Question

The no. of equations and variables in Peirce’s geometry

• A. 7, 11
• B. 11, 7
• C. 8, 12
• D. 12, 8

Hint:

Peirce’s geometry is an over-determined system, which is why simplifying assumptions are essential in fabric geometry analysis.

Answer 1

The Correct Option is D

Step 1: Understanding Peirce’s geometry.
Peirce’s geometry is a mathematical model used to describe the geometry of woven fabric structures, particularly the path and interlacement of yarns.
Step 2: Role of equations and variables.
In Peirce’s geometric model, the fabric structure is defined using a set of simultaneous equations that relate yarn diameter, spacing, crimp, and fabric thickness.
Step 3: Standard formulation.
Peirce’s geometry consists of 12 governing equations involving 8 independent variables. This makes the system over-determined and requires simplifying assumptions.
Step 4: Conclusion.
Hence, the correct number of equations and variables in Peirce’s geometry is 12 and 8 respectively.