# Why care about spherical trig?

Last spring I wrote a post on spherical trigonometry, the study of triangles drawn on a sphere (e.g. the surface of the Earth). Mel Hagen left a comment on that post a few days ago saying I am revisiting Spherical Trig after 30 years by going back over some of my books that I have […]

# Why 90% solutions may beat 100% solutions

I’ve never written a line of Ruby, but I find Ruby on Rails fascinating. From all reports, the Rails framework lets you develop a website much faster than you could using other tools, provided you can live with its limitations. Rails emphasizes consistency and simplicity, deliberately leaving out support for some contingencies. I listened to […]

# Why heights are normally distributed

The canonical example of the normal distribution given in textbooks is human heights. Measure the heights of a large sample of adult men and the numbers will follow a normal (Gaussian) distribution. The heights of women also follow a normal distribution. What textbooks never discuss is why heights should be normally distributed. Why should heights […]

# Why Unicode is subtle

On its surface, Unicode is simple. It’s a replacement for ASCII to make room for more characters. Joel Spolsky assures us that it’s not that hard. But then how did Jukka Korpela have enough to say to fill his 678-page book Unicode Explained? Why is the Unicode standard 1472 printed pages? It’s hard to say anything pithy about […]

# Rapidly convergent series for ellipse perimeter

The previous post looked at two simple approximations for the perimeter of an ellipse. Approximations are necessary since the perimeter of an ellipse cannot be expressed as an elementary function of the axes. Kepler noted in 1609 that you could approximate the perimeter of an ellipse as the perimeter of a circle whose radius is […]

# Can you look at experimental results along the way or not?

Suppose you’re running an A/B test to determine whether a web page produces more sales with one graphic versus another. You plan to randomly assign image A or B to 1,000 visitors to the page, but after only randomizing 500 visitors you want to look at the data. Is this OK or not? Of course […]

# A “well-known” series

I was reading an article [1] that refers to “a well-known trigonometric series” that I’d never seen before. This paper cites [2] which gives the series as Note that the right hand side is not a series in φ but rather in sin φ. Motivation Why might you know sin φ and want to calculate […]

# Up and down the abstraction ladder

It’s easier to go up a ladder than to come down, literally and metaphorically. Gian-Carlo Rota made a profound observation on the application of theory. One frequently notices, however, a wide gap between the bare statement of a principle and the skill required in recognizing that it applies to a particular problem. This isn’t quite […]

# Hallucinations of AI Science Models

AlphaFold 2, FourCastNet and CorrDiff are exciting. AI-driven autonomous labs are going to be a big deal [1]. Science codes now use AI and machine learning to make scientific discoveries on the world’s most powerful computers [2]. It’s common practice for scientists to ask questions about the validity, reliability and accuracy of the mathematical and […]

# Regex to match SWIFT-BIC codes

A SWIFT-BIC number identifies a bank, not a particular bank account. The BIC part stands for Bank Identifier Code. I had to look up the structure of SWIFT-BIC codes recently, and here it is: Four letters to identify the bank Two letters to identify the country Two letters or digits to identify the location Optionally, […]