IA ideas library
Maths IA ideas in art, music and design
Art and music are full of mathematics: sine waves in sound, ratios in scales, symmetry groups in patterns, curves in typography and logos. These ideas are good for students who want an IA that feels creative.
Beware the golden ratio: it is the single most over-used IA context, and most claims about it do not survive measurement. If you use it, make testing the claim the point of the IA.
Next step: shortlist ideas with the free IA topic explorer, which filters starting points by course, interest and how easy the data is to get. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.
How art & music explorations reach the top bands
Personal engagement (C)
Use an artwork, instrument or design you know or make yourself, and measure it yourself. Explain the aesthetic question as well as the mathematical one.
Reflection (D)
Test popular claims honestly (the golden ratio is often not where people say it is) and reflect on how measurement choices affect the result.
Use of mathematics (E)
SL: Geometry, trigonometry, sequences or functions used to model or test a real piece of art or music, with measurements and error discussed.
HL: Complex numbers, parametric curves, transformations as matrices, or Fourier-style sums of sinusoids, used to explain the structure rigorously.
An HL version
Describe the construction with parametric or complex-number methods, or prove a property of the pattern or scale you studied.
Art, music & design ideas (14)
- Is the golden ratio really everywhere? Testing a popular claimAI SLAI HLAA SLAA HLSolid
- Why does a piano have twelve notes per octave?AA SLAA HLAI SLAI HLSolid
- Why do a flute and a violin sound different on the same note?AA SLAA HLAI SLAI HLSolid
- Symmetry in Islamic geometric art: which wallpaper groups appear?AA HLAA SLAmbitious
- How are letters drawn on a screen? Bézier curvesAA HLAA SLAI HLSolid
- How accurate is the perspective in a Renaissance painting?AA SLAI SLAA HLAI HLSolid
- Why do sunflower seeds form spirals? The golden angleAA SLAA HLAI SLAI HLSolid
- What curve do straight lines make in string art?AA SLAA HLSolid
- Why are camera f-stops 1.4, 2, 2.8, 4, 5.6?AA SLAI SLAA HLAI HLAccessible
- Why do guitar frets get closer together? A geometric sequence on the fingerboardAA SLAI SLAA HLAccessible
- Why do two nearly-equal notes 'wobble'? Beats and trigonometric identitiesAA SLAA HLAI SLAI HLSolid
- Spreading beats evenly: Euclid's algorithm and musical rhythmAA SLAA HLSolid
- How fast does a speaker get quieter? Decibels, logarithms and distanceAA SLAI SLAA HLAI HLAccessible
- Are popular songs getting faster or shorter? Statistics on music dataAI SLAI HLAA SLAccessible
Also relevant (14)
- Is a hanging chain a parabola? Catenary versus quadratic modelsAA SLAA HLAI SLAI HLSolid
- Which function best describes the arch of a famous bridge?AA SLAI SLAccessible
- Can statistics tell two authors apart?AI SLAI HLAA SLSolid
- Do TV series really get worse over time?AI SLAI HLAccessible
- Designing a working sundial for my latitudeAA SLAA HLAI SLAI HLSolid
- Beyond Fibonacci: what ratio do other recurrence sequences approach?AA HLAA SLSolid
- Why does Pascal's triangle make a fractal?AA HLAA SLSolid
- Why is the main body of the Mandelbrot set a cardioid?AA HLAmbitious
- Infinite perimeter, finite area: designing your own snowflake curveAA SLAI SLAA HLAccessible
- Fold a strip, unfold it: the dragon curveAA SLAA HLSolid
- Animating a logo with transformation matricesAI HLAA HLSolid
- How does a game draw 3D on a flat screen? Projection matricesAI HLAA HLAmbitious
- The hidden angles of a hip roof: 3D trigonometryAA SLAI SLAA HLSolid
- The path of a bike valve: parametric equations of a cycloidAA HLAI HLAmbitious
Frequently asked questions
Is the golden ratio a good IA topic?
Only if you test a claim properly — for example, measure many examples, estimate measurement error and use a statistical test to decide whether the ratios really cluster near 1.618. Simply finding it in a painting is not enough.
What maths is behind music?
Sound waves are sums of sine functions, musical intervals are frequency ratios, and equal temperament uses a geometric sequence with ratio the twelfth root of 2.
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Related types of IA: Fractals & chaos
Taking Music or Visual Arts? Maths IA ideas for music students · Maths IA ideas for visual arts students
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