# Semi Log Graph Paper

Volume of Solid of Revolution.

## Log-log Graphs

Log-log paper with logarithmic horizontal axis one decade and logarithmic vertical axis four decades with equal scales on letter-sized paper. Log-log paper with logarithmic horizontal axis one decade and logarithmic vertical axis four decades on letter-sized paper. Log-log paper with logarithmic horizontal axis one decade and logarithmic vertical axis five decades with equal scales on letter-sized paper.

Log-log paper with logarithmic horizontal axis one decade and logarithmic vertical axis five decades on letter-sized paper. Log-log paper with logarithmic horizontal axis two decades and logarithmic vertical axis two decades with equal scales on letter-sized paper. Log-log paper with logarithmic horizontal axis two decades and logarithmic vertical axis two decades on letter-sized paper. Log-log paper with logarithmic horizontal axis three decades and logarithmic vertical axis three decades with equal scales on letter-sized paper.

Log-log paper with logarithmic horizontal axis three decades and logarithmic vertical axis three decades on letter-sized paper. Log-log paper with logarithmic horizontal axis four decades and logarithmic vertical axis four decades with equal scales on letter-sized paper. Log-log paper with logarithmic horizontal axis four decades and logarithmic vertical axis four decades on letter-sized paper.

Log-log paper with logarithmic horizontal axis five decades and logarithmic vertical axis five decades with equal scales on letter-sized paper. Log-log paper with logarithmic horizontal axis five decades and logarithmic vertical axis five decades on letter-sized paper.

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Logarithmic Graph Paper Click any paper to see a larger version and download it. Probability Long Axis by 1-Cycle Log. Probability Long Axis by 2-Cycle Log. Semilog Paper-1 Decade by 10 Divisions. Semilog Paper-1 Decade by 12 Divisions. Semilog Paper-1 Decade by 20 Divisions. Semilog Paper-1 Decade by 24 Divisions. Semilog Paper-1 Decade by 30 Divisions.

It turns out that there is a relationship between the rank of a word's occurrence and the frequency of its use. That relationship was observed by George Kingsley Zipf in the first half of the 20th century. The Zipf Distribution is an observation comparing rank and frequency of word occurrences. Zipf originally developed his law in response to the observation that the frequency of words was inversely proportional to the rank of each word. For example, the most common 20 words in English are listed in the following table.

The table is based on the Brown Corpus , a careful study of a million words from a wide variety of sources including newspapers, books, magazines, fiction, government documents, comedy and academic publications. The first 20 words in the Brown Corpus, published in This Corpus is the count of how often one million words were used in a variety of books, newspapers and other publications. This gives us a hyperbola , that we met before.

The dark blue data points represent the top 20 occurring English words with the first few labeled. I just did trial and error in Excel until I found the closes fit. There is a fairly large gap in the pattern for the words "to", "a" and "in", but it settles down and is quite consistent after that. We now plot the top English words and use a log-log scale log of the rank for the horizontal axis and log of the frequency for the vertical axis.

If a distribution gives us a straight line on a log-log scale, then we can say that it is a Zipf Distribution. We see that there is a remarkably consistent result for the top most-used English words. For your information, the last few in the list of words are:. For example, out of the most recent , page views in Interactive Mathematics , the most commonly visited page is the homepage, with 27, views. The theoretical Zipf Distribution the pink line is obtained as follows.

The power used, 0. After the page ranked th, the pattern breaks down, but interestingly, from the th to the th page, there is still a consistent relationship between rank and frequency. Hans Rosling's Countries, Years, 4 Minutes. Interesting semi-logarithmic graph - YouTube Traffic Rank. Zipf Distributions, log-log graphs and Site Statistics. Log Laws by MichaelA [Solved! Semi-log graph by Alan [Solved! Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight.

Join thousands of satisfied students, teachers and parents! Exponential and Logarithmic Functions 2. Graphs of Exponential and Logarithmic Equations 3. Logarithms to Base 10 5.

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