Pascal's Triangle and Geometry

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SUMMARY

This discussion centers on the relationship between Pascal's Triangle and geometry, specifically how the nth row of Pascal's Triangle can be utilized to construct an (n-2)-dimensional simplex. Participants express difficulty in finding comprehensive texts on the subject, with references provided to resources such as the Math Forum and a PDF from Cambridge University detailing Pascal's treatment of the arithmetic triangle, which likely covers geometric implications.

PREREQUISITES
  • Understanding of Pascal's Triangle and its properties
  • Familiarity with simplex geometry
  • Basic knowledge of combinatorial mathematics
  • Ability to interpret mathematical texts and proofs
NEXT STEPS
  • Research the construction of simplices using Pascal's Triangle
  • Explore the mathematical implications of Pascal's Triangle in higher dimensions
  • Read "Pascal's Treatise on the Arithmetical Triangle" for historical context
  • Investigate the applications of combinatorial mathematics in geometry
USEFUL FOR

Mathematicians, geometry enthusiasts, educators, and students interested in the intersections of combinatorial mathematics and geometric constructs.

vsage
Does anyone here know of any lengthy texts on the subject? I have been hard-pressed to find anything past the fact that the nth row can be used to construct an (n-2)-dimension simplex.
 
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something that might interest u,
http://mathforum.org/isaac/problems/prob1.html

and

http://www.lib.cam.ac.uk/RareBooks/PascalTraite/pascalintro.pdf
(its about pascal treatment of the arithmetic triangle, prolly it discusses something abt pascal triangle and its relation to geometry[??])
 
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