In many cases there will be links to reports of my explorations.

In some cases there is a collection of problems, constituting a domain of exploration.

Domain Titles | Initiating Problem(s) |

Core Area & Core Perimeter | What is the ratio between the area of a shape and the are of
the curve enveloped by the lines which bisect the area of the shape?
Same for perimeters Animation for triangles |

Polynomial Explorations |
A collection of explorations of properties and
features of polynomials as introduction to functions and the calculus,
but going beyond what is normally included in getting to grips with
polynomials |

Intermediate Curvature Theorem | If a function is twice differentiable on an interval, and if three points are chosen in that interval, is there a point on the curve at which the curvature is the same as the curvature of a circle through those three points (the Menger curvature)? |

Mean and Intermediate Value Theorems | |

Petrol Pump Problem | A collection of generalisations of a problem in Krutetskii: if there are petrol pumps placed around a circular track, with just enough petrol in total for a car to make a complete circuit, is there somewhere on the track where a car can start and make it all the way, picking up petrol at the pumps? |

Fractional Difference | In how many ways can the fraction 1/n be written as the difference of two unit fractions? |

Least Common Multiples | In how many ways can n be the least
common multiple of two (positive) numbers? What connections if any are there with Fractional Difference? |

John Mason's Index page John Mason's Personal Page CME Main Page

Comments and Questions: j.h.mason @ open.ac.uk