Wikimedia Commons

File:Graphe des nombres polydivisibles.svg

Original file ‎(SVG file, nominally 720 × 540 pixels, file size: 40 KB)

Captions

Captions

Add a one-line explanation of what this file represents

Summary edit

Description
Français : En mathématiques, un nombre polydivisible est un entier naturel s'écrivant avec les chiffres a b c d e ..., qui possède les propriétés suivantes :
  1. Son premier chiffre a n'est pas 0.
  2. Le nombre formé par ses deux premiers chiffres a b est un multiple de 2.
  3. Le nombre formé par ses trois premiers chiffres a b c est un multiple de 3.
  4. Le nombre formé par ses quatre premiers chiffres a b c d est un multiple de 4.
Date
Source Own work
Author Guillaume Jacquenot
SVG development
InfoField
 
The source code of this SVG is invalid due to an error.
 
This W3C-invalid plot was created with Matplotlib.
Source code
InfoField

Python code

# -*- coding: utf-8 -*-
# 
# Script to generate in English and French, graphs for the
# birthday problem.
#
# **************************************************************
# http://en.wikipedia.org/wiki/Polydivisible_number
# From Wikipedia, the free encyclopedia:
# In mathematics a polydivisible number is a number with digits
# abcde... that has the following properties :
# 
# Its first digit a is not 0.
# The number formed by its first two digits ab is a multiple of 2.
# The number formed by its first three digits abc is a multiple of 3.
# The number formed by its first four digits abcd is a multiple of 4.
# etc.
#
# Text under the
# Creative Commons Attribution-ShareAlike License
# **************************************************************
#
# Guillaume Jacquenot
# 2013/05/01

from pylab import *
import numpy as np

def getData():
    r=np.array(
        [[ 1,     9,    9],
         [ 2,    45,   45],
         [ 3,   150,  150],
         [ 4,   375,  375],
         [ 5,   750,  750],
         [ 6,  1200, 1250],
         [ 7,  1713, 1786],
         [ 8,  2227, 2232],
         [ 9,  2492, 2480],
         [10,  2492, 2480],
         [11,  2225, 2255],
         [12,  2041, 1879],
         [13,  1575, 1445],
         [14,  1132, 1032],
         [15,   770,  688],
         [16,   571,  430],
         [17,   335,  253],
         [18,   180,  141],
         [19,    90,   74],
         [20,    44,   37],
         [21,    18,   17],
         [22,    12,    8],
         [23,     6,    3],
         [24,     3,    1],
         [25,     1,    1]])
    return r

def makePlot(\
        generateEnglishPlot = True,\
        outputFilename = 'Graph_of_polydivisible_number.svg'):
    if generateEnglishPlot:
        xlabel_ = 'n Number of digits'
        ylabel_ = 'Number of polydivisible numbers'
        leg1 = 'F(n)'
        leg2 = 'Estimate of F(n)'
    else:
        xlabel_ = 'n Nombre de digits'
        ylabel_ = 'Nombre de nombres polydivisibles'
        leg1 = 'F(n)'
        leg2 = 'Estimée de F(n)'
    r=getData()
    plot(r[:,0], r[:,1], marker = 'o', label = unicode(leg1, 'utf8'))
    plot(r[:,0], r[:,2], marker = '^', label = unicode(leg2, 'utf8'))
    grid(True, ls='-', c='#a0a0a0')
    legend(loc='right')
    xlabel(xlabel_)
    ylabel(ylabel_)
    savefig(outputFilename)
    show()

makePlot(generateEnglishPlot = True, outputFilename = 'Graph_of_polydivisible_number.svg')
makePlot(generateEnglishPlot = False, outputFilename = 'Graphe_des_nombres_polydivisibles.svg')

Licensing edit

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current19:36, 1 May 2013Thumbnail for version as of 19:36, 1 May 2013720 × 540 (40 KB)Gjacquenot (talk | contribs)User created page with UploadWizard

You cannot overwrite this file.

There are no pages that use this file.

File usage on other wikis

The following other wikis use this file:

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Graphe_des_nombres_polydivisibles.svg&oldid=864076530"