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Bourgoin, plate 30
Tonight, I worked on Arabic
Geometric Pattern as given on
plate 30 of the Bourgoin
book. This is a repeating pattern within a square, where
there is a fourfold rotation along the center of the square
(as shown on the right). I needed to establish the size
of the square in terms of the unit vector. For the
three preceding plates this had been of the form:
a + b.sin(60°), where a and
b are integers. I soon recognized there was
something strange with this plate, because the square
was divided into four smaller squares, and it is known
that there are no rational a and b such that
a = b.sin(60°). At first I thought
a equals 3.5 and b equals 4. 4sin(60°) =
3.464 (and a little bit), which is close to 3.5, but not
exactly the same. I tried some other combinations, but did
not find any. I was about just trying to find a value by
approximation when I noticed some interesting triangle
which is marked with colours in the image shown on the
top right. From this triangle we can conclude that the
length of the blue line times two equals the sum of the
lengths of the blue and green line divided by sin(60°).
From this we can derive that the size of the square is
3/(1-tan(30°)) = 7.098 (and a little bit). When I used
this value, and applied some fudge factors for some other
coordinates, I did find a solution that looked pleasing.
If one looks closer, one notices that there is a problem
with the angle of the light blue line. It has an angle
of about 59.525°.
Underlying health condition
For many victims of the Swine Flu it is said that they had an 'underlying
health condition'. But rarely it is said which condition
it concerned. There are also people with no underlying
health condition, such as
18 year old Madelynne Butcher, who die from the flu.
It seems that many of those marked as having an underlying
health condition, such as
27 year old Ryan Johnson who was New York City police
officer, where living perfectly normal lives. It almost
seems as if the words 'underlying health condition' are
used as not to alarm the general public that the swine flu
is a possible deathly disease that can just hit anyone living
a normal healthy life. Especially when I saw the picture of
Madelynne Butcher, I had to think of Annabel who on holiday in Spain with my sister and her
niece, where there are many cases of Swine Flu.
In the past weeks, I have been working on my Nonogram solver again. This actually was kick started
by Exact Cover and ZDD. This
made me think about ways to represent all solutions of a
nonogram in a tree-like fashion. If you look at one particular
filling of a row or a column it is possible to assign numbers
to the cells that express how far you have come with using the
cells that need to be placed. You start by prepending an imaginary
empty cell with the number zero. The number for each cell is now
one more than the previous when either that cell or its successor
are filled, otherwise the number is the same. For a row or column
that is not yet completely filled, it is possible to calculate
which numbers could occur at each cell if one would look at
all possible ways to complete the row or column. Because each cell
of a nonogram is part of a row and a column, one could also look
at the combinations of numbers for the row and the column that could
occure. Furthermore, one can reason about the combinations that can
occure in each group of four ajoint cells. If certain combinations
are excluded this likely will have implications for surrounding
groups of four ajoint cells. I applied the program to the solution I found on February 27, 2006, and after about one day, this resulted in
the above partial solution. The image was created with the use of
two small programs from the output generated by the nonogram solver.
Later I discovered that the output of the first row and the first
column is incorrect.
This evening, I biked to the house of Rudi to play
Go. I arrived at the same moment as Huub. When we went in, we
found that Rudi and Taco already had started a game. I looked at
the board and made the remark that they already had entered the
end game. It was not exactly the end game, but not very far from
it. Lets say: "Late middle-game". Huub and I started a game, where
I got a three stone handicap. I really did not think much about the
strategical aspects of the game, just making a lot of small moves,
and at about one third of the game, I was seriously behind. In the
end I lost with about thirty points. When we finished our game,
the game between Taco and Rudi had not come to an end yet.
I left quite soon on my bike. It was still warm, and I left without
coat. I took the Derkinkweg, which is a small road, just outside Enschede,
without any lightning. And because the light of my bike is not so
strong, I had to watch quite carefully where the road was going.
I realized that I would be in trouble, if I would stop, because
then I would be standing in the dark, without being able to see
where the road was going.
Today, was the hottest day of the year.
Of course, you never can be sure, but the chances are small. When I
left the office the temperature was still above 32 degrees Celsius,
and I could not bike fast. But when I was in the city a cool breeze
started to blow and in the next hour the temperature almost dropped
ten degrees (graph). Than later in
the evening, there was some thunder and some rain.
This weekend I worked on a modification of my Nonogram solver, that also takes into account the number of filled
cells in the upper left corner as an additional metric, besides the
row and column state numbers. The idea is that this would be an additional
constraint. I hoped that the restriction would be stronger than the
expansion resulted by the increasement of possible states in each cell,
but that proofed not to be the case. The number of states that the
the program found in each cell
increased, and I did not see any dramatic reductions to appear. The
memory usages of the program also increases to such an extent that I
fear that the program cannot terminate on the given problem. Memory use
was already a problem in the previous version.
I am not sure whether I will proceed in this direction any further or
declare it a dead-end and try out different ideas.
This evening, I went to the university to play Go.
The bar was closed, and the only persons present where Rudi and Taco,
who already had begun playing a game. I watched them until Huub arrived.
We agreed on a two stone handicap for me. At middle of the end-game,
Huub made some moves that made me nervous, and instead of thinking
about my moves, I played too quickly, and resigned after when about
twenty stones where cut-off. I could have easily avoided it being
cut-off. We decided to continue the game, just for the purpose of
counting, and concluded that I would have won with 64 against 42
points, had I not been so stupid. After playing the first twenty
moves again, we watched Rudi and Taco finish their game.
When I went outside around half past ten, I discovered that I could
still bike without coat. As it was warm enough. At home in the
garden, I could vaguely see the milky way. Just when I wanted to go
inside, I saw a bright light in the sky passing overhead very slowly
and quickly dim. I felt it must have been a satillite and I used
Heavens Above to search
for more information. It seems I saw
a flare of Iridium 80.
This months interesting links
KMZ file of movements
| July 2009
| September 2009
| Random memories