# An Ornamental Geometric Inequality2

Posted by Cleve Moler,

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

# Iterative Refinement for Solutions to Linear Systems4

Posted by Cleve Moler,

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 Colormaps2

Posted by Cleve Moler,

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 Conjecture2

Posted by Cleve Moler,

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 Spiral2

Posted by Cleve Moler,

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

# Season’s Greetings, 20142

Posted by Cleve Moler,

# Jahnke and Emde, Revisited1

Posted by Cleve Moler,

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 Logo6

Posted by Cleve Moler,

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

Posted by Cleve Moler,

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 >>

These postings are the author's and don't necessarily represent the opinions of MathWorks.