Questions tagged [archimedes]

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer.

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Did Newton discuss and/or use the principle of moments?

This question comes from a point of view of a student in current times. The general curriculum for a physics student presents that a static analysis of a simple system requires that the forces in each ...
86 views

Archimedes - method of mechanical theorems - centroid of hemisphere

Hoping a philomath can help - I'm searching how Archimedes calculates the centroid of a hemisphere without calculus as behind the below sentence in the wikipedia entry on "the Method of ...
384 views

Did Archimedes view fractions as "numbers"?

For quite some time I had the wrong impression that classical Greek mathematicians didn't use fractions. (I don't remember where I had this from.) But I recently looked into Heath's book about ...
121 views

I want to know the source of why Archimedes' broken chord theorem is Archimedes good

I found "The Arabian scholar Abu'l Raihan al'biruni" has attributed to Archimedes the theorem of the broken chord in web. But I couldn't find a book or papers that this Arabian scholar wrote.
2k views

How was the sum of squares formula discovered by Archimedes?

AFAIK, Archimedes is credited with discovering the following formula for computing the sum of squares: $$1^2 + 2^2 + 3^2 + \cdots + n^2 = \frac{n(n+1)(2n+1)}{6}$$ This seems to have come up in his ...
286 views

How did Archimedes arrive at his principle in his time?

Archimedes principle: Any object, wholly or partially immersed in a stationary fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. I get that this can be ...
195 views

Looking for an online version of Archimedes' "The Method" (in Greek)

To me, one of the most exciting mathematical achievements of antiquity is Archimedes' The Method. It is crazy to think that, had it not been for its miraculous recovery in the early 20th century, it ...
235 views

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

My question is only about a certain hystorical gem. The purpose of this question is to explore how vast were Archimedes's contributions to geometry that are not connected to calculus (i.e calculation ...
1k views

How did Archimedes's water clock work?

I read that several principles of Al-Jazari's monumental water clocks were based upon earlier designs of water clocks by Archimedes, for example the use of valves, feedback system and flow control ...
119 views

What were Archimedes's improvements to the screw pump?

In order to understand my motivation to answer this question, I'll remark that Vitruvius said that the screw was inclined by the small angle of a 3:4:5 triangle. So it means that perhaps there was ...
1k views

What are Archimedes's contributions to the principle of the screw pump?

I read that the famous screw pumps were used before Archimedes (in the hanging gardens of Babylon for example), and that the Archimedean screw is named after him because he "developed a rigorous ...
336 views

Various sources, such as Cicero's Republic state that Archimedes had made a machine consisting of glass spheres that represented the Eudoxian system of the world. Considering that Callipus died over ...
371 views

How did Archimedes complete this impossible task? [closed]

I am reading this book on Archimedes, famous mathematician of his days and now, and it was found that he caculated the amount of sand in the known Universe at his days, which is from Mercury to ...
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What is so mysterious about Archimedes' approximation of $\sqrt 3$?

In his famous estimation of $\pi$ by inscribed and circumscribed polygons, Archimedes uses several rational approximations of irrational values; a typical example is that he states, without ...