Is the best packing of 17 unit squares on a euclidean plane within precisely a square of the sides with length 4,6692... known as the feigenbaum constant? The best solution known is about 4,676

Background

The Feigenbaum constant (approximately 4.669201609102990671853203820466...) is a mathematical constant discovered by Mitchell Feigenbaum in the 1970s. It describes the ratio of successive bifurcation intervals in certain non-linear maps. The square packing problem involves finding the maximum number of unit squares (1x1) that can fit inside a larger square without overlapping.

Resolution Criteria

This market will resolve to YES if mathematical proof exists or is published showing that the optimal packing of 17 unit squares inside a square with sides equal to the Feigenbaum constant (4.669201609102990671853203820466...) is known and proven to be optimal. The market will resolve to NO if no such proof exists or if it's proven that the optimal packing is not known.

Considerations

• The square packing problem and the Feigenbaum constant are distinct mathematical concepts with no known relationship

• Square packing problems are typically solved through geometric and combinatorial methods

• The Feigenbaum constant is irrational, which means the square's area would also be irrational

• For most irrational square side lengths, determining the exact optimal packing of unit squares is a complex mathematical problem

• The market resolution depends on mathematical proof, not computational approximations or conjectures

• Update 2024-21-12 (PST): This market will resolve on December 2034. (AI summary of creator comment)

• Update 2024-25-12 (PST): - Resolution Date: The market will resolve on December 2034. (AI summary of creator comment)