Let's try and get 1,000,000 replies to this post

to many stories/theories coming from all angles I don't know what to believe.
Off topic I saw 300 rise of an empire. It was average. Eva Green like always is a just a goddess but everything else just average
 
I saw 300 as well. I agree, it was average but I definitely don't see a goddess in her. Maybe it was the poor make-up, maybe what she said or just not my type. The movie had great visual effects and musical themes but, as I said, had much bad dialogue and was too similar throughout the movie. I still enjoyed watching it though.
 
Another problem if any of you maths smarties get bored:
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One guy moved from A to B along the longer curve of the circle. Another guy moved from A to O, from O to B and from B back to A along the shorter curve. They both travelled 410m. How long is the radius?
 
Well, @The Flash, this exercise does not necessarily have to be seen as geometry. It is a system of equations to be solved :) Four unknowns (the lengths of the four curves AO, OB, AB and BA with AB indicating the short curve and BA the long one) and four equations. Here we go:

Equation I: AO = OB (the two are both equal to the radius of the circle)

Equation II: AB + BA = 2 * pi * AO (circumference of a circle is 2 * pi * radius)

Equation III: AO + OB + AB = 410

Equation IV: BA = 410

Equation I lets us forget about OB for now. Equation IV gives us the value of BA. So, let us insert equation IV into equation II to get rid of BA:

Equation IIb: AB + 410 = 2 * pi * AO

Equation IIIb: 2*AO + AB = 410

So, let us eliminate AB from equation IIb by sorting terms in equation IIIb and replacing AB with 410 - 2*AO:

Equation IIc: 410 - 2*AO + 410 = 2*pi*AO

Let us group the terms including AO on the right hand side:

820 = (2 + 2*pi)*AO

Thus, the radius AO equals 820/(2 + 2*pi)
 
Ok, this one is cool. :bigsmile:

Label the lines AO and OB r for radius and label the short arc AB as x and the long arc AB as y.

Since we know that both distances travelled are 410m we can write this down as two equations:

y = 410
2r + x = 410

therefore,

2r + x = y.

We also know for a fact that the circumference, C, is equal to 2*pi*r and this can be rearranged to give:

r = (x+y)/2*pi,

which can be substituted in to the previous equation to give

(x+y)/pi + x = y.

Take out x as a common factor, substitute in y=410 and solve for x. Then substitute x back into 2r+x=410 to get the radius. :)

Comprendez?
 
After thorough thinking, I can understand the solution. However, I hope this kind of an exercise won't make it into the tests, it's just too much for me to handle on my own, I'm afraid.
 
I have an A level in maths and an A* at GCSE, spent a year doing engineering at uni which naturally involved lots of math too...

... and yet I haven't a clue what any of you are talking about. Just goes to show how quickly it's all forgotten when you don't use the knowledge for anything.
 
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