Numbers and Acrostics: Two Notes on Jason’s Prayer at Pagasae in Apollonius’ Argonautica

Spellbinding Performance: Poet as Witch in Theocritus' Second Idyll and Apollonius' Argonautica

Some notes on locomotion at low and intermediate Reynolds numbers

Assumption: The body shape relative to the body frame is a given function of time B0(t). We call this the standard shape. The current body shape B(t) is obtained under a translation and rotation of the body frame. The latter is defined by a positional matrix. To say that locomotion has occurred at time t means we have realized at time t a nonzero translation. Example: steady locomotion in two d...

Notes on Algebraic Numbers

This is a summary of my 1994–1995 course on Algebraic Numbers. (Revised and improved on 1993– 1994!) The background assumed is standard elementary number theory—as found in my Level III course—and a little (Abelian) group theory. Corrections and suggestions for improvement are welcome, and will be credited in future editions! I first learned algebraic number theory from Stewart & Tall’s book ([...

Notes on Generalized Fermat Numbers

There are two different definitions of generalized Fermat numbers (GFN), one of which is more general than the other. In [5], Ribenboim defines a generalized Fermat number as a number of the form Fa,n = a n + 1 with a > 2, while Riesel ([6]) further generalizes, defining it to be a number of the form a n + b n . Both definitions generalize the usual Fermat numbers Fn = 2 n + 1. The only known F...

Notes on p-adic numbers

as one can check using induction on l. The usual absolute value function |x| satisfies these conditions with the ordinary triangle inequality (4). If N(x) = 0 when x = 0 and N(x) = 1 when x 6= 0, then N(x) satisfies these conditions with the ultrametric version of the triangle inequality. For each prime number p, the p-adic absolute value of a rational number x is denoted |x|p and defined by |x...