Sine, cosine, tangent

  • LOGOSquares
    problem
    Favourite

    Logosquares

    Age
    16 to 18
    Challenge level

    Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

  • Three by One
    problem
    Favourite

    Three by One

    Age
    16 to 18
    Challenge level

    There are many different methods to solve this geometrical problem - how many can you find?

  • Belt
    problem
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    Belt

    Age
    16 to 18
    Challenge level

    A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.

  • Shape and territory
    problem
    Favourite

    Shape and Territory

    Age
    16 to 18
    Challenge level

    If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?

  • So Big
    problem
    Favourite

    So Big

    Age
    16 to 18
    Challenge level
    One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2
  • Coke machine
    problem

    Coke Machine

    Age
    14 to 16
    Challenge level
    The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
  • 30-60-90 Polypuzzle
    problem

    30-60-90 Polypuzzle

    Age
    16 to 18
    Challenge level
    Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.
  • Sine Problem
    problem

    Sine Problem

    Age
    16 to 18
    Challenge level
    In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
  • Farhan's Poor Square
    problem

    Farhan's Poor Square

    Age
    14 to 16
    Challenge level
    From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
  • Small Steps
    problem

    Small Steps

    Age
    16 to 18
    Challenge level
    Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
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