Secrets of Archimedes (a great mathematician and founder of Pi)

Archimedes (287 BC - 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series and gave a remarkably accurate approximation of pi. He also defined the spiral bearing his name, formulae for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.

Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder. Archimedes had proven that the sphere has two-thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.

Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.

Tips to get more out of Google

Google's home page may look simple, but don't be fooled. Behind that solitary search box lies the power that most of us never tap - not because we don't want to, but because we don't know about it.

But with the right commands and shortcuts, you can start using Google in ways you never imagined: as a calculator, a weather forecaster, a travel agent, a movie locator, search places, and much more.

Search prefixes
One powerful way to refine your searches is by using search prefixes: words that you follow with a colon and then the search term itself.

For instance, use the prefix 'site' to specify that you'd like to restrict your search to a particular site. The search phrase 'site:microsoft.com windows XP downloads,' for example, tells Google that you'd like it to retrieve links to downloads applicable to Windows XP from Microsoft's web pages.
 
File prefixes
You can use the 'filetype' prefix to search for specific types of documents or files. This is very useful if you're searching for, say, Excel files - or for PDFs that you can download and print out in an attractive format. Let's say, for example, that you'd like to search for a PDF of Ernest Hemingway's novel The Sun Also Rises. The proper search phrase would be 'sun also rises filetype:pdf.'

Other handy prefixes include 'define,' for searching for definitions, and 'related,' to search for sites that are similar to ones you like. The 'define' prefix is especially nice for students, young and old, who can instantly retrieve definitions of a word from a wide variety of sources.
 
Trigger words
You can also perform targeted searches by using what Google calls 'trigger words' - or words that tell the search engine to return specific types of information, such as the local weather or local showtimes for currently running movies. Like search prefixes, some of these trigger words work best when they are followed by a colon and then by the relevant search phrase.

There are a couple dozen trigger words. Some of the more useful include 'weather,' 'movies,' and 'tracking.' For instance, a search for 'weather:Berlin' will quickly return the five-day weather forecast for Berlin, Germany, as well as dozens of related links to weather in that city.

Use the trigger word 'movie:*** it will ask you for your location if you haven't registered it already with the search engine. Once you provide that information, Google will instantly return a listing of movie theatres where the film is playing, along with showtimes. The triggers 'film' and 'showtimes' work identically, by the way.
 
Math genius
The Google search field is a veritable math genius as well. In fact, if you simply type a math equation in the search box, you'll get nothing but the (correct) answer in return. Try it with a simple math problem first. Type 5 * 7, click Search, and Google shows you the result: 5 * 7 = 35.

Math lovers can take the Google search field to the next level, too, with complex problems such as 5*9+(sqrt 10)^3. The answer, 76.6227766, is returned in the blink of an eye.
 
Conversions
Simpler conversions -- such as for currency and temperature -- are a cinch for Google, too. Need to find out how many pounds you can get for a certain number of dollars? Easy. Just type, for instance, '1 GBP to USD' .

Similarly, if you want to get a quick conversion from Fahrenheit to Centigrade, just type, for instance, '98 f to c.' Again, you'll get the answer before you can finish typing.
 
Add words at the end of the search phrase
You can add certain words to the end of search phrases in Google to unleash additional features. If you need a quick map, for instance, just type the word 'map' after the name of any country, city, or town. Google will display a thumbnail map, which you can click to explore in a larger, scrollable format using Google Maps.

Similarly, to find an image of a search phrase, just add the word 'image' at the end of the phrase. For example, typing 'Jefferson image' brings up images of Thomas Jefferson. And adding 'time' to the end of the name of a city or country will result in Google's telling you what time it is in that place.

Click here to explore more options to refine your search.