Where is the best seat in the cinema?

AA SLAA HLAI SLAI HL Solid Also in: Geometry & Voronoi

Research question

In which row of my local cinema is the vertical viewing angle of the screen greatest, and how does raked seating change the answer?

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

Why it makes a good exploration

Sit too close and you look up at the bottom of the screen; too far and the screen shrinks. The angle the screen subtends has a maximum you can find with calculus — the same problem the astronomer Regiomontanus posed in 1471.

The mathematics you'll need

Inverse trigonometric functions to express the viewing angle
Differentiation (or technology) to maximise the angle
Coordinate geometry for raked (sloped) seating
Comparing with industry viewing-angle guidelines

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

Estimate screen height, screen bottom height and row spacing (pace it out, or use published seat plans).

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.
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

Set up θ(x) = arctan((a + h)/x) − arctan(a/x).
Find the maximum analytically or with technology.
Add raked seating: eye height rises with each row.
Compare with recommended viewing angles.
Reflect: horizontal angle, comfort, sound.

Pitfalls that cost marks

Measuring from the floor instead of eye level.
Not justifying the assumption that a bigger angle is better.
Leaving the derivative unsimplified and unverified.

Showing personal engagement

Measure your own favourite cinema or school hall.
Compare IMAX and standard screens.
Survey friends' preferred rows and compare with your model.

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

Taking it further

Optimise both vertical and horizontal viewing angles together, or find the seat that minimises neck strain.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).