Expert: Sherman D. - 2/22/2005

Question
1)why is (-1)*(-1)=1 ?
2)sinx=opp/hyp for right-angle triangles,
 so what does it really means to sinx, x> or =90 degree (not the 180-x formula or the sine waves, but to draw a triangle with x> 90 degree and use the formula opp/hyp).
3)there's ways to come up with the number e, so what's the way to come up with pi.
4)A question which I can't solve it for ages,
  1)draw a square
  2)draw a circle taking the corner of the square as its center with radius = length of the square.
  3)draw the same for all corners
  4)you will see 2 leaf-liked shapes overlapping each other.
  5)what is the area of the center part?
   I've lost the answer, but I know no special knowledge like calculus is needed.
5)why is d(e^x)/dx = e^x?  

Answer
Here are the ones i can answer.

3.) The closest value that people have come up with is Pi = (22/7)

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4.) With no picture, here is my guess
Area = Pi * r^2
Since the center of each circle is taking each corner, only 4th of it is being used
Area = (1/4)(Pi * r^2)

multiply that by 4 and of course you get the area of just the circle, so you get Area = Pi * r^2

now take the area of the square and subtract Pi * r^2 from it, so you get

Area of Square = (2r)^2
As = 4r^2

Shaded Area = 4r^2 - (Pi * r^2)
Shaded Area = (4 - Pi)r^2

Sorry i couldn't be of much more help.