WOLFRAM|DEMONSTRATIONS PROJECT

Triangle-Closed Planar Sets

​
closed set
freeplay
grid control
show grid
ortho grid
snap to grid
grid spacing
​
triangle control
show triangles
outline triangles
opacity
point size
storage control
delete last stored
reset
selected seed triangle
side lengths:
AB =
0
, BC =
0
, AC =
0
degrees:
α =
0
, β =
0
, γ =
0
tilt: δ =
0
(r,α) = (
0
,
0
)
points stored:
0

You are given a special triangle
T
(or a set of three non-collinear points) as a seed for a subset
S
of the plane.

For all pairs of points A, B in
S
you are asked to find the "closure point" C = C(
T
) such that the triangle ABC is similar to
T
.

Once C is found, we add it to the set
S
.

S
is called the
T
-closure or triangle-closure of
T
.

The cases where
S
is not a dense subset of the plane are the most interesting ones. Can you find a few?

Several examples of non-dense sets
S
are given (choose one from the "closed set" options).