Objectives
Students explore a simple Bezier curve in the form of a parabola, however the control points on the Bezier curve mean the parabola can be dilated, translated and rotated quickly and easily. Students soon discover a world of mathematics that can be used to help unwind the complexity of a parabola that has been rotated. The world of mathematics nicely links several areas of the Specialist Mathematics curriculum.
Vocabulary
- Bezier Curve
- Parametric Equations
- Cartesian Equation
- General Equation for a conic
- Implicit differentiation
- Chain rule
- Axis of Symmetry
- Rotation
About the Lesson
Students start with a simply geometric construction reminiscent of the string graphs, the result is a simple Bezier curve. From these humble beginnings students use a dilation to create a locus that can be transformed and flexed like all good Bezier curves. The curve can be modelled with parametric equations which students use to determine the cartesian representation. A combination of the chain rule and implicit differentiation help to find the gradient of the relations, but where is the turning point? So much mathematics in this beautiful activity.