What is the value of the integers a and b where sqrt(8-4sqrt3) =
sqrt a - sqrt b?
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Bricks are 20cm long and 10cm high. How high could an arch be built
without mortar on a flat horizontal surface, to overhang by 1
metre? How big an overhang is it possible to make like this?
Published June 1998,February 2011.
In this article Alex and Neil from
Madras College give a generalisation of the Three By
One problem. See also the article by
the same authors,
8 Methods for 'Three by One' which, as
the title suggests, brilliantly solves the same problem using 8
different topics in mathematics thus exemplifying the unity of the