# Tag Info

### What is so mysterious about Archimedes' approximation of $\sqrt 3$?

There's a very simple geometrical response that provides a rounded solution which might reflect on this problem at http://www.gjbath.com/SQR3.htm. It's so much easier seeing it! This involves ...
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### What is so mysterious about Archimedes' approximation of $\sqrt 3$?

Archimedes might, of course, have used a better method. (He also produces the approximation $\frac{1351}{780}$, for which the foregoing is not obviously practical...) I disagree on the foregoing not ...
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Accepted

### How was the sum of squares formula discovered by Archimedes?

Although it is commonly said that Archimedes summed the geometric series in Quadrature of the Parabola, and summed squares of integers in On Conoids and Spheroids and On Spirals, that is not what he ...
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Accepted

### Did Archimedes view fractions as "numbers"?

No, Archimedes, and ancient Greeks generally, did not see fractions as numbers, and they did not use fractions as we use them today, they did not use them at all. What they used was ratios of ...
• 77.7k
Accepted

### What does this quote by Paul Halmos mean?

The meaning of the quote is more likely to be, that Archimedes' reasoning was on such a high level, that no one (example: the clever graduate student) could teach him to reason better because ...
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Accepted

### Did Archimedes make use of a Pappus chain according to the Book of Lemmas?

No, he did not. Wikipedia's editor was most likely misled by somewhat clumsy arrangement of the text in the Heath's 1897 translation of the Book of Lemmas. Right under the statement of Proposition 8 ...
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### How did Archimedes's water clock work?

al-Jazari (and Ridwan too) explicitly says that Archimedes is the source for several of the components of his clock(s); he also says that one component of Archimedes' clock (the flow regulator) does ...

### How did Archimedes arrive at his principle in his time?

Fortunately there is some documentary evidence about Archimedes' discovery, in his work "On Floating Bodies", which survives in manuscript forms (https://en.wikipedia.org/wiki/On_Floating_Bodies). ...
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1 vote
Accepted