For each delta of theta during animation does the radius of curvature change by the same percentage from the previous plotted point? It looks like each is near 10% regardless of which vertex the points are closer to (only their lengths change but appear to stay percent relative in size for any two jux points)
@Michael Barton If you have the equation for the curve of the evolute then you can take its derivative. The points of the curve of the evolute, known as "centers of curvature" can be easily given though it'll be difficult for me to convey to you the components of a simple formula as is easily derived without a geometric diagram. Introduction to Calculus and Analysis, Vol. 1 (by Richard Courant and Fritz John), p. 424, equation. 58, prerequista diagram on p. 359, figure. 4.23. It is in parametric form which can be simply eliminated with a rearrangement of the set of equations f(^-1)(t)=x into f(x)=t and g(^-1)(t)=y into g(y)=t and setting f(x)=g(y). There's a very tiny Wikipedia page on "Center of curvature", but really, Richard Courant's diagram and derivation is superior.
Perfect, this gave me the visuals that I needed to make sense of evolutes. Thanks!
Top Video! Hat mir sehr geholfen!
What is the name of the software?
For each delta of theta during animation does the radius of curvature change by the same percentage from the previous plotted point? It looks like each is near 10% regardless of which vertex the points are closer to (only their lengths change but appear to stay percent relative in size for any two jux points)
@Michael Barton
If you have the equation for the curve of the evolute then you can take its derivative.
The points of the curve of the evolute, known as "centers of curvature" can be easily given though it'll be difficult for me to convey to you the components of a simple formula as is easily derived without a geometric diagram.
Introduction to Calculus and Analysis, Vol. 1 (by Richard Courant and Fritz John), p. 424, equation. 58, prerequista diagram on p. 359, figure. 4.23.
It is in parametric form which can be simply eliminated with a rearrangement of the set of equations f(^-1)(t)=x into f(x)=t and g(^-1)(t)=y into g(y)=t and setting f(x)=g(y).
There's a very tiny Wikipedia page on "Center of curvature", but really, Richard Courant's diagram and derivation is superior.