Coordinates

  • Four Points on a Cube
    problem

    Four points on a cube

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?
  • Plane to See
    problem

    Plane to see

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
  • Napoleon's Hat
    problem

    Napoleon's hat

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

  • Cushion Ball
    problem

    Cushion ball

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
  • Ladder and Cube
    problem

    Ladder and cube

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

  • Just Opposite
    problem

    Just opposite

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
  • Cut Cube
    problem

    Cut cube

    Age
    16 to 18
    Challenge level
    filled star filled star filled star
    Find the shape and symmetries of the two pieces of this cut cube.
  • The Lily Pond
    problem

    The lily pond

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    Freddie Frog visits as many of the leaves as he can on the way to see Sammy Snail but only visits each lily leaf once. Which is the best way for him to go?
  • Coordinates and Descartes
    article

    Coordinates and Descartes

    Have you ever wondered how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.

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