There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
A spherical balloon lies inside a wire frame. How much do you need
to deflate it to remove it from the frame if it remains a sphere?
Find the distance of the shortest air route at an altitude of 6000
metres between London and Cape Town given the latitudes and
longitudes. A simple application of scalar products of vectors.
Form a sequence of vectors by multiplying each vector (using vector
products) by a constant vector to get the next one in the
seuence(like a GP). What happens?
In this puzzle different things happen for odd and even numbers - find out why.
Go to last month's problems to see more solutions.
The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates why they are useful.
An account of multiplication of vectors, both scalar products and