Where Would You Put a 51st Star on the U.S. Flag?
Historical Background
The United States flag has undergone several changes throughout history, with the number of stars representing the number of states in the union. The current 50-star flag was adopted in 1959, following the admission of Hawaii as the 50th state.
Designing a 51-Star Flag
If another state were to join the union, the question arises: where would the 51st star be placed on the flag? One approach is to crowd source designs, as was done when Puerto Rico voted on statehood. However, a more elegant solution was devised by mathematician Skip Garibaldi.
Garibaldi’s Star Patterns
Garibaldi developed a system for organizing the stars on a rectangular flag with either horizontal or vertical symmetry. He identified six distinct patterns:
- Long: Alternating rows of even and odd numbers of stars, beginning and ending with the longer row. (Current 50-star flag)
- Short: Similar to the long pattern, but beginning and ending on the shorter row. (Not yet used on the American flag)
- Alternate: Like the long and short patterns, but with an equal number of odd and even rows. (45-star flag)
- Equal: Every row has the same number of stars. (30-star and 48-star flags)
- Wyoming: The first and last rows have one more star than the interior rows. (1890 flag, 26-star, 32-star, and 37-star flags)
- Oregon: The middle row has two fewer stars than all the other rows. (33-star flag)
Specific Arrangement for a 51-Star Flag
For a 51-star flag, Garibaldi’s solution recommends three rows of nine and three rows of eight. This arrangement maintains the rectangular shape and horizontal symmetry of the flag.
Considerations for Flag Design
When designing an American flag, certain rules must be followed:
- The star pattern must fit within a rectangle.
- The stars should be arranged in either horizontal or vertical symmetry.
- The colors of the flag should remain red, white, and blue.
Alternative Approaches
Some have suggested adding the 51st star to the side of the flag, but this would create an asymmetrical appearance. Crowd-sourced designs have also emerged, including a Pac-Man-shaped star formation.
Mathematical Elegance
Garibaldi’s solution provides a mathematically elegant way to organize the stars on the flag, ensuring a balanced and aesthetically pleasing design. It allows for the addition of stars while maintaining the traditional rectangular shape and symmetry of the American flag.