UC Davis Math Circle Problem List

If you have any thoughts or questions about these problems, we encourage you to contact us.

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Drawing random points in the Sierpinski Gasket

Draw a triangle.

Pick a vertex (pink circle).

(a) Draw a point there.
(b) Pick another vertex (pink circle).
(c) Find the point half way between that vertex and the point you just drew.
(d) Draw a point there. Go to step (b).

You will only ever draw points in the Sierpinski Gasket. Why?

If you have any thoughts or questions about this, we encourage you to contact us!

The Sierpinski Gasket

The Sierpinski Gasket is the set of points that are leftover after the following process.

(1) Start with a solid equilateral triangle.
(2) Take the triangle whose vertices are the midpoints of the boundary edges, and remove its interior.
(3) Repeat step (2) with all of the remaining triangles.

For example...

Step (1)	After step (2)
After step (3)	Repeating steps (2) and (3).

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