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Difference between revisions of "Logarithmic paper"

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''double logarithmic paper''
 
''double logarithmic paper''
  
A special form of ruled paper; it is usually made typographically (Fig. a) as follows: On each of the axes of a rectangular <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606201.png" />-coordinate system one marks the decimal logarithms of numbers <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606202.png" /> (on the horizontal axis) and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606203.png" /> (on the vertical axis) (cf. also [[Logarithm of a number|Logarithm of a number]]); then lines are drawn through the resulting points <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606204.png" /> parallel to the axes.
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A special form of ruled paper; it is usually made typographically (Fig. a) as follows: On each of the axes of a rectangular $(u,v)$-coordinate system one marks the decimal logarithms of numbers $u$ (on the horizontal axis) and $v$ (on the vertical axis) (cf. also [[Logarithm of a number|Logarithm of a number]]); then lines are drawn through the resulting points $(u,v)$ parallel to the axes.
  
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/l060620a.gif" />
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/l060620a.gif" />
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Figure: l060620a
 
Figure: l060620a
  
There is also semi-logarithmic paper (single logarithmic paper) (Fig. b): On one of the axes of a rectangular <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606205.png" />-coordinate system the values of numbers <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606206.png" /> are marked, and on the other the decimal logarithms of numbers <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606207.png" />.
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There is also semi-logarithmic paper (single logarithmic paper) (Fig. b): On one of the axes of a rectangular $(u,v)$-coordinate system the values of numbers $u$ are marked, and on the other the decimal logarithms of numbers $v$.
  
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/l060620b.gif" />
 
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/l060620b.gif" />
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Figure: l060620b
 
Figure: l060620b
  
Logarithmic paper and semi-logarithmic paper are used for drawing the graphs of functions which (in those coordinates) may take a simpler and more obvious form, and in many cases are straight lines. On logarithmic paper straight lines represent functions given by equations of the form <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606208.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l0606209.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l06062010.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l06062011.png" /> are constant coefficients; on semi-logarithmic paper straight lines represent functions given by equations of the form <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060620/l06062012.png" />.
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Logarithmic paper and semi-logarithmic paper are used for drawing the graphs of functions which (in those coordinates) may take a simpler and more obvious form, and in many cases are straight lines. On logarithmic paper straight lines represent functions given by equations of the form $v=au^b$, $u>0$, where $a>0$ and $b$ are constant coefficients; on semi-logarithmic paper straight lines represent functions given by equations of the form $v=ab^u$.

Latest revision as of 20:38, 3 May 2014

double logarithmic paper

A special form of ruled paper; it is usually made typographically (Fig. a) as follows: On each of the axes of a rectangular $(u,v)$-coordinate system one marks the decimal logarithms of numbers $u$ (on the horizontal axis) and $v$ (on the vertical axis) (cf. also Logarithm of a number); then lines are drawn through the resulting points $(u,v)$ parallel to the axes.

Figure: l060620a

There is also semi-logarithmic paper (single logarithmic paper) (Fig. b): On one of the axes of a rectangular $(u,v)$-coordinate system the values of numbers $u$ are marked, and on the other the decimal logarithms of numbers $v$.

Figure: l060620b

Logarithmic paper and semi-logarithmic paper are used for drawing the graphs of functions which (in those coordinates) may take a simpler and more obvious form, and in many cases are straight lines. On logarithmic paper straight lines represent functions given by equations of the form $v=au^b$, $u>0$, where $a>0$ and $b$ are constant coefficients; on semi-logarithmic paper straight lines represent functions given by equations of the form $v=ab^u$.

How to Cite This Entry:
Logarithmic paper. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Logarithmic_paper&oldid=32138
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article