Math Problem Statement
Illustrate the pack the circles with diameter equal to 24 inches using square and hexagon.
Solution
The illustration shows the two types of circle packing as described: square packing on the left, and hexagonal packing on the right. The square packing has more gaps between the circles, while the hexagonal arrangement shows a denser configuration with circles fitting more closely together.
Would you like more details or have any questions about the packing arrangement?
Here are five related questions you might find interesting:
- How do you calculate the packing density for square and hexagonal arrangements?
- What is the difference in efficiency between square and hexagonal packing?
- Can hexagonal packing be applied to 3D objects, such as spheres?
- How does circle packing change with different boundary shapes?
- What real-world applications use hexagonal packing for efficiency?
Tip: Hexagonal packing is about 91% efficient, while square packing only achieves about 78.5% efficiency!
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Math Problem Analysis
Mathematical Concepts
Geometry
Circle Packing
Tessellation
Packing Density
Formulas
Area of a circle: A = πr^2
Packing density for square packing: Density = π/4 ≈ 78.5%
Packing density for hexagonal packing: Density = π/√12 ≈ 90.7%
Theorems
Circle Packing Theorem
Suitable Grade Level
Grades 10-12
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