Magic Squares of Squares (are PROBABLY impossible) - Numberphile
Numberphile・2 minutes read
Magic squares of squares involve specific numbers arranged in a 3x3 grid where all columns, rows, and diagonals total to 15, dating back to the Lo Shu in 2200 BC. Various attempts at creating these magic squares are discussed, highlighting the complexity and challenges in finding true magic squares of squares.
Insights
- The earliest magic square, Lo Shu, dates back to 2200 BC and was discovered by Emperor Yu on a turtle's back, showcasing the ancient origins and legends associated with these mathematical constructs.
- Finding a true magic square of squares is complex, with various attempts like the Parker Square and Bremner Square falling short due to repeated or non-square entries, emphasizing the challenge and precision required in creating these unique grids.
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Recent questions
What are magic squares of squares?
Magic squares of squares are 3x3 grids with specific numbers arranged so that all rows, columns, and diagonals add up to 15.
What is the history of magic squares?
The earliest known magic square is the Lo Shu, dating back to 2200 BC, discovered by Emperor Yu on a turtle's back.
What is the Parker Square?
The Parker Square is a challenging version of a magic square of squares with all entries being square numbers, falling short due to repeated entries and a diagonal sum discrepancy.
How do magic squares scale up?
Scaling up magic squares involves multiplying all elements by a factor, maintaining the same relationships and structure despite numerical changes.
What is the significance of the Parker surface?
The Parker surface contains 368 known rational or elliptic curves, potentially aiding in the search for magic squares of squares, with uncertainty about the existence of a 3x3 magic square on the surface.
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