What is the sierpinski triangle?

Question

and what is it used for?

Answer 1

the way I remember it is that you start with an equilateral triangle, and pick a random point P inside the triangle. then for each of the three corners of the triangle, you fill in the point that's exactly in the middle between P and the corner. then for each of these three new points, you do the same, and continue the process forever. the neat thing is that, no matter what point you picked P to be, the pattern eventually stabilizes and becomes a fractal (there are nice pictures in the wikipedia article).

Answer 2

The Sierpinski triangle, also called the Sierpinski gasket, is a fractal named after Wacław Sierpiński who described it in 1915. Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction.

Answer 3

This is fractal mathematics, and not easy to explain in few words. I'm not sure that it is applied intentionally as decoration or anything else. It's interest is in the strange numbers for its dimension and area, like all fractals its dimension is not a whole number, it is between 1 and 2, and its area is zero I can't improve on the following as an introduction, but be warned, it's not exactly easy !

Answer 4

It's a pretty cool triangle that is filled with smaller triangles inside.
It's a mathematically generated pattern, named after a polish mathematician that invented it.

It's used to teach how to use fractals. A fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole".

Also used in art, graphic design etc.

Answer 5

Some good answers here. I'll just add that the area of the triangle is zero, because each new iteration when creating the triangle eliminates 1/4 of the area. Eventually, the triangle "disappears".

Answer 6

It's a recursive function on a 2-D manifold, first described by the Polish mathematician after whom it is named. It's interesting because (like the Koch 'snowflake. and numerous other 'space-filling curves) in the limit it cannot be embedded in an integer-dimensioned measurement space, which makes it be one of the so-called 'fractal' functions.

Doug

Answer 7

i don't know