My favourite technology-based maths problem
This is my favourite technology-based maths problem, and possibly my favourite maths problem. It needs to be attempted in software that has linked geometrical and algebraic views (and preferably some others too). GeoGebra or TI-Nspire are ideal for this. Start with a square of variable side with one vertex on the origin and one on the positive x-axis: The problem is to create a rectangle with the same area as the square whose sides are in the ratio 2:1. Creating the initial square in GeoGebra Add a point A at the origin. Add a point B on the x-axis. Use the Regular Polygon tool selecting vertices at A and B and set the number of vertices to 4. Creating the initial square in TI-Nspire Add a new Graphs page. Add a point at the origin by finding the Intersection Point of both axes . Add a new Point On the x-axis. Display the Coordinates of this point. Use Measurement Transfer to transfer the value of the x-coordinate to the y-axis. Add a line Perpendicular t