I have always imagined that paradise will be a kind of library.
 Jorge Luis Borges
Sighted on AbeBooksa favorite site. info on source
I have always imagined that paradise will be a kind of library.
1 + 2 + .. n = n(n+1)/2 
x^{2} = r^{2}  (ry)^{2}. 
width times area 
2 (1/n)^{2} (Σk) 
(1/n)^{2} (n1) n 
(1) (11/n) = 1 
(1/n)^{3} (Σk^{2}) 
(1/n)^{3} (n1)(n)(2n1)/6 
(1/n)^{3} (n1)(n)(2n1)/6 = 
πr^{3} (1  1/3) = 
V = 4/3 πr^{3} 
(uv)' = u v' + v u' 
∫u v' = u v  ∫v u' 

from math import sqrt 
Many years later Newton told at least four people that he had been inspired by an apple in his Woolsthorpe gardenperhaps an apple actually falling from a tree, perhaps not. He never wrote of an apple. He recalled only:I began to think of gravity extending to the orb of the Moon . . .
gravity as a force, then, with an extended field of influence; no cutoff or boundary& computed the force requisite to kep the Moon in her Orb with the force of gravity at the surface of the earth . . . & found them answer pretty nearly. All this was in the two plague years of 16651666. For in those days I was in the prime of my age for invention & minded mathematicks and Philosophy more than at any time since.
The apple was nothing in itself. It was half of a couplethe moon's impish twin. As an apple falls toward the earth, so does the moon; falling away from a straight line, falling around the earth.
a = GM/r^{2} 
R = EM distance 
mean distance from E to M (km) 
BX/CX = x
. Using the standard formula for area of a triangle, and recognizing that the heights are equal in each case, we can show that the areas (designated as ABC
) of the triangles below are in the same ratio:ABX / ACX = x 
ABP / ACP = x 
y = CY / AY
and z = AZ / BZ
, then:BCP / ABP = y 
ABP BCP ACP 
BX CY AZ 
AZ = AC cos α 
AC cos α AB cos β BC cos γ 
Counter
class from here.import random, math 
(uv)' = u v' + v u' 
(u/v)' = (v u'  u v')/v^{2} 
v (1/v) = 1 
d/dx [ v (1/v) ] = 0 
d/dx(u/v) = (1/v) du/dx + u d/dx(1/v) 
(1/v)' = (v^{1})' = v^{2} v' 
sin(s+t) = sin s cos t + cos s sin t 
x1 = cos s 
d^{2} = (cos s  cos t)^{2} + (sin s  sin t)^{2} 
= 2  2 cos s cos t  2 sin s sin t 
x1 = cos (st) 
d^{2} = (cos (st)  1)^{2} + (sin (st))^{2} 
cos(st) = cos s cos t + sin s sin t 
cos(s+t) = cos(s  t) 
sin(s+t) = cos(90s  t) 
sin t / x = tan s 
x = sin t cos s / sin s 
sin s = sin(s+t) 
cos x + i sin x = e^{ix} 
cos(s+t) = cos s cos t  sin s sin t 
cluster
function finds the two points that are the closest together, and averages them together, using the weights.import string 
"In one of the first studies of the Poisson distribution, von Bortkiewicz considered the frequency of deaths from kicks in the Prussian army corps. From the study of 14 corps over a 20year period, he obtained the data shown in [the] Table. Fit a Poisson distribution to this data and see if you think that the Poisson distribution is appropriate."
deaths number of corps with x deaths 
$ python kicks.py 
import math 