How to Draw the Olympic Rings Mathematically?

Inequalities (Relations) for the Olympic Rings:

1. (Blue Ring)  min(max(R₁(x,y), -y), max(R₁(x,y), y, -R₄(x,y))) < 0
2. (Black Ring)  min(max(R₂(x,y), -y, -R₄(x,y)), max(R₂(x,y), y, -R₅(x,y))) < 0
3. (Red Ring)  min(max(R₃(x,y), -y, -R₅(x,y)), max(R₃(x,y), y)) < 0
4. (Yellow Ring)  min(max(R₄(x,y), -y, -R₁(x,y)), max(R₄(x,y), y, -R₂(x,y))) < 0
5. (Green Ring)  min(max(R₅(x,y), -y, -R₂(x,y)), max(R₅(x,y), y, -R₃(x,y))) < 0

Functions:

• R₁(x,y) = (sqrt((x+2d)² + (y-h)²) - a)² - b²
• R₂(x,y) = (sqrt(x² + (y-h)²) - a)² - b²
• R₃(x,y) = (sqrt((x-2d)² + (y-h)²) - a)² - b²
• R₄(x,y) = (sqrt((x+d)² + (y+h)²) - a)² - b²
• R₅(x,y) = (sqrt((x-d)² + (y+h)²) - a)² - b²

Constants:

• a = 49.25
• b = 4.75
• d = 58.5
• h = 25

Download Examples:

• olympic_rings.zip

( Mathematical softwares used: Graph, gnuplot )