Curvature and the Shape Operator

The Osculating Circle

Now is your chance to play with the osculating circle. Below is the graph of a fourth-degree polynomial, a currently selected point, and the relevant osculating circle. Use the slider to move the current point along the whole range of the graph. Watch the size of the circle grow/shrink and note how the circle "switches" sides of the function, depending on whether the curvature is positive or negative.

Metric Pattern Theory » Additional Chapters » Curvature and Shape Operator » Page 8/28

Web adaptation (XHTML + CSS + SVG + JS) by Shane Steinert-Threlkeld of Mathwright Microworld originally done by Priyan Weerappuli, Dr. J T Ratnanather which was supported by NIH P41-RR15241 and NSF NPACI. This adaptation is part of "Interactive Introduction to Computational Medicine" technology fellowship granted by JHU Center for Educational Resources.