Pythagorean Block Idea Finally on Web Site

Ages ago, I posted these two posts to this newsgroup:
I remember the LEGO of my youth. Now, the door/window pieces of that
day are no more, and the angle bricks for rooftops are replaced by
some with a gentler slope. The pieces used for curved walls are only
seen in special sets for making spaceships or cement mixers.
Back in the old days, Lego consisted of general purpose sets, instead
of kits to make specific models, with figures and so on. Some of the
nicer new brick types, like the archways, tend not to be available in
the general-purpose sets, but instead in the castle sets, for example.
I'd like to see a general construction set with more variety. In
addition to bringing back old brick types, here are some suggestions
for new ones:
1. A set of interface bricks between the two rooftop standards.
_______
| /| o
That is, | /
|
bricks looking like this: | / | o
|___/
|
| o | | o
|___|___|
o o
2. Bricks that allow walls to be built at an angle, making use of the
famous 3-4-5 Pythagorean triangle.
This is done by making standard bricks in 2 x 5 size, and producing
base mats with a number of studs missing. Special bricks for the
corners will also be needed. I'll explain more fully in a later post.
and
My previous post (Wanted from mfr. ... Different Bricks) has, I see,
started a bit of a thread. However, I was in a rush, so I had cut
short my last suggestion as to a new family of bricks.
One member is very conventional: a 2 x 5 brick. It's used to keep down
the number of odd corner bricks required.
The main member consists of two kinds of base mats, one left-handed
and one right-handed. A base mat consists, usually, of a lot of studs
like this ...
o o o o o o o o o o o o
o o o o o o o o o o o o
o o o o o o o o o o o o
and so on.
Letting . stand for an omitted stud, my proposed base mats look like
this...
o . . . . o . . . . o . . . . o . .
. o . . . . o . . . . o . . . . o
. . . o . . . . o . . . . o . . .
o . . . . o . . . . o . . . . o .
. . o . . . . o . . . . o . . . .
o . . . . o . . . . o . . . . o . .
and the same thing, reflected in a mirror. (As the remaining studs are
in a regular square pattern, the asymmetry comes from the fact that
the edges of the mat are still cut on the basis of the original
pattern of studs, before some were omitted.)
---
|P .|. . . o . . . . P . . . . o . .
|. .|o . . . . o . . . . o . . . . o
|. .|. . o . . . . X . . . . o . . .
|. Q|. . . . R . . . . o . . . . o .
|. .|. o . . . . o . . . . o . . . .
|R .|. . . o . . . . o . . . . o . .
---
Now, in the diagram above, we see the outline of a 2x6 brick resting
on the mat, held by three studs, marked P, Q, and R. And 3 other studs
on the mat are marked P, X, and R. The first pair of studs marked P
and R, inside the outline, is separated by a distance of 5 spaces by
inspection. The second pair is also 5 spaces apart, since the
displacement is 4 spaces horizontally and 3 spaces vertically, by the
famous Pythagorean 3-4-5 triangle.
With 1 x 1 bricks, you can easily test that the stud marked X
corresponds to the omitted stud above the Q (basically, tilting the
pattern through the odd angle which also allows brick placement causes
a parity reversal). Or, it can be proven because 5 units, the diagonal
of a 1 x 2 rectangle, and the diagonal of a 1 x 3 rectangle, can be
seen to be the lengths of the sides in the triangles made by both
groups of points, requiring the triangles to be similar or exact
reversals.
The idea is that the base level would be built mostly with 2 x 10
bricks, with some 2 x 5 bricks at the ends of diagonal wall segments;
four mats, alternating in the two parities, could be used to allow
structures to be built in the shape of shallow octagons.
Well, that was a long time ago; more than two years, at least.
*Finally*, the latter of the two ideas presented has been illustrated,
with diagrams in color, on my web site at
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in the event anyone is interested in having a look.
John Savard
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John Savard
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