29 MAY 2014 by ideonexus

 The Kiss Precise

Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is half the square of their sum.
Folksonomies: mathematics poetry
Folksonomies: mathematics poetry
  1  notes

If four circles A, B, C, and D, of radii r1, r2, r3, and r4, are drawn so that they do not overlap but each touches the other three, and if we let b1 = 1/r1, etc., then

(b1 b2 b3 b4)^2 = 2(b1^2 b2^2 b3^2 b4^2).

21 JUN 2012 by ideonexus

 There is No End to Mechanical Progress

[To] mechanical progress there is apparently no end: for as in the past so in the future, each step in any direction will remove limits and bring in past barriers which have till then blocked the way in other directions; and so what for the time may appear to be a visible or practical limit will turn out to be but a bend in the road.
  1  notes

Because each development removes barriers to previous explorations.