Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

IA idea · Geometry, trigonometry & Voronoi diagrams

Designing a working sundial for my latitude

AA SLAA HLAI SLAI HL Solid Also in: Art & music, Environment, Trig & navigation

Research question

What angles should the hour lines of a horizontal sundial make for my latitude, and how accurate is a sundial built to that design compared with clock time across the year?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

A sundial is trigonometry you can build. The hour-line formula tan θ = sin φ · tan(15° × h) comes straight from 3-D geometry — and testing your dial reveals the equation of time.

The mathematics you'll need

Trigonometric functions and inverse functions
3-D geometry of the Earth's axis
Deriving tan θ = sin φ tan(15h)
Comparing measured and clock time; periodic error

Where the data comes from

Build a dial for your latitude and read it at set times on several days; compare with sunrise/sunset data.

timeanddate.com sun calculator — Sunrise, sunset and day length for any city and date.
GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

A possible outline

Explain why the gnomon points to the celestial pole.
Derive the hour-line formula.
Compute angles for your latitude and build the dial.
Test against clock time on different dates.
Explain the errors: time zones, longitude, equation of time.

Pitfalls that cost marks

Using the formula without derivation.
Aligning to magnetic rather than true north.
Ignoring daylight saving time.

Showing personal engagement

Build it from materials at home and photograph it.
Correct the reading for your longitude within the time zone.
Compare summer and winter accuracy.

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

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Trigonometric functions and inverse functions; 3-D geometry of the Earth's axis
AA HL	Good fit	Trigonometric functions and inverse functions; 3-D geometry of the Earth's axis
AI SL	Good fit	Trigonometric functions and inverse functions; 3-D geometry of the Earth's axis
AI HL	Good fit	Trigonometric functions and inverse functions; 3-D geometry of the Earth's axis

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: using the formula without derivation; and aligning to magnetic rather than true north. Say how each one affects your answer.

Use of mathematics (E)

SL: trigonometric functions and inverse functions; 3-D geometry of the Earth's axis; deriving tan θ = sin φ tan(15h); comparing measured and clock time; periodic error, each explained in your own words and carried out correctly.

How geometry & voronoi explorations reach the top bands in general: Geometry, trigonometry & Voronoi diagrams IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Model the equation of time as a sum of two sinusoids and correct your dial's readings.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL geometry & voronoi exploration adds.

See a complete IA, marked

When is the sea warm enough for our swimming club? A sinusoidal model of sea temperature (AI SL) is a complete geometry & voronoi exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL, AA HL, AI SL and AI HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Trigonometric functions and inverse functions, 3-D geometry of the Earth's axis, deriving tan θ = sin φ tan(15h) and comparing measured and clock time; periodic error.

Where can I get data for this IA?

Build a dial for your latitude and read it at set times on several days; compare with sunrise/sunset data. Checked sources and tools: timeanddate.com sun calculator and GeoGebra.

Turn this idea into your IA

The planner opens with “Designing a working sundial for my latitude” filled in: the question, the maths and the data sources.

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