The Three Impossible Constructions

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About This Infographic

This interactive infographic explores the three famous classical problems that mathematicians proved cannot be solved using only compass and straightedge:

1. Squaring the Circle - Constructing a square with the same area as a given circle
2. Doubling the Cube - Constructing a cube with twice the volume
3. Trisecting an Angle - Dividing any arbitrary angle into three equal parts

Why Are They Impossible?

These problems are not just "very hard" — they are mathematically proven impossible with compass and straightedge alone. The proofs involve showing that certain numbers (like ∛2 or √π) cannot be constructed.

Problem	Year Proved	Mathematician	Key Obstacle
Squaring the Circle	1882	Lindemann	π is transcendental
Doubling the Cube	1837	Wantzel	∛2 is not constructible
Trisecting an Angle	1837	Wantzel	Requires solving cubic equations

How to Use

1. Hover over each card to see a preview
2. Click any card to read detailed information
3. Learn the history of each problem
4. Discover fun facts about these ancient challenges

Important Note

These problems CAN be solved with other tools: - A marked ruler (neusis construction) - Origami - Special curves (quadratrix, conchoid)

The impossibility is specific to the restricted tools of compass and straightedge!

Learning Objectives

• Understand the historical significance of construction problems
• Recognize that some problems are mathematically impossible
• Appreciate the limits of compass and straightedge constructions

Bloom's Taxonomy Level

Understanding and Evaluating - Understanding impossibility proofs and historical context.

Iframe Embed Code

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