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26 **27** 28 29 30 31

## Saturday, December 4, 1999

### Staring at a painting

As usual, I walked by the gallery
`Beeld en Aambeeld'. This morning I decided to go in,
and ask about the painting by
Billy Foley
which has been in my mind lately because I realized that it would
fit in our bedroom. After some questions, I found out that it was
only recently sold to someone on an art fair in Hengelo. They also
told that there had been a great interest for his works, and that
more is coming. Strange, but somehow I had the idea that the painting
already had gone back to Ierland.
Within an hour, I came across a book about a man that claimed to
have become *enlighted* after having stared at a wall for nine
years. What does enlightment mean if appearently you could afford
the luxury of only staring at a wall. I wonder if this man did
any work during these nine years. His family, or his vilage, must
have provided this "saint", or should I say "mad man", with food and
housing.

But, I could not stop thinking about the idea of a man becoming
obsessed by a painting, and ending up staring at it for nine years.
Might be an interesting idea for a novel.

## Friday, December 10, 1999

A variant of the *traditional* goat puzzle is stated as follows: "A farmer tethers
his goat outside the fence of a circular field so that it can eat an area
equal to 1/2 the field. What is the length of the robe". Note that as the
goat moves within the tangent, the chain begins to wrap around the outside
of the fence.
At first sight this looks like a very complex problem. What is the area cover
by a robe sweeping around a circle? Lets start with a unit circle, and first
assume that the robe is shorter than **pi** (that is half the
circumference of the unit circle). Say that the length of the robe equals
*l*, and that the part of the robe that is free from the
circle while it wraps around the circle equals *x*. For each
*x* the end of the robe will move about *x* * d*x*
when *x* is changed for a value of `d`*x*. The
surface that is covered equals to approxamily *x*^{2}/2 * d*x*.
If we integrate this area where *x* varies from 0 to *l*
we get the expression *l*^{3}/6 for the area of which
the robe wraps on one side of the circle.
From this follows that formulea for the surface covered by the goat if
the robe has length *l* is:

Suprisingly, this expression is not so complicated as one whould expect.
To solve the riddle we have to solve the following 3^{rd} degree equation:
`2`*l*^{3} + 3**pi** * *l*^{2} - 3**pi** = 0

There is an analytical solution to this equation, but I am not going to
give it here.
But what if the robe is longer than **pi**? Because then the robe
will go more than half around the circle, and then there is a small area that
the goat can reach from going around the circle from both sides.
An important point is the furtherst point opposite the point where the robe
is attached to the fence, which can be reached by the goat. This is the
furtherst point that the goat can reach from going round the circular fence
from both sides. When the goat reaches this point, some part of the robe
is wrapped around the fence, and some part is not. Lets assume that the
length of this part equals *a*. Then the total surface
(after some calculations) appears to be:

`
`**pi** * *l*^{2}/2 +
*l*^{3}/3 - *a*^{3}/3 +
*l* - **pi**

The value of *a* is determined by the following equation:
`
asin(`*a*/sqrt(*a*^{2} + 1)) - *a* + *l* - **pi** = 0

To calculate the lenght of the robe that matches with some given surface
appears to be rather hard, if the robe needs to be longer than
**pi**.

## Tuesday, December 14, 1999

### The eight 'o clock news

This evening, Annabel suddenly asked me:
"why do you watch the news?". I replied with "To know what happens in
the rest of the world". Then she asked why I wanted to know this.
A damn good question, I have to admit.
Then she told me that watching the eight 'o clock news often makes
her get nightmeres.

## Monday, December 27, 1999

### The Rules

Today, I bought the book *The Rules* by Ellen Fein and Sherrie
Schneider for Annabel. I am going to give
it to her when she is old enough to understand it, which might be only
in a decade.

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