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 Sqrt

Differential geometric graphics (16 graphics)

Intrinsic curvature curves

Curves with intrinsic curvature , with ranging from 0 (red) to 2 (violet). parametrizes the curve.

Intrinsic curvature-torsion curves

Curves with intrinsic curvature and intrinsic torsion with ranging from 0 (red) to (violet). parametrizes each curve.

Phase portraits

Phase portrait of the function. The left graphic shows the curves . The curves are parametrized by with varying (dark red curves) and φ varying (yellow curves). The right graphic shows the curves . The curves are parametrized by with varying (dark blue curves) and φ varying (violet curves).

Generalized phase portrait of the function. The left graphic shows the curves . The curves are parametrized by with varying (dark red curves) and φ varying (yellow curves). The right graphic shows the curves . The curves are parametrized by with varying (dark blue curves) and φ varying (violet curves).

Offset curves

Wavefront caustic of the function . The gray curve is the function . The red lines are normals on this curve. The blue curves are the caustics formed by the normals.

Pursuit curves

Pursuit curves with respect to the function . The gray curve is the function . The red curves are pursuit curves that start at different positions.

Evolute

Evolute and osculating circles of the function . The gray curve is the function . The osculating circles are colored according to their radius and the blue curve is the evolute. The green lines connect the centers of the osculating circles with the points where the circles touch the curve.

Involutes

Involutes of the function . The gray curve is the function . The involutes are shown as red curves.

Pedal curves

Family of pedal curves of the function .

Family of contrapedal curves of the function .

Wavefront caustic surfaces

Wavefront caustics of the real part and the imaginary part of the function . The upper two graphics show the two wavefront caustic surfaces of the real part and the lower two graphics show the two wavefront caustic surfaces of the imaginary part.