent (like making stationery choices for next year :-)

Goals for the Week (or at least what's left of it)

Goals for this week:

• Be prepared for the chance of a lifetime (if it should happen in the next seven days!)
• See challenges as growing experiences.
• Persuade Gauss and Pascal to stop killing baby birds.
• Set my last exam for the year :) 
• Sing more.

Punting Down the Cam

[WARNING: this is a sentimental post about bygone days...*sniff*]

I believe I am actually a child of the 20s. Probably my favourite novel of all time is Dorothy L. Sayers' Gaudy Night, set in beautiful Oxford in the stately interwar days when women had just been admitted to universities and everyone still wore academic dress to College dinners... And, of course, when the best Sunday afternoon activity was to take a leisurely punt down the river. Sigh.






When I was fortunate enough to be sponsered on a "literary tour" of the UK a few years back, one of my most favourite outings was when we went punting. It certainly made a nice change from yet another stately home... Though Blenheim et al are stupendously magnificent, they are also terribly hard on the feet.








Not that punting is an art for the lazy. For those of you that don't know, punting is the art of pushing a boat down the river by means of a long pole prodded repeatedly into the muddy river bed and used as a lever.

Apart from negotiating bridges which are mainly too low to get the pole (or yourself) through upright, one also has to cope with steering (mainly with the assistance of the ardent paddlers) and going upstream. Going upstream is mostly a case of one punt forward - two floats back.


 

And of course: very HOT work (unless you fall in, which I fortunately didn't!) ... By the end of the outing I was much thinner, mainly due to removing layers of clothing!

Nonetheless - oh to return to those stately days...

Statistics (with a pitstop by the Oxford English Dictionary)

So there's this nifty spot where you can go look at the stats of your blog. And it's very interesting. One of the most interesting things about it is this: when I post something new, my readership skyrockets in South Africa (i.e. here). When I don't post anything new, most of my readers come from the US (though I had a brief spate of popularity in India after I posted a mini-series involving Indian mathematicians).

Is this just because more people use the internet on a regular basis in the US? 'Cos I have a nasty feeling it's mostly incidental/search-engine/accidental traffic.

What is driving this particular pattern??? Any suggestions?

***

Pitstop!!

What is the difference in meaning between incidental and accidental in this context?

The pocket OED that I have in my classroom (call me old fashioned but I still haven't gotten used to online dictionaries) says that incidental means "having a minor role in relation to more important thing or event".

Accidental (helpfully) means "happening or done by accident". Well thanks OED. Accident is defined as "event that is unexpected or without apparent cause".

My analysis - incidental relates to the importance while accidental relates to the intentionality of the event in question (i.e. visiting Daydreaming in Maths).

Do you agree??

***

excuses excuses

-  lost camera - lost phone - no internet at home - hectic time at work -

- I miss blogging -

The Life Cycle of a Box

We are busy moving house and have lots of fun with cardboard boxes. There is an entire world of interest behind the common cardboard box!

We got a whole bunch of boxes (like 20 or so) second hand from the Pick 'n Pay up the road. Turns out they have a whole container out the back, next to the loading area where trucks come and go, wholly dedicated to the sorting, distributing and recycling of cardboard boxes.


Once the omo, chips, whiskey, apples and cooldrinks have been removed from the boxes, they are ferried in elderly reject shopping trolleys through to this gentleman who rules over the box container...

He works from 8am to 7pm in the small, dark container, which makes loud farting noises if you tread on the floor in the wrong place. Anyway, you tell him what kinds of boxes you'd like (he's got lots - all the way from teeny tiny to enormous) and then he helps you to pull them out of the heap. He's really good at divining what size a box is just by looking at the flap that's sticking out of the pile.

After all that, it seems quite ungrateful just to take the boxes off, put them back together with packing tape and stuff a whole lot of books, crockery, clothes and kittens in them.

But of course once the kitten is tired of sitting in the box...

 

...he can always eat it!

  

"Look mom, I killed it!"

I'm not sure if this is a fitting end to such a noble creature as the cardboard box. On the whole I think it might be. 

A Discourse on Purpose

For some reason today I realised that I haven't written a "proper" blog post for ages. My "hectic maths" label is becoming quite empty, and even photographs taken by myself have been pretty scarce.

Part of the reason for this is that I've started a cellphone experiment at school which involves being online with the kids a LOT, via twitter, class blog and so on. So I've been using up all my internet energy - or a lot of it anyway!

Another reason is that I've been thinking quite a bit about what the purpose of Daydreaming in Maths actually is. My class blog has a clearly defined purpose, but in some ways its purpose has eroded Daydreaming's.

Is this a blog for my students? Well, not really. But not NOT either.

Is this a blog for ME? Well, if its just for me maybe I should get a diary and stop filling the internet with random cr**p.

