Enlargements and scale factors
problem
Von Koch Curve
Age
16 to 18
Challenge level
Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.
problem
Squareflake
Age
16 to 18
Challenge level
A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.
problem
Sierpinski Triangle
Age
16 to 18
Challenge level
What is the total area of the triangles remaining in the nth stage
of constructing a Sierpinski Triangle? Work out the dimension of
this fractal.
problem
Flower Show
Age
14 to 16
Challenge level
How long will it take six gardeners to dig six circular flower beds?
problem
Squirty
Age
14 to 16
Challenge level
Using a ruler, pencil and compasses only, it is possible to
construct a square inside any triangle so that all four vertices
touch the sides of the triangle.
problem
Conical Bottle
Age
14 to 16
Challenge level
A right circular cone is filled with liquid to a depth of half its
vertical height. The cone is inverted. How high up the vertical
height of the cone will the liquid rise?
problem
Matter of Scale
Age
14 to 16
Challenge level
Can you prove Pythagoras' Theorem using enlargements and scale factors?
problem
Hex
Age
11 to 14
Challenge level
Explain how the thirteen pieces making up the regular hexagon shown
in the diagram can be re-assembled to form three smaller regular
hexagons congruent to each other.
problem
Golden Triangle
Age
16 to 18
Challenge level
Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.