A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?
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.
From the information you are asked to work out where the picture
was taken. Is there too much information? How accurate can your
What is the total area of the triangles remaining in the nth stage
of constructing a Sierpinski Triangle? Work out the dimension of
Photocopiers can reduce from A3 to A4 without distorting the image.
Explore the relationships between different paper sizes that make
Prove Pythagoras Theorem using enlargements and scale factors.
Triangle ABC is equilateral. D, the midpoint of BC, is the centre
of the semi-circle whose radius is R which touches AB and AC, as
well as a smaller circle with radius r which also touches AB and
AC. . . .
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?
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.
We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
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.