Is it a blog for the general public? Er...not sure if the general public is that interested in Maths and my crazy musings.

Is it a blog for other people that know me? Well in that case maybe I'm better off emailing them more regularly.

So what s the purpose of Daydreaming?

Aaaah...there's a question to please the soul of irony!

Message from the soul of irony (i.e. the brain):

Dear JJR - please note that daydreaming does not serve a purpose. It represents an absence of purpose. Therefore your question is irrelevant. Kind regards etc.

 
Well that's helpful...any suggestions from anyone else?

Message from the id:

Dear JJR -please note that this blog represents nothing more than a place to stash your ideas and impressions. The fact that it is open to the public simply provides you with an illusion of importance. Kind regards etc.

Not sure I like that answer - can I have another one please?


Message from the ego:

Dear JJR - please note that you are providing an extremely insightful and important service to society by writing this blog. If you stop, the world will surely be lacking that certain something. You fulfill a crucial role in the continuance of our cultural identity. Kind regards etc.

I'll shut up now...for now!

Wonderful Whiteboard Wednesday

An original artwork by Simon (grade 8)

Random Quote for Monday

"When I'm a veteran with only one eye,

I shall do nothing but look at the sky" 

incredible artwork from...

Counting at the Seaside

I'm on holiday folks, so no hectic maths for a bit... instead I've been collecting pictures of numbers. Today I counted from 0 to 5 on and around the beautiful beach at Muizenburg.

 Hum...the usual problem with "counting" zero. Am I encroaching on hectic maths after all?

One clock-tower on Muizenburg station. Not one o'clock.

Two walking people (husband and father-in-law if you must know)

Can you spot the three?

Four beach huts...

Five (or is it six?) steps gone adrift...

Recent Reading and Rants

Big news guys: I've been cheating on my blog! With an old hobby - reading! At least two or three times in the past two weeks of silence I have stayed up late finishing a particularly delicious novel. Ah...

These are some of the things I've been reading. I may have missed a few in this list. As you can see, my bedside reading pile is getting a bit out of control

The Hunger Games (Suzanne Collins): dystopia fantasy. Thrilling, unexpected, sensitive. I will definitely be reading the sequels as soon as I can get my hands on them.

Sabriel (Garth Nix): classic fantasy. In a word - brilliant. Scary, but brilliant. If you're going to read one fantasy novel for teenagers, this is it.

Postcards from the Edge (Carrie Fisher): the story of an ex-druggie Hollywood actress, told in fragments. Funny, tragic, absurd and random. I reserved judgment until the last chapter, but the ending pulled the whole thing together beautifully.

News from Thrush Green (Miss Read): old, kitsch, adorable. Restful reading.

The Avenging Saint (Leslie Charteris): old, predictable thriller/teccie. Also restful if you like that kind of thing, which I do. Involves car chases, fights on yachts, rescuing millionaires' daughters from certain death etc..

The Physics of the Impossible, Introducing Stephen Hawking, Newton's Notebooks: I know these last three seem a bit highbrow for my taste, but don't worry. I've only been dipping into them because they're living on my husband's bedside table. So no review of these ones I'm afraid. You'll have to wait till I get a new brain.

You will also observe that there is very little official "literature" on my list. This is because (let's face it) most literature is difficult and/or unpleasant to read. So I don't, unless I have to. [disclaimer: there are many exceptions to this rule. wonderful ones. but they still aren't exactly leisure reading. and who the heck decides what is literature and what isn't anyway.]


Rant Over.


I hope to contribute a little more to the stream of internet *stuff* this week, thus in my own small way contributing to the creation of a species entirely dependent on machines (this is my way of saying "I'll try to post more")


Goodnight to you all.

Daydream...

Car Games

Some Variations on "The Number Plate Game"...

The Original: spot all the numbers from 1 to 100 (in order) on car number plates. The digits must be in the correct order and not separated.

Fibonacci: spot all the fibonacci numbers (stop at 144 - otherwise it gets too difficult!). The same rules apply.

Hint - the Fibonacci sequence of numbers works like this. Each term of the sequence is the sum of the previous two terms. It starts 1; 1; 2; 3...

Prime Numbers: spot all the prime numbers between 0 and 100. 

Hint - a prime number is only divisible by one and itself. 1 doesn't count as a prime number.

Squares:
Cubes:
Powers of Two:
Powers of Three:

The variations are endless. After some experimentation however, I suggest you stop when you get to three digits. Otherwise it takes so long to get the next number in the sequence that everyone loses interest!

Happy long weekend! I wish you a festive lack of traffic.

XKCD: Heaven and Hell

 GO! NOW!

http://xkcd.com/724/

http://www.xkcd.com/888/

Something to Cheer Me Up

Cricket related blues aren't fun...but here is something which never fails to cheer me up.