IA idea · Art, music & design
How accurate is the perspective in a Renaissance painting?
Research question
Do the receding parallel lines in [a painting] meet at a single vanishing point, and how large are the deviations when measured on a high-resolution image?
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Why it makes a good exploration
Renaissance painters used geometry to create depth. Extending lines on a digital image and measuring where they meet tests how precisely a famous artist applied the rules.
The mathematics you'll need
- Equations of lines from points
- Intersections of lines and their spread
- Distance from a point to a line
- Descriptive statistics of errors
Where the data comes from
Use a high-resolution public-domain image from a museum's online collection.
- GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.
A possible outline
- Explain one-point perspective.
- Identify receding lines and extract points.
- Compute intersections.
- Measure spread and errors.
- Reflect on deliberate distortions and image resolution.
Pitfalls that cost marks
- Choosing lines that are not truly parallel in the scene.
- Low-resolution images.
- Ignoring the artist's intentional choices.
Showing personal engagement
- Compare two artists or a painting and a photograph.
- Draw your own perspective scene and measure it.
- Discuss whether deviations are errors or artistry.
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 | Equations of lines from points; Intersections of lines and their spread |
| AA HL | Good fit | Equations of lines from points; Intersections of lines and their spread |
| AI SL | Good fit | Equations of lines from points; Intersections of lines and their spread |
| AI HL | Good fit | Equations of lines from points; Intersections of lines and their spread |
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: choosing lines that are not truly parallel in the scene; and low-resolution images. Say how each one affects your answer.
Use of mathematics (E)
SL: equations of lines from points; intersections of lines and their spread; distance from a point to a line; descriptive statistics of errors, each explained in your own words and carried out correctly.
How art & music explorations reach the top bands in general: Art, music & design IA ideas. Guides: A · B · C · D · E · self-grade sheet.
Taking it further
Use the vanishing point and the horizon to estimate the viewer's position relative to the painting.
Extending it for HL
Add an HL technique the question genuinely needs: what an HL art & music exploration adds.
See a complete IA, marked
Is a hanging chain a parabola? Comparing catenary and quadratic models (AA SL) is a complete art & music exploration, marked on every criterion.
Frequently asked questions
Which IB Maths course is this IA idea for?
It works for AA SL, AI SL, AA HL and AI HL. We rate it Solid: it needs some independent work beyond class examples.
What mathematics does this IA use?
Equations of lines from points, intersections of lines and their spread, distance from a point to a line and descriptive statistics of errors.
Where can I get data for this IA?
Use a high-resolution public-domain image from a museum's online collection. Checked sources and tools: GeoGebra.
Turn this idea into your IA
The planner opens with “How accurate is the perspective in a Renaissance painting?” filled in: the question, the maths and the data sources.
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