Fractals and Equilateral Triangles

Dr. Tom Crawford from the University of Oxford presents a video for Maths Week London, focusing on the perimeter and area of fractals, specifically the Koch snowflake. Starting with an equilateral triangle, he explains how to calculate its perimeter and area. The video then details the iterative process of creating the Koch snowflake, a fractal with an infinite perimeter but a finite area. The mathematical principles behind the fractal's growth are explored, demonstrating the beauty and complexity of fractals.

What is a fractal?

• A shape with a fixed size

• A shape with no symmetry

• A shape with a repeating pattern at every scale

• A shape with a finite perimeter

What is the perimeter of an equilateral triangle with side length 1?

• 1

• 2

• 3

• 4

How is the area of an equilateral triangle calculated?

• Base times height

• Half base times height

• Height squared

• Base squared

What is the first step in creating the Cox Snowflake?

• Remove the middle segment

• Double the length of each side

• Add a wedge

• Divide each side into three parts

What happens to the perimeter of the Cox Snowflake as iterations increase?

• It becomes zero

• It becomes infinite

• It remains constant

• It decreases

How does the area of the Cox Snowflake change with each iteration?

• It becomes infinite

• It approaches a finite value

• It decreases

• It remains constant

What is the final conclusion about the Cox Snowflake?

• It has a finite perimeter and area

• It has an infinite perimeter and finite area

• It has an infinite perimeter and area

• It has a finite perimeter and infinite area