Posts 111 - 120 of 151

Results for: History

An Ornamental Geometric Inequality 2

I came across this "ornamental geometric inequality" in a tribute to Lothar Collatz.... read more >>

Iterative Refinement for Solutions to Linear Systems 4

Iterative refinement is a technique introduced by Wilkinson for reducing the roundoff error produced during the solution of simultaneous linear equations. Higher precision arithmetic is required for the calculation of the residuals.... read more >>

Origins of Colormaps 2

Steve Eddins has recently posted a series in his blog about colormaps. I want to add one more post. With release R2014b, we are retiring jet as the default colormap, after many years of faithful service. But did you ever wonder where jet originated, and how it came to be the default? And did you ever come across colormaps like pink and bone?... read more >>

The Three n Plus One Conjecture 2

If $n$ is odd, replace $n$ by $3n+1$, if not, replace $n$ by $n/2$. Repeat. A famous conjecture made by Lothar Collatz is that no matter what value of $n$ is chosen to start, the process eventually terminates at $n=1$. Do not expect a proof, or a counterexample, in this blog. ... read more >>

Prime Spiral 2

The prime spiral was discovered by Stanislaw Ulam in 1963, and featured on the cover of Scientific American in March, 1964. ... read more >>

Jahnke and Emde, Revisited 1

An incredible book, published in several editions from 1909 to 1933, by German mathematicians Eugene Jahnke and Fritz Emde, contains definitions and formulas for mathematical functions, hand-calculated tables of function values, and meticulous hand-drawn 2- and 3-dimensional graphs. An English edition was published by Dover in 1945.... read more >>

MathWorks Logo, Part Five, Evolution of the Logo 5

Our plots of the first eigenfunction of the L-shaped membrane have changed several times over the last fifty years.... read more >>

MathWorks Logo, Part Four, Method of Particular Solutions Generates the Logo

The Method of Particular Solutions computes a highly accurate approximation to the eigenvalue we have been seeking, and guaranteed bounds on the accuracy. It also provides flexibility involving the boundary conditions that leads to the MathWorks logo. ... read more >>

MathWorks Logo, Part Three, PDE Toolbox 2

The Partial Differential Equation Toolbox contains tools for the analysis of PDEs in two space dimensions and time. It is perhaps not surprising that one of the primary examples involves the L-shaped membrane.... read more >>

MathWorks Logo, Part Two. Finite Differences 2

After reviewing the state of affairs fifty years ago, I use classic finite difference methods, followed by extrapolation, to find the first eigenvalue of the region underlying the MathWorks logo.... read more >>

Posts 111 - 120 of 151