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Steve's Mathsoul Poster

Steve has a business called More Traffic, advising how to optimise search engine traffic to websites.
Many factors are involved, and Steve is advising a client tomorrow on just one of these factors, called PageRank.  Its calculation method is not disclosed by Google, but is widely thought to be democratic, recursive, and to use logs or a logarithmic scale.

PageRank seems to be calculated by taking the logarithm of the total 'link vote value' which a page has been awarded from other pages linking to it. The 'link vote value' received from an inbound link seems to be equal to the PageRank of the page the link comes from, divided by the number of outbound links from that page.

 So a page with PageRank of 8, and 4 outbound links, contributes a 'link vote value' of 2 to each of its 4 links. (Other calculations apply to special pages such as directories with many usefull links.)

Steve's Poster Questions
Using this 'unequal' democratic link value method, which inbound link case would contribute most 'link vote value' to a web page: (a) a link from a PageRank 10 page with 15 outbound links, or (b) links from four different pages with PageRank 2, and only three outbound links each?
Q2. Construct a scenario with three partially interlinked websites, and calculate each of their 'link vote values' assuming that each has a 'starting' PageRank of 5. Using excel or paper repeat the PageRank calculation this time using the 'link vote values' just determined for each page.  How many times do you need to carry out this recursive process before the 'link vote values' no longer change?
Q3. Google PageRanks are never higher than 10.  Explain, with an example, how logs can be used to spread ranks from 0 to 10, from data involving even very large numbers.

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Mathsoul supplies posters with interactive student services, to schools and colleges. Mathsoul posters help teachers to engage and energize mathematics students.

Student Motivation. The Mathsoul My-Story series of posters show people, with personal stories of classroom mathematics helping in life beyond the classroom.

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