It's uncommon for a differential equation, especially a nonlinear PDE, to have a closed-form solution. But some important nonlinear PDEs can be solved in closed form.

John D. Cook Consulting Blog

24.04.2024

Choosing a Computer Language for a Project

New computer languages are sometimes proposed with claims of great advantages compared to existing languages. What criteria should use if we decide to adopt?

John D. Cook Consulting Blog

22.04.2024

On greedy algorithms and rodeo clowns

This weekend I ran across a blog post The Rodeo Clown Theory of Personal Development. The title comes from a hypothetical example of a goal you don't know how to achieve: becoming a rodeo clown. Let’s say you decide you want to be a rodeo clown. And let’s say you’re me and you have no

John D. Cook Consulting Blog

21.04.2024

Finding strings in binary files | strings(1)

How would you look for text embedded in a binary file? How long a string might you find by chance?

John D. Cook Consulting Blog

20.04.2024

Extract text from a PDF

Extracting text from a PDF file using GNU less or Python's pypdf. Why its not entirely clear just what a text extractor should do.

John D. Cook Consulting Blog

20.04.2024

Length of a general Archimedean spiral

Length of a general Archimedean spiral and how it behaves in the limit as the number of times around increases.

John D. Cook Consulting Blog

19.04.2024

How big will a carpet be when you roll or unroll it?

If a carpet is rolled up into a cylinder with a hole in the middle, how long will it be when you unroll it? Or how big will a carpet be when you roll it?

John D. Cook Consulting Blog

17.04.2024

Length of an Archimedes spiral

Approximating an Archimedian spriral by concentric rings. Approximation error for long spirals.

John D. Cook Consulting Blog

17.04.2024

Hypergeometric function of a large negative argument

How to evaluate a hypergeometric function at a large, negative argument, even thought the defining power series diverges.

John D. Cook Consulting Blog

16.04.2024

More is less

The command line utilities "less" and "more" are a pun on the aphorism "less is more."

John D. Cook Consulting Blog

12.04.2024

Precise answers to useless questions

I recently ran across a tweet from Allen Downey saying So much of 20th century statistics was just a waste of time, computing precise answers to useless questions. He's right. I taught mathematical statistics at GSBS [1, 2] several times, and each time I taught it I became more aware of how pointless some of

John D. Cook Consulting Blog

11.04.2024

Solar system means

The size and mass of some solar system bodies are remarkably close to the means of other bodies.

John D. Cook Consulting Blog

11.04.2024

Odds of pairs in poker with five, six, or seven cards

Why is poker usually played with five cards rather than six or seven? For one thing, pairs don't act like you might expect when you deal more cards.

John D. Cook Consulting Blog

10.04.2024

Earth is to Jupiter and Jupiter is to the Sun

The size of Jupiter is roughly the geometric mean of the sizes of the Earth and the Sun.

John D. Cook Consulting Blog

09.04.2024

Gravity on Jupiter

The surface gravity on Jupiter is less than you might imagine. Why is this?

John D. Cook Consulting Blog

06.04.2024

Are guidance documents laws?

Is a guidance document for a law itself a law? No, but sorta. It's complicated.

John D. Cook Consulting Blog

02.04.2024

More Laguerre images

More fractal-like images generated by Laguerre's root-finding method.

John D. Cook Consulting Blog

29.03.2024

A Bayesian approach to proving you’re human

A Bayesian approach to captchas can reduce user frustration and more often distinguish humans from bots.

John D. Cook Consulting Blog

28.03.2024

Antenna length: Another rule of 72

The Rule of 72 for interest and the Rule of 72 for dipole antenna length

John D. Cook Consulting Blog

27.03.2024

Hallucinations of AI Science Models

AI methods already make great impacts on scientific discovery. But questions of reliability and trustworthiness remain. Here we discuss the mathematical issues.

John D. Cook Consulting Blog

25.03.2024

Double super factorial

Double super factorial is a cross between a double factorial and a super factorial. Examples of double super factorials that equal factorials.

John D. Cook Consulting Blog

23.03.2024

Laguerre’s root finding method

Laguerre's root-finding method differs from Newton's method in several ways: it is specialized to polynomials, is faster, and converges from nearly every start.

John D. Cook Consulting Blog

21.03.2024

Breach Safe Harbor

Breach Safe Harbor refers to the breach of encrypted health information

John D. Cook Consulting Blog

21.03.2024

MD5 hash collision example

Demonstrating an MD5 hash, how to compute hash functions in Python, and how to diff strings.

John D. Cook Consulting Blog

17.03.2024

Distance from a point to a line

Two ways of finding the distance from a point to a line, one easy to derive and another that behaves better numerically.

John D. Cook Consulting Blog

15.03.2024

Experiences with Thread Programming in Microsoft Windows

Thread programming under Microsoft Foundation Class on Windows can have gotchas. Silent errors can impact program correctness. Here are tips to avoid problems.

John D. Cook Consulting Blog

14.03.2024

Accelerating Archimedes approach to computing pi

Gregory's recursive algorithm for speeding up Archimedes approach to computing pi.

John D. Cook Consulting Blog

10.03.2024

A simple accurate approximation for how much a catenary sags

Given the length of a catenary and the distance between between its supports, estimate how much lower the catenary is in the middle.

John D. Cook Consulting Blog

10.03.2024

Unique letter patterns | normalized cryptograms

Looking for words that have a unique pattern of letters, such as Mississippi. What is the shortest word with a unique pattern? The longest word?

John D. Cook Consulting Blog

09.03.2024

How to Organize Technical Research?

Effectively organizing research findings is critical to making new technical discoveries. Notetaking practices of experimentalists can teach important lessons.

home›John D. Cook Consulting Blog›Science

John D. Cook Consulting Blog - Science

Numerical differentiation with a complex step

Logistic regression quick takes

Numerical application of mean value theorem

MCMC and the coupon collector problem

Up and down the abstraction ladder

Making documents with makefiles

Applied abstraction

Standard deck of 52 playing cards and alternatives | Unicode

What can JWST see?

Fizz buzz walk

Closed-form solutions to nonlinear PDEs

Choosing a Computer Language for a Project

On greedy algorithms and rodeo clowns

Finding strings in binary files | strings(1)

Extract text from a PDF

Length of a general Archimedean spiral

How big will a carpet be when you roll or unroll it?

Length of an Archimedes spiral

Hypergeometric function of a large negative argument

More is less

Precise answers to useless questions

Solar system means

Odds of pairs in poker with five, six, or seven cards

Earth is to Jupiter and Jupiter is to the Sun

Gravity on Jupiter

Are guidance documents laws?

More Laguerre images

A Bayesian approach to proving you’re human

Antenna length: Another rule of 72

Hallucinations of AI Science Models

Double super factorial

Laguerre’s root finding method

Breach Safe Harbor

MD5 hash collision example

Distance from a point to a line

Experiences with Thread Programming in Microsoft Windows

Accelerating Archimedes approach to computing pi

A simple accurate approximation for how much a catenary sags

Unique letter patterns | normalized cryptograms

How to Organize Technical Research?

home
›
John D. Cook Consulting Blog
›
Science