I am this close to becoming a teacher attrition rate statistic...
Monday, May 28, 2012
Sunday, May 27, 2012
Wednesday, May 23, 2012
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.
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.
Me: And you defined e as the base of the natural logarithm.
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):
Wednesday, May 16, 2012
Tuesday, May 15, 2012
Sunday, May 13, 2012
Friday, May 11, 2012
Wednesday, May 9, 2012
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.
Tuesday, May 8, 2012
Friday, May 4, 2012
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.
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?)
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!