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.
Me:...

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






3.14159265358979323846264338327950288419716939937510
  58209749445923078164062862089986280348253421170679
  82148086513282306647093844609550582231725359408128
  48111745028410270193852110555964462294895493038196
  44288109756659334461284756482337867831652712019091
  45648566923460348610454326648213393607260249141273
  72458700660631558817488152092096282925409171536436
  78925903600113305305488204665213841469519415116094
  33057270365759591953092186117381932611793105118548
  07446237996274956735188575272489122793818301194912
  98336733624406566430860213949463952247371907021798
  60943702770539217176293176752384674818467669405132
  00056812714526356082778577134275778960917363717872
  14684409012249534301465495853710507922796892589235
  42019956112129021960864034418159813629774771309960
  51870721134999999837297804995105973173281609631859
  50244594553469083026425223082533446850352619311881
  71010003137838752886587533208381420617177669147303
  59825349042875546873115956286388235378759375195778
  18577805321712268066130019278766111959092164201989
  38095257201065485863278865936153381827968230301952
  03530185296899577362259941389124972177528347913151
  55748572424541506959508295331168617278558890750983
  81754637464939319255060400927701671139009848824012
  85836160356370766010471018194295559619894676783744
  94482553797747268471040475346462080466842590694912
  93313677028989152104752162056966024058038150193511
  25338243003558764024749647326391419927260426992279
  67823547816360093417216412199245863150302861829745
  55706749838505494588586926995690927210797509302955
  32116534498720275596023648066549911988183479775356
  63698074265425278625518184175746728909777727938000
  81647060016145249192173217214772350141441973568548
  16136115735255213347574184946843852332390739414333
  45477624168625189835694855620992192221842725502542
  56887671790494601653466804988627232791786085784383
  82796797668145410095388378636095068006422512520511
  73929848960841284886269456042419652850222106611863
  06744278622039194945047123713786960956364371917287
  46776465757396241389086583264599581339047802759010
 

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.






area/perimeter/maskingtape


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)









Repeat...


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 :-) )

A=πr2
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

Diversification

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!

.JJR.