# Patience Chinese Rings Puzzle

Posted by Cleve Moler,

MIT's Professor Daniel Frey recently introduced me to an ancient mechanical puzzle known as "Chinese Rings", "Patience", or "Baguenaudier." I have modified Daniel's simulator to produce a new app. The state space of the puzzle forms a hypercube.... read more >>

# Ulps Plots Reveal Math Function Accuracy2

Posted by Cleve Moler,

"ULP" stands for "unit in the last place." An ulps plot samples a fundamental math function such as $\sin{x}$, or a more esoteric function like a Bessel function. The samples are compared with more accurate values obtained from a higher precision computation. A plot of the accuracy, measured in ulps, reveals valuable information about the underlying algorithms.... read more >>

# Fitting and Extrapolating US Census Data

Posted by Cleve Moler,

A headline in the New York Times at the end of 2016 said "Growth of U.S. Population Is at Slowest Pace Since 1937". This prompted me to revisit an old chestnut about fitting and extrapolating census data. In the process I have added a couple of nonlinear fits, namely the logistic curve and the double exponential Gompertz model.... read more >>

# Season’s Greetings Fractal6

Posted by Cleve Moler,

I don't recall where I found this seasonal fractal. And I can't explain how it works. So please submit a comment if you can shed any light on either of these questions.... read more >>

# My First Matrix, RGB, YIQ, and Color Cubes2

Posted by Cleve Moler,

When I was in high school in the 1950's, I didn't know anything about matrices. But I nearly encountered one when I wrote a paper for my physics class about the color scheme that allowed new color TV broadcasts to be compatible with existing black-and-white TV receivers.... read more >>

# Four Fundamental Subspaces of Linear Algebra, Corrected

Posted by Cleve Moler,

(Please replace the erroneous posting from yesterday, Nov. 28, with this corrected version.)... read more >>

# Four Fundamental Subspaces of Linear Algebra3

Posted by Cleve Moler,

Here is a very short course in Linear Algebra. The Singular Value Decomposition provides a natural basis for Gil Strang's Four Fundamental Subspaces.... read more >>

# My Favorite ODE

Posted by Cleve Moler,

My favorite ordinary differential equation provides a good test of ODE solvers, both numeric and symbolic. It also provides a nice illustration of the underlying existence theory and error analysis.... read more >>

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