Tuesday, May 29, 2012

I am this close to becoming a teacher attrition rate statistic...

Wednesday, May 23, 2012

Mathematical Constants III

Word Cloud: e Euler number
from gogeometry

I will never forget my first encounter with the constant e. It was my first week of university. I was trying to complete the first of many Maths tutorials. I came accross this funny symbol: ln(...)

Since I couldn't find an explanation of what "ln" meant in my 700 page textbook (which was otherwise excellent, by the way), I went to my tutor. Our dialogue went something like this:

Me: What does ln (pronounced lin) mean?
Tutor: You don't know what lin means?
Me: That's right, I'm asking what ln means.
Tutor: Ln is the natural logarithm.
Me: Okay...
Tutor: It's just a logarithm with base e.
Me: What's e?
Tutor: It's a constant that forms the base of  the natural logarithm.
Me: But you said that the natural logarithm was a log with base e.
Tutor: Yes.
Me: And you defined e as the base of the natural logarithm.
Tutor: Yes.

Needless to say, this dialogue continued around in circles for about ten minutes before we both gave up in disgust. Even though I learned how to use ln and e, they have remained largely mysterious to me.

It's gonna take a few posts...but I plan to correct that! Join me on my mission...

And just to lighten up your day (and its ALMOST on topic):


Chess Tournament

Wednesday, May 16, 2012

Tuesday, May 15, 2012

Friday, May 11, 2012

sports medley

 Hockey in jail??? Nope, just protection for spectators (and the astroturf)!

Planning a chess tournament with the Swiss pairing system...

Wednesday, May 9, 2012

Famous Mathematical Constants II


Tada! The first two thousand digits of Pi! And its growing everyday...*sniff*

Disclaimer - I did NOT calculate this myself. I got it from here.


Teaching area to grade 9s - fun with masking tape and whiteboard pens! In fact, this is basically an excuse to have more fun and scoot around on the floor in Maths...

My latest emergency. Getting a key jammed in another teacher's classroom door, thereby rendering said door unable to open...

One pair of pliers and a screwdriver later - emergency averted!

Tuesday, May 8, 2012

The geometrical shapes graveyard.
In the middle of the night, when I can't sleep, my imagination creates fairy-scapes.

Friday, May 4, 2012

Famous Mathematical Constants I

Pi (not pie) is usually attributed to Archimedes. In any case, it's been around for a long time. And we use it in a lot of places (more on that later).

But first - what does pi represent?

In order to answer this question, I need to remind you about a tiny piece of geometry - about circles.

The measurement around the rim of a circle is called the circumference. The measurement across the centre of the circle (from edge to edge) is called the diameter.

Now at some point someone started investigating the relationship between the circumference and the diameter of the circle. Something like I did (and you can do it too if you don't believe me), except they did it a lot more times and probably a lot more accurately.

Draw a circle using a compass or other circle drawer. Measure the circumference of the circle with a piece of string.

Measure the piece of string.

Draw and measure the diameter.

Calculate circumference divided by diameter (called the ratio between circumference and diameter)


You see, if you do this accurately enough (which I definitely didn't) then you find that ratio is always the same. In fact it's always roughly equal to 3,14159... an irrational number which we call pi!

Now the first (and I think the most important use after all this fiddling around with string) of pi is to find the circumference of a circle more efficiently than measuring it with a piece of string!

Knowing just the diameter (or radius - half the diameter), we can use pi to calculate the circumference!

C = dπ = 2πr

And then we can also use pi to calculate the area of a circle (you might notice that the circumference is the derivative of the area :-) )

Here are some alternative ways of writing pi. As you can imagine, each one is linked to a very special and mostly very advanced branch of Mathematics. Here are some super awesome everyday applications of pi.

That's all from me for today...we'll tackle e next time!

Wednesday, May 2, 2012


So I've been thinking (uh oh)
And browsing the web (big uh oh)
And pinning (er... did I already say uh oh?)

My conclusion:

I'm splitting Daydreaming.

Oh no! It's kind of like the break up of your favorite band, isn't it?

Daydreaming in Maths will go back to being mostly about hectic Maths stuff...

Out of Perspective will become my repository for random/personal posts...

And when I have more creative writing to inflict on the world, it will go to a third wittily named but as yet unborn blog.

I hope to still see y'all visiting and commenting (those that do), at whichever location(s) suit you. All previous Daydreaming content will stay where it is, as a kind of memorial to days gone by.

I also hope to be more focused in each enterprise - and therefore produce more posts of higher quality.

Wish me luck!