Education Technology

Advanced String Graphs Part 1

Activity Overview

The famous designs of Santiago Calatrava represent beautiful examples of the synergy between mathematics, engineering and architecture. In this activity students model the cables of the “Bridge of Stings” in Jerusalem using a family of straight lines. The envelope formed by these straight lines can also be modelled by a single equation defining the curve. Students determine equations to straight lines, solve simultaneous equations, generate parametric equations and finally a single equation to model the resulting curve.


  • Cartesian and parametric forms of lines and parabolas
  • Solutions to simultaneous equations
  • Generalisation of families of lines using parameters


  • Parameter
  • Simultaneous equations
  • Envelope

About the Lesson

Students determine the equation(s) to a set of linear functions that collectively form a curve. At first glance the curve looks hyperbolic, however upon further investigation students discover that the curve is parabolic. A set of parametric equations can be used to describe consecutive points of intersection. The parametric equations can then be resolved into the general form of a conic.