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 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 […]

Partial functions and total functions

I was thinking about writing a post about entire functions and it occurred to me that I should say something about how entire functions are unrelated to total functions. But then I realized they’re not unrelated. I intend to say something about entire functions in a future post. Update: See The ring of entire functions. […]

Hypergeometric equation

I’ve asserted numerous times here that hypergeometric functions come up very often in applied math, but I haven’t said why. This post will give one reason why. One way to classify functions is in terms of the differential equations they satisfy. Elementary functions satisfy simple differential equations. For example, the exponential function satisfies y′ = […]

Hidden double factorial example

A while back I wrote several about multi-factorials and gave examples of triple factorials and quadruple factorials in action. I didn’t do a post on double factorials because they are more common. But an example I ran into recently changed my mind. If you skim a table of power series you will run into a […]