IA idea · Geometry, trigonometry & Voronoi diagrams

Designing a working sundial for my latitude

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

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?

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

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

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

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.

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 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.

Taking it further

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

Turn this idea into your IA

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