1 / 7

Symbolic Mapping of a Finite Projective Plane - Mathematical Structure Exploration

Explore the unique symbolic relationships in a finite projective plane of order 7, assigning symbols to cards in a structured manner that unveils hidden patterns and connections. Discover the mathematical beauty behind the pairing of cards and symbols in parallel lines across multiple directions. Uncover the significance of specific numbers in this intriguing ordering system.

dominy
Download Presentation

Symbolic Mapping of a Finite Projective Plane - Mathematical Structure Exploration

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. How do they do that?

  2. Assign a symbol to cards on a straight line. • Each pair of cards define a unique line... • ...so have a unique symbol in common! • 7 parallel lines per direction. • 8 directions... • Can assign extra cards for intersection of parallel lines. • These also need a symbol in common. 49 cards 56 symbols 57 cards 57 symbols

  3. Finite projective plane of order n=7. • n2+n+1 cards • n2+n+1 symbols • n+1 cards / symbol • n+1 symbols / card • A set of cards with a nice mathematical structure!

  4. ...almost. Not included in pack

  5. Another representation of the structure

  6. Matching symbols occur at relative positions (mod 57)0, 1, 3, 13, 32, 36, 43, 52What is special about these numbers that makes this ordering possible?

More Related