ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel


Updated on June 20, 2010

This article might be more accurately titled ‘Pythagoras and The Pythagoreans’ since some of the mathematical discoveries accredited to Pythagoras may well have been made by one of the other members of the brotherhood he founded.

Pythagoras was born in about 572 BC on the Greek island of Samos in the North Aegean Sea, just off the coast of Asia Minor. Being not far from Thales’ home town of Miletus, it’s possible that Pythagoras studied under the older man. Like Thales, Pythagoras travelled and is known to have stayed for a time in Egypt. When he returned to Samos, he found the island occupied by the tyrant Polycrates who had allied himself with the Persian King. Pythagoras fled Samos and moved to the Greek settlement of Crotona in southern Italy.

At Crotona, he founded the famous Pythagorean School. His school was an academy for the study of mathematics, natural science and philosophy, but it was also a secret brotherhood with its own rites and observances. The members of the school believed in the pursuit of philosophical and mathematical studies as the basis for a good moral life. Their philosophy was summed up in their motto ‘All is number’, and is based on the assumption that all mathematics is constructed around the whole numbers.

The symbol of the Pythagoreans was the star pentagon or pentagram, a five-pointed star formed by drawing the diagonals of a regular pentagon.




Pythagoras is incorrectly accredited with the famous ‘Theorem of Pythagoras’ which says: ‘In any right angled-triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides’ i.e. c2 = a2 + b2.

The simplest case of Pythagoras’ Theorem is the 3-4-5 triangle where 52 = 32 + 42

Although Pythagoras may well have discovered this result independently, it had been known to the Babylonians for centuries before Pythagoras’ birth. Pythagoras and his followers did, however, contribute significantly to mathematics, especially geometry and the early theory of numbers. He is also credited with the introduction of proof into mathematics.

The brotherhood, known as ‘The Pythagoreans’, became so powerful that the local rulers in southern Italy destroyed their buildings and caused the brotherhood to disperse. One account says that Pythagoras died in the flames, another that he fled to Metapontum where he later died. Nevertheless the brotherhood continued in existence for another two hundred years after its founder’s death in around 500 BC.

A contribution of Pythagoras to mathematics

Pythagoras is accredited by Iamblichus, a fourth century philosopher, with the discovery of the so called ‘amicable’ numbers. Two numbers are called ‘amicable’ if each of them is equal to the sum of the proper divisors of the other. (The proper divisors of a number are all the numbers that divide into it except the number itself.)

The simplest example of a pair of amicable numbers is 220 and 284.

The proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110

and 1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284

The proper divisors of 284 are 1, 2, 4, 71 and 142

and 1 + 2 + 4 + 71 + 142 = 220

The next pair of ‘amicable’ numbers is 17,296 and 18,416 which weren’t discovered until 1636 AD by Pierre de Fermat.


This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

Show Details
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
ClickscoThis is a data management platform studying reader behavior (Privacy Policy)