Discover fractals like the Sierpinski triangle and Koch snowflake, and explore solid shapes, nets, and geometric constructions.
A fractal is a shape made of smaller copies of itself repeated infinitely. The Sierpinski triangle is formed by repeatedly removing the middle triangle from a larger one.
If a Sierpinski triangle starts with 1 triangle and each step triples the number of smaller triangles, how many triangles exist after 3 steps?
3³ = 27 triangles
What happens to the total area of a Sierpinski triangle as the number of steps increases?
The area shrinks toward zero, since each step removes 1/4 of the remaining area
A net is a 2D pattern that folds up into a 3D solid shape. Understanding nets helps visualize surface area and how solids are constructed.
How many faces does the net of a cube have?
6 square faces
What solid does a net with 1 rectangle and 2 triangles (as end caps) typically fold into?
A triangular prism
1. If a fractal pattern quadruples the number of shapes at each step, how many shapes exist after 2 steps?
2. How many faces does the net of a triangular pyramid (tetrahedron) have?
3. What is the defining feature of any fractal shape?
4. A cube net has 6 squares. If each square has side 4 cm, find the total surface area shown by the net.
5. Why can the same 3D solid have more than one valid net?