MHB What are the uses of the top and bottom beads on a Chinese abacus?

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The discussion centers on the functions of the top and bottom beads on a Chinese abacus. Users express confusion about the purpose of having five beads on the "earth" strings when the number five is represented by moving one bead down on the "heaven" string. There is also a request for resources to learn about the abacus, including its history and types. Some participants suggest using Wikipedia for information, although concerns about its reliability are mentioned. The conversation highlights a need for clearer explanations regarding the specific uses of the beads on the Chinese abacus.
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Does anybody here know where is the site to learn all about abacus, from its definition, history, types, and levels? I've been searching on Google but only found abacus learning courses which don't even talk about those. Thanks in advance for your help.
 
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I don't trust a site which can be edited by anyone.
 
I have found some sites. However, I am still confused about why does Chinese abacus have 5 beads on each "earth" strings if they make the number 5 by moving down 1 bead on the "heaven" string. What are the use of both the top most and the bottom most beads? Those two seem irrelevant.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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