Questions tagged [archimedes]

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

Filter by
Sorted by
Tagged with
4
votes
0answers
103 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.
8
votes
2answers
1k 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 ...
3
votes
2answers
205 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 ...
1
vote
1answer
162 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 ...
5
votes
1answer
213 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 ...
7
votes
1answer
857 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 ...
2
votes
0answers
106 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 ...
5
votes
1answer
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 ...
7
votes
2answers
304 views

Did Archimedes know about Callipus?

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 ...
2
votes
1answer
353 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 ...
33
votes
5answers
2k views

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 ...
4
votes
1answer
118 views

About Archimedes methods in the discovered palimpsest

I think Archimedes had some great non-infinitesimal methods for discovering the area and volume of shapes. Some very visual methods involving his method of exhaustion for the volume of a sphere for ...
17
votes
1answer
427 views

Did Archimedes use epicycles in his planetarium?

Archimedes constructed a planetarium where as described by Cicero "he had thought out a way to represent accurately by a single device for turning the globe those various and divergent movements with ...