Graphing Line Designs

I bet you didn't think that line designs had anything to do with calculus...but they do!

Look carefully at this parabola. Do you see the curve it forms as it approaches the origin? Well this shape formed by the graph is very similar to that of the shape formed in line designs! Specific line designs actually have mathematical formulas that can be related to graphing in calculus!

Equation:

x^2/3 + y^2/3 = L^2/3

Equation:

x²/a² - y²/b² = 1

Equation:

x^2/3 + y^2/3 = L^2/3

^{every line has an equal length of L}

Equation:

x² - 2xy + y² - 2Lx - 2Ly + L² = 0

x-intercept: c

y-intercept: L - c

Erin Appenzoller