Curved fold

Can a curve be folded into a piece of paper?

Key stage: 3
Subjects: mathematics, geometry


Can you fold a curve in a piece of paper? Can you actually figure out the equation of such a curve, just from your folds?

This activity looks at a simple fold of straight lines that generate a parabola. Or you can take it further to fold any of the conic sections.

Included are some illustrations of the fold created using the freely-available digital geometrical package Geogebra.

The activity can be taken as a starting point for pupils to investigate curves such as parabolae in the real work (this can be reported back to the class through display work) but can take pupils as far as deriving an equation of a parabola. If your point is to get pupils working with a digital tool, then you may also introduce your class to Geogebra and encourage them to form dynamic geometrical constructions.

The activity can be used to address concepts such as distance, perpendicular bisector and equations of curves.

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