| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 83.1 | | ORPHAN::BRETT | | Thu Jun 28 1984 12:26 | 7 |
|
None - the first guy divided into 4 squares, the first being 1X1 KM, the
remainder being 0X0 KM - and got lynched by the other three, who then
agreed their father was barmy, split it equally and lived happily ever
after.
/Bevin
|
| 83.2 | | TURTLE::GILBERT | | Thu Jun 28 1984 19:51 | 15 |
| The first son takes a piece that is 1x3/4, figuring that each of his three
brothers will get a piece of size 1/4x1/3, which is the same SHAPE as his own.
The following table summarizes the divisions.
Son takes leaving share
First 1.0 x .75 3 * .333333 x .25 .75
Second .967707 x .25 2 * .0161464 x .25 .241927
Third .245757 x .0322928 1 * .00424333 x .0322928 .007936
Forth .00424333 x .0322928 .000137
Thus, the last son gets a plot of land that's roughly 4.25 meters by 32 meters.
Just enough for a fine driveway, or to raise a bumper crop of spaghetti.
- Gilbert
|
| 83.4 | new solution | HERON::BUCHANAN | fragmentary blue | Mon Oct 31 1988 11:57 | 81 |
| 83.5 | Nice idea! | AKQJ10::YARBROUGH | I prefer Pi | Mon Oct 31 1988 13:02 | 23 |
| Hmmm. I have trouble with the fractal that gets generated in the vicinity
of the smallest squares below, e.g. -+
|
<---d---> +-----------+
v
+-----+-+---------------+-+-----+ ^
| +-+ +-+ | |
| 2 | | 3 | d
|-+ +-+ +-+ +-+ |
+-+---+-+ +-+---+-+ v
| |
| |
| |
| 1 |
especially since a different fractal gets generated for each value of d.
Although that is certainly an ingenious dissection, I think I'd disqualify
it on the grounds that it not acheivable *legally* - the lawyers would be
employed forever trying to get a good measurement! Also, the assumption
that son 1 is greedy implies that he would reduce d to 0, in violation of
my specification that degenerate dissections are disallowed.
Lynn Yarbrough
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| 83.6 | | HERON::BUCHANAN | fragmentary blue | Mon Oct 31 1988 14:41 | 18 |
| 83.7 | Gotta keep a sense of humor | AKQJ10::YARBROUGH | I prefer Pi | Mon Oct 31 1988 15:55 | 36 |
| 83.8 | peace! | HERON::BUCHANAN | fragmentary blue | Mon Oct 31 1988 21:36 | 42 |
| 83.9 | | CLT::GILBERT | Multiple inheritence happens | Mon Oct 31 1988 23:06 | 18 |
| I like it! Note that the same approach generalizes to an arbitrary
number of sons. The following illustrates the case for 3 sons:
+---------+---------+---------+---------+---------+
| | | | | |
| | | | | |
| | +-+ +-+ | | +-+ +-+ | |
| +-+ +-+ +-+ +-+ +-+ +-+ |
| |
| |
| |
| |
| |
| |
| |
| |
| |
+-------------------------------------------------+
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| 83.10 | | HERON::BUCHANAN | fragmentary blue | Tue Nov 01 1988 08:15 | 18 |
| > Note that the same approach generalizes to an arbitrary
> number of sons. The following illustrates the case for 3 sons:
Yes, I was being needlessly self-constrained. Any number of brothers
can be handled. And if I rotate my
sub-squares by forty-five degrees, (ie they look like diamonds)
then I can stick them like polyps to the walls of the field, and each wall can
have diamonds attached to it, without running into difficulties of non-
connectivity.
Also, I needn't have all the subsquares the same size.
Further, I when it comes to embedding sub-diamonds into each of the
diamonds, then I can choose for each diamond which of the four faces is to
be considered the North face (ie that corresponding to the North face of the
original field.
Andrew
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| 83.11 | fluff -> lawyer | HERON::BUCHANAN | fragmentary blue | Wed Nov 02 1988 11:52 | 23
|