A Hasse diagram of divisibility relationships among regular numbers up to 400. As shown by the horizontal light red lines, the vertical position of each number is proportional to its logarithm. Inspired by similar diagrams in a paper by Kurenniemi [1].
David Eppstein a(z) angol Wikipédia projektből, a mű szerzője művét közkinccsé nyilvánította. Ez a világ minden részén érvényes. Egyes országokban ez jogilag nem lehetséges. Ha így van, akkor: David Eppstein jogot ad bárkinek, hogy bármilyen célból, feltétel nélkül használhassa ezt a fájlt, kivéve a törvény által kötelezően előírt feltételeket.Public domainPublic domainfalsefalse
Source code
The Python source code for generating this image:
from math import log
limit = 400
radius = 17
margin = 4
xscale = yscale = 128
skew = 0.285
def A051037():
yield 1
seq = [1]
spiders = [(2,2,0,0),(3,3,0,1),(5,5,0,2)]
while True:
x,p,i,j = min(spiders)
if x != seq[-1]:
yield x
seq.append(x)
spiders[j] = (p*seq[i+1],p,i+1,j)
def nfactors(h,p):
nf = 0
while h % p == 0:
nf += 1
h //= p
return nf
seq = []
for h in A051037():
if h > limit:
break
seq.append((h,nfactors(h,2),nfactors(h,3),nfactors(h,5)))
leftmost = max([k for h,i,j,k in seq])
rightmost = max([j for h,i,j,k in seq])
leftwidth = int(0.5 + log(5) * leftmost * xscale + radius + margin)
rightwidth = int(0.5 + log(3) * rightmost * xscale + radius + margin)
width = leftwidth + rightwidth
height = int(0.5 + log(limit) * yscale + 2*(radius + margin))
def place(h,i,j,k):
# logical coordinates
x = j * log(3) - k * log(5) + i * skew
y = log(h)
# physical coordinates
x = (x*xscale) + leftwidth
y = (-y*yscale) + height - radius - margin
return (x,y)
print '''<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="%d" height="%d">''' % (width,height)
print ' <g style="fill:none;stroke:#ffaaaa;">'
l = 1
base = 1
while l <= limit:
y = -yscale*log(l) + height - radius - margin
print ' <path d="M0,%0.2fL%d,%0.2f"/>' % (y,width,y)
l += base
if l == 10*base:
base = l
print " </g>"
print ' <g style="fill:none;stroke-width:1.5;stroke:#0000cc;">'
def drawSegment(p,q):
x1,y1=p
x2,y2=q
print ' <path d="M%0.2f,%0.2fL%0.2f,%0.2f"/>' % (x1,y1,x2,y2)
for h,i,j,k in seq:
x,y = place(h,i,j,k)
if i > 0:
drawSegment(place(h//2,i-1,j,k),(x,y))
if j > 0:
drawSegment(place(h//3,i,j-1,k),(x,y))
if k > 0:
drawSegment(place(h//5,i,j,k-1),(x,y))
print " </g>"
print ' <g style="fill:#ffffff;stroke:#000000;">'
for h,i,j,k in seq:
x,y = place(h,i,j,k)
print ' <circle cx="%0.2f" cy="%0.2f" r="%d"/>' % (x,y,radius)
# pairs of first value with size: size of that value
fontsizes = {1:33, 5:30, 10:27, 20:24, 100:20, 200:18}
for h,i,j,k in seq:
x,y = place(h,i,j,k)
if h in fontsizes:
print " </g>"
print ' <g style="font-family:Times;font-size:%d;text-anchor:middle;">' % fontsizes[h]
lower = fontsizes[h] / 3.
print ' <text x="%0.2f" y="%0.2f">%d</text>' %(x,y+lower,h)
print " </g>"
print "</svg>"
Eredeti feltöltési napló
Az eredeti leírólap itt volt. Az itt következő felhasználónevek az en.wikipedia projektre hivatkoznak.
2007-03-14 05:08 David Eppstein 1363×809×0 (13167 bytes) A [[Hasse diagram]] of [[divisibility]] relationships among [[regular number]]s up to 400. Inspired by similar diagrams in a paper by Kurenniemi [http://www.beige.org/projects/dimi/CSDL2.pdf].
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