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Thursday, September 9, 1999
July 7, 1977
Today, I was phoned by a cousin of mine, who on this special day (9-9-99)
had to think about another day like this more than 22 years ago, namely
July 7, '77, when he was staying with us during the holiday. We recalled
what we were doing those days. We tried to solve the goat problem: how long should the cord be, to let a goat eat only the
half of a circular field if the pole is on the boarder of the field. Or in
other words: what is the radius of the circle which divide the unit circle
on half, if the center of this circle is on the unit circle.
We could not solve the problem at that time. This evening I though about
it, and did find the solution, only using some elementary math. Only the
following formulas are needed:
- Surface triangle equal to: ab.sin(gamma)
- Surface pie of circle: r.phi / 2
- Cosine rule: a^{2} + b^{2} - c^{2}
= 2ab.cos(gamma)
- sin(gamma)^{2} + cos(gamma)^{2} = 1
With these you can derive the formula for the surface of a triangle given
the length of the three sides:
sqrt(2a^{2}b^{2} +
2a^{2}c^{2} +
2b^{2}c^{2} -
a^{4} - b^{4} - c^{4}) / 4
(alternative formulea)
The goat problem is a special case of calculating the area of
the intersection of two circle with radii r and s
whoes center points are d apart.
When two circle intersect there are four important points,
namely the two center points of the circles, and the two intersection
points. Lets look at the triangle made of one of the intersection
points and the two center points. The sizes of all the sides are
known, thus also the angles between them using the cosine rule.
The area of the intersection equals the areas of the pies of the
two circles minus the area of the triangles. This leads to the
following formula:
s.acos((s^{2} + d^{2}
- r^{2})/2sd) +
r.acos((r^{2} + d^{2}
- s^{2})/2rd) -
sqrt(2r^{2}s^{2} +
2r^{2}d^{2} +
2s^{2}d^{2} -
r^{4} - s^{4} - d^{4}) / 2
For the goat problem s = d = 1, and r is the
requested radius. To find r, the following equation needs
to be solved:
acos(1 - r^{2}/2) +
r.acos(r/2) - r.sqrt(4 - r^{2}) / 2 = pi / 2
There are no analytical solutions to this equation.
(follow-up on goat problem,
follow-up on interesting dates)
Wednesday, September 15, 1999
On my way to the cafeteria, which is on the otherside of the parking
place, I could not help picking seven shining
chestnuts that lay under some chestnuts
trees on the border of the parking place. I put them in my pocket,
and later when I returned to my working place, I laid them out on
my computer. During the course of the afternoun they lost their shinging
appearance, just like the once I found last
year.
Saturday, September 18, 1999
It looks like Annabel inherited my passion
for chestnuts. We went to a chinese take-away restaurant, and while
waiting for our order to be ready, Annabel went outside and started
to collect as many chestnuts as she could. This was exactly the
same place where we picked them last year.
Friday, September 24, 1999
Programming and art
What do have programming and art to do with each other?
Donald E. Knuth is writing a series of books
with the title The Art of Programming.
But is the act of programming an art, or just the
application of well established rules to arrive at
a working program.
Of course, the first requirement for programming is
knowing the language. But that is the same with painting,
knowing how to put paint with a brush on the canvas.
For both one has to know the basic techniques, and
in both fields there are people who stand far above
all the others.
In Advanced C++ programming styles and idioms
James Coplien states "Style distinguishes excellence
from accomplishment". This is true for both art
and programming.
There is however one sad thing. Where the work of a
painter can be valued by a lay person, the work of
a programmer can only be valued by the experts.
And yet another sad thing is that there is but only
a weak correlation between the observable behaviour
of a program, and the style of the code.
Saturday, September 25, 1999
Today the third Kabuki day organized by
the Dutch Kabuki Network. There were about 15 families
present. We attended it for the second time.
Last year
we weren't sure about Andy's diagnoses yet. That made it
a little different for now. What follows is a personal
impression, and by no means complete. (For reasons of
privacy, I will be vague with respect to refering to
persons.)
The focus for this day was much on behavioural aspects.
We had one short lecture explaining an investigation of
behavioural aspects of childeren with KS. There are about
15 children joining in this academical study. This
study will look into the cognitive abilities, the
neuropsycological profile, and language abilities of the
children. The "California Child Q-test" and the "Child
Behaviour Checklist" will be used. Our son Andy (becoming
two in a few weeks) is too young to join the test.
Nevertheless, the people performing the research will
have a look at him. The aim of the research is to come
up with practical advise for the parents, but also a
scientifical publication will follow.
After one hour of this, we had an extended lunch, after
which we sat together to share about the development of
and the problems with our children. This again showed
how varied the Kabuki children are, but also some
of striking similarities there are. Some children are
slim because the eat slow. Others are on a diet because
the eat too much. Eating seems to be an important topic
for many Kabuki children.
Two people reported problems with their child after
being exposed to flashing lights.
Of course, problems with the ears were discussed. One
parent shared their experiences with a cosmetic operation
on the ears of their child. Some other parents noted that
temporarily stopping/reducing speech therapy can have a
positive effect on the speech development.
It was good to come together and have ample time to talk
and share. We will definitely go again next year.
I realize that it is a blessing to live in a densely
populated country. The average travel time for people
to attend this day was only two hours.
(Second Dutch Kabuki day
and Fourth Dutch Kabuki day)
Tuesday, September 28, 1999
Roses
The roses, which I gave to Li-Xia on her birthday
in May, are still producing a nice fragerence, I discovered to my surpries.
The roses are almost dried completely. They have been standing in
the living room all the time.
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