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I received my Ph.D in mathematics from Ohio State in 1994 under the direction of Gerald Edgar and have been a professor of mathematics at The University of North Carolina - Asheville since 1997. In recent years, I've also worked as a part-time consultant to Wolfram Research focusing on development of mathematical content for WolframAlpha.


15h
comment Infinite number of points in the Sierpinski Triangle
You didn't remove everything! You didn't remove $1$. Or $1/3$. Or $1/9$. Or $1/27$. Or any number of the form $1/3^k$.
21h
comment Infinite number of points in the Sierpinski Triangle
The Sierpinski triangle certainly contains a line segment, so there's infinitely many points right there.
23h
comment Floating-point arithmetic error
@user177196 That's really a formatting issue. Try 1-(0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1).
1d
comment What are some interesting cases of $\pi$ appearing in situations that are not / do not seem geometric?
@Ian Of course, that is exactly the origin. Does the statement seem geometric as is? Without that knowledge? :)
1d
answered Floating-point arithmetic error
1d
answered What are some interesting cases of $\pi$ appearing in situations that are not / do not seem geometric?
1d
comment Basic Number Theory in Mathematica
I reset your input to display as code, as I assume you need to type that verbatim into WolframAlpha. The question is probably more appropriate for mathematica.se, however.
1d
revised Basic Number Theory in Mathematica
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1d
revised Basic Number Theory in Mathematica
rolled back to a previous revision
2d
answered Anyone can integrate $e^{-\frac{x^2}{3}}$ by hands?
2d
comment Numerical Approximation for 2D Curvature
Can you post the data? Or a link to the data? One option would be to interpolate the points. Mathematica, Matlab, Scipy, and (I'm certain) that many other good numerical environments all have excellent built in tools for this. Once you interpolate the points, you have a vector valued function that, for most purposes, you can manipulate just like any other function. You can compute values, derivatives, cross-products, norms, and curvature.
2d
comment $\epsilon$-$\delta$ proof of a sinc limit in Complex variables
@herashefat Understandable and will do! All the more reason to point it out. :)
2d
comment $\epsilon$-$\delta$ proof of a sinc limit in Complex variables
@columbus8myhw Was my iphone. :) I think it's this.
2d
answered Inequalities involving the sine of Complex Variable z
2d
revised Graphing algorithm
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2d
revised How do I find the error of nth iteration in Newton's Raphson's method without knowing the exact root
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2d
comment How do I find the error of nth iteration in Newton's Raphson's method without knowing the exact root
@Pp.. It is certainly possible that Newton's method converges to a cycle nowhere near any of the roots. An example is $p(z)=z^5-z-1$. By fiddling with the parameters, it can be arranged that the points in the cycle are close together, yielding the appearance of convergence to a single point. In this case, though, we don't "move on" to convergence to an actual root.
2d
revised How do I find the error of nth iteration in Newton's Raphson's method without knowing the exact root
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2d
comment How do I find the error of nth iteration in Newton's Raphson's method without knowing the exact root
@Pp.. I'll be darned - how'd I miss that? At any rate, I do appreciate your input, as I'm happier with the example as it now stands.
Jan
27
comment How do I find the error of nth iteration in Newton's Raphson's method without knowing the exact root
@Pp.. I don't see where the OP assumes convergence. One might think that he assumes the existence of a root, which my updated example has. In fact, my example does converge to the actual root near zero, though, I think one needs a fairly deep understanding of how Newton's method works in the complex case to see why.