y=x^5-sin(y^2) with y=25*x^4
Incidentilly, if you look from the top down at all the places where the leg meets the seat, they are all circles. Observe:
No doubt there are easier ways to make chairs, but I was in the mood to use Sine tonight.
Thursday, March 18, 2010
As Spring Nears
It seems like summer outside, and spring hasn't even started. In that spirit, here is a graph.
y=x^5-sin(y^2) with y=25*x^4
y=x^5-sin(y^2) with y=25*x^4
Thursday, March 11, 2010
Unsolvable Problem
I'd bet money I was given an unsolvable problem. Now, there are plenty of problems in mathematics that aren't solved yet. For instance, nobody knows how to find a, b and c such that a^n + b^n = c^n for any n greater than 2. A guy named Fermat claimed he knew how, but its pretty sketchy: just before his death he wrote in the margin of a book that he found a "a truly marvelous proof that it is impossible", but "this margin is too narrow to contain it." Not exactly the way to mathematical progress, Pierre...
I'll save you the gory details and show you my Excel worksheet which I constructed after all else failed:
I apologize for the poor quality. At any rate, this is a bond amortization schedule. I was given the two numbers in bold, from which I calculated the i=9.53% you see in the side using a cool Excel function called "Goal Seek". The problem asked for me to return the book value at time=0, which I worked backwords to find $1528.62.
All was good, or so I thought. The problem also mentions that the bond is redeemable at $1,000 at the end of n years. That means that at some point the book value should equal $1,000. And this is precisely why my pencil and paper failed me: the book value never gets to 1,000. I cut out the middle stuff to show you the book value at 100, 500 and 1,000 years. As you can see, it isn't going to go any lower than 1258.89 (see the boxed cell)!
So on the one hand I got a seemingly legitimate answer by ignoring that sentence, but it has never seemed a very wise strategy to go about solving math problems by proving they contradict themselves. Class is in half an hour... hopefully that will shed some light on the subject.
I'll save you the gory details and show you my Excel worksheet which I constructed after all else failed:
I apologize for the poor quality. At any rate, this is a bond amortization schedule. I was given the two numbers in bold, from which I calculated the i=9.53% you see in the side using a cool Excel function called "Goal Seek". The problem asked for me to return the book value at time=0, which I worked backwords to find $1528.62.
All was good, or so I thought. The problem also mentions that the bond is redeemable at $1,000 at the end of n years. That means that at some point the book value should equal $1,000. And this is precisely why my pencil and paper failed me: the book value never gets to 1,000. I cut out the middle stuff to show you the book value at 100, 500 and 1,000 years. As you can see, it isn't going to go any lower than 1258.89 (see the boxed cell)!
So on the one hand I got a seemingly legitimate answer by ignoring that sentence, but it has never seemed a very wise strategy to go about solving math problems by proving they contradict themselves. Class is in half an hour... hopefully that will shed some light on the subject.
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