Ken's blog

time elapsed between: 4th day of the month 11:59:59 PM 6th day of the month 6:06:06 AM $ units You have: (6 day + 6 hr + 6 min + 6 s)...

everyone wants to know the opposite direction, how to exit line-editing "ex mode" and return to visual mode in vi, so it is tough ...

consider the following GNU Makefile and invocations in the bash shell: C = c Q ?= q .PHONY:default default: @echo C=$(C) @...

at the time of writing, the largest known prime number is the Mersenne prime 2^136279841 - 1, a 41-million-digit number. the sum of the re...

consider adding one infinite element to the integers or reals under addition and seeing if it remains a group. first, consider defining 1 ...

pick one of the many methods for placing N "equally spaced" points on a sphere (e.g., Thomson problem, Tammes problem), compute th...

odd numbers have multiplicative inverses modulo 2^n (even numbers do not). ? for(n=1, 8, print1(2^n,":"); for(j=1, 2^(n-1), i=2*j...

is the 21 cm (1420 MHz) hydrogen line the easiest radio astronomy "target"?  not really a target if observing the hydrogen radiati...

at first glance, a giant gun seems not a very practical method for space launch, because very few payloads, certainly not humans, can surviv...

{0, 1, 2} are special.  find or create (interesting) theorems that are true precisely for each of the 8 possible subsets of those numbers un...

first, here are integers from -20 to 100.  to negate a balanced ternary number, swap + and -, leave 0 unchanged. -+-+ -20 -+0- -19 -+00...

the point at coordinates (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24) in 24-dimensional space is ...

is not the most right way to pronounce world chess champion "Max Euwe", but neither is it the most wrong: "Max You". ...

a square (or rectangle) fundamental polygon is good for 2D games. previously on the various spaces (manifolds) that a fundamental polygon c...

on a modern computer, Pari/GP can usually factor RSA-style numbers (the worst case for factoring) of 60 digits (199 bits) in 30 seconds or l...

previously, a commutative ring with reduction polynomial i^3+1 .  this time, the polynomial (i^4-1)/(i-1) = i^3 + i^2 + i + 1 because of its...

Bernoulli numbers are mysterious, showing up in lots of places, e.g., the zeta function , the gamma function , sums of powers (Faulhaber...

degrees missing from being flat at vertex: tetrahedron 180 octahedron 120 cube 90 icosahedron 60 dodecahedron 36 (angle defect)*(n...

golden ratio: phi = (1 + sqrt(5)) / 2 the version of Binet's formula for the nth Fibonacci number which uses the round-to-the-neares...

let (relativistic kinetic energy) = (relativistic mass-energy) - (rest mass-energy) (rest mass-energy) = m * c^2 let resq = "remain...