Pre-Cal Class, February 3rd/09

Good evening fellow bloggers. It's Dion here! In class today we went over several things including proportions and we continued our discussion on why a circle has 360 degrees.

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I'll start with our circle discussion! We did not finish it, however, we left off at the reason no one uses a different way to count the degrees in a circle is because everyone is just so familiar with the way it is now and it is so widely known. Mr. K. tried dividing a circle by our new unit of measurement called "the Dion". Approximately 10 1/2 Dions made up a circle. There is nothing to say we cannot measure circles like this except no one but us knows about this new system. Unless everyone in the world knew there is no point. We also learned that 360 may have been chosen because of its beautiful divisibility. The number 360 is divisible by 24 numbers (including the number 24, coincidence, I think not!). We are going to continue this discussion in tomorrow's class.

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We also discussed proportions and the many ways to manipulate them in class today. For some reason the "math equation maker" is not working for me... lucky I don't need anything to complex. Basically, a proportion is:

"a" and "d" are called the extremes of the proportion while "b" and "c" are the means of the proportion. We can manipulate this in many ways as following:

Invert both sides:

Exchange the extremes:

Exchange the means:

Adding "a" and "c" as well as "b" and "d":

    Which simplifies to:

The products of the extremes s equal to that of the products of 

the means:

 

Which simplifies to:

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Two extra side notes!

1) When solving equations using Pi, due to the fact that Pi is infinite there is no exact value for Pi.  When solving an equation involving Pi to keep the answer exact leave  it in the form with Pi. For example :

3Pi instead of 9.4247856

Decimals are inaccurate and fractions are friends not fiends!!!

2)A complex fraction is  one fraction over another!!! Example being:

1/2 / 3/4

To solve, simply invert the denominator fraction and multiply them together!!!

1/2 * 4/3 = 4/6 = 2/3

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Well that is all for this evening. I'm sorry if my post is not terribly exciting or have any pictures. My next post should hopefully have some!! I'll see everyone in class tomorrow!! Also questions 11-20 are for homework which Mr. K. has already posted!!! One more thing!!! Tomorrows scribe shall be........Anthony!!!!!!!!!!!!!! WOOO!!!!! GO ANTHONY!!!!

"When we get to the end of the Greek alphabet, mathematics will end."