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August 20, 2007
Math Monday
I have an original green rectangle, and the only thing I know is that one side is 1 unit tall. However (and this is a big however), when I break it into a square and a rectangle, the new blue rectangle is SIMILAR to the original rectangle, which means that all sides are proportional. What is the other measurement of the original rectangle?
Bonus for anyone who can tell me why the original rectangle is special. I'll post the solution on Wednesday.
Posted by G at August 20, 2007 03:34 PM
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My rusty high school algebra (with some Google assists) tells me that the original rectangle was 1 x 1.618 units. Its area was 1.618 square units. When divided into a square (1 square unit) and a 1 x 0.618 rectangle, the rectangle has an area of 0.618 square units.
To solve for x:
x/1 = 1/(1+x)
1 = x2 + x
x2 + x - 1 = 0
(x + 1.618) (x - 0.618) = 0
x = -1.618, 0.618
x = 0.618
The googling came in when I needed to factor that equation, since fractions aren't my thing. It also told me that this is something called the Golden Rectangle, but I've never been able to wrap my brain around precisely what that *is* other than that it demonstrates properties of the Fibonacci sequence.
Posted by: Mike B. at August 20, 2007 04:27 PM
Eek math homework
Posted by: james at August 20, 2007 07:59 PM
You know, I was going to answer EXACTLY what Mike B. did.
No, really, I was. I TOTALLY was.
You do believe me, don't you?
Posted by: tom at August 21, 2007 08:32 AM
Nerds are always hot in bed.
Posted by: homer at August 21, 2007 11:44 AM
ALL rectangles are special, G!!
Posted by: Lee at August 22, 2007 02:34 AM
Uh.... So, how's the workout going?
Posted by: Tony at August 23, 2007 05:56 AM