IA idea · Geometry, trigonometry & Voronoi diagrams

Is a satellite dish really a parabola, and where is its focus?

AA SLAA HL Solid Also in: Modelling, Calculus

Research question

Does the cross-section of a real satellite dish fit a parabola, and does the fitted focus coincide with the position of the receiver arm?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Parabolic reflectors focus signals at a single point. Measuring a real dish, fitting a parabola, and checking whether the receiver is at the focus is a neat test of a geometric property.

The mathematics you'll need

Quadratic functions and the focus–directrix definition (explain)
Least-squares fitting
The reflective property via gradients and angles
Offset dishes as part of a parabola

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Measure depth at points across a dish (or a wok/bowl) with a straight edge and ruler; measure the receiver position.

GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the focus–directrix definition.
Measure the profile and fit a parabola.
Find the focus and compare with the receiver.
Demonstrate the reflective property with gradients.
Reflect on offset dishes and measurement error.

Pitfalls that cost marks

Measuring an offset dish as if it were symmetric.
Not converting y = ax² to focal length correctly (f = 1/(4a)).
Too few measurement points.

Showing personal engagement

Measure a dish at home.
Test with a torch and a foil-lined bowl.
Compare with a telescope mirror.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Prove the reflective property of the parabola using the gradient and the angle between lines.

Turn this idea into your IA

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