blog_23_six_circles_theorem.pdf |

a_triangle_with_regions_formed_by_cevians.pdf |

In this piece, we invoke the same least-time idea but in the well-known context of a lifeguard running across sand at a beach. We show with a little calculus how the law of refraction, Snell’s law, emerges. Then, we consider what a least-time path should look like if the sand were to vary in its softness between the lifeguard station and the water.

Finally, we see that the same mathematical ideas can be applied to the brachistochrone problem that Johann Bernoulli proposed and we give a relatively easy solution.

blog_16_beach_and_brachistochrone.pdf |

blog_21_fibonacci_compilation.pdf |

blog_20_21_puzzles.pdf |

blog_19_piano_maths.pdf |

blog investigates geometric methods that were developed by the 17th century French philosopher, mathematician and Scientist Rene Descartes and

the 19th century philosopher, essayist and mathematician Thomas Carlyle. This is great material for classroom investigations or project work.

blog_13_quadratic_roots_and_the_carlyle_circle.pdf |

blog_12_gardner_triples_handout.pdf |

According to Gamow’s original story, there was a young and adventurous man who found, among his grandfather’s papers, a parchment that revealed clues to the location of a great treasure. According to the parchment, the treasure was buried on a certain island, and using two prominent trees and an old broken Gallows the exact location could be obtained. Alas the Gallows were gone, and despite the young man digging holes all over the island, the treasure remained hidden.

While the authors in this blog have added their own colour to the story the original puzzle remains completely intact. Three separate proofs are given that show that the location of the Gallows was irrelevant to finding the treasure, but please don’t tell that young man.

blog_18_gamows_puzzle.pdf |

blog_15_cubic_roots_with_a_ruler.pdf |