• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Pythagoras of Sámos.

Extracts from this document...


Rojas, Jonathan, Period Five

Monday, May 5, 2003

Pythagoras of Sámos

        Born on the island of Sámos, Pythagoras—known as Pythagoras of Sámos—was a Greek politician, astronomer, philosopher and religious leader; he is truly the original “Renaissance Man”.  However, it is not for any of the previously mentioned that Pythagoras is renowned.  Indeed, it is for his study of geometry and other mathematics that he is known worldwide by those studying math.  He laid the groundwork for all of the other great mathematicians that have succeeded him: Euclid, in his study of Euclidian geometry, Aristotle, in his exploration of philosophy, Newton, in his study and findings regarding the science of calculus, among other great figures in the field of science.

        Although any other could have perhaps achieved the same status, Pythagoras was born into greatness that assured him of his place in history.  After his birth on the island of Sámos, Pythagoras was instructed in the teachings of the early Ionian philosophers Thales, Anaximander, and Anaximenes.  Clearly, Pythagoras would go far with these great figures guiding him.  However, all Pythagoras’ genius and free will called for his departure from Sámos because of Polycrates—the king of the Aegean island of Sámos during the Greek Age of Tyrants in the 6th century bc.

...read more.


        Having impacted the many fields of science, Pythagoras has had a great influence on the world today and the twenty-five hundred years past.  Pythagoras’ philosophies are hardly evanescent; his endorsement of numbers in the “corporeal world,” as he dubbed it, maintain their impact on the world today.  Modern astronomers and mathematicians have maintained that his proofs and theories are valid.  For instance, it is accepted that the earth is spherical and that the planets of this galaxy circle the sun.  Moreover, the Pythagorean Theorem is still accepted, unlike some of the theories proposed by other scientists, such as Avogadro.  Though the latter theorem is the most popular—and thereby most widely taught—his most ingenious theorems are present in the study of calculus and advanced trigonometry.  For instance, the Pythagorean identities are considered among the greatest discoveries of trigonometry, the base is as follows:

sin2 x + cos2 x = 1; this is the base from which other Pythagorean trigonometric identities can be derived.  The use of these equations and identities are present throughout mathematics—the foremost being trigonometry and calculus.  

...read more.


        In summary, Pythagoras of Sámos was the paradigm of a prodigy.  Through his studies and findings, the people of the world were able to further their understanding of mathematics and a plethora of other sciences.  His genius accounts for the influence of most of the studies of the great mathematicians that superseded him, and many sciences were either founded or flourished because of Pythagoras’ works.  Truly, it is because of Pythagoras that the world has made such technological advancements; without his influence, the sciences may have been in their primitive state as they were centuries ago.

Works Cited

  1. A History of Mathematics and The Golden Ratio.  http://goldennumber.net/index.html.  Date Accessed: 4-16-03.  Date Created: 1999.  ©1999-2003 The Evolution of Truth.
  2. Copernicus Agent 6.0 WebCrawler Edition.  ©1993-2003 Copernicus Corporation.  All Rights Reserved.
  3. Copernicus Open Directory Project & The Liberty Alliance.  
    ©1995-2003 Copernicus Corporation.  All Rights Reserved.
  4. Google Search Engine.  ©1994-2003 Google Technologies Incorporated.  All Rights Reserved.
  5. Mathematicians of the Past.  http://www-gap.dcs.st-and.ac.uk/ ~history/Mathematicians/Pythagoras.html.  Date Accessed: 4-16-03.  Date Created: January 1999.  ©1999-2003 School of Mathematics and Statistics: University of St Andrews, Scotland.
  6. Microsoft Encarta Reference Library 2003 DVD-Edition.  ©1993-2003 Microsoft Corporation.  All Rights Reserved.
  7. Microsoft Networks MSN Learning and Research Plus MSN-8 Edition.  ©1995-2003 Microsoft Corporation.  All Rights Reserved.
...read more.

This student written piece of work is one of many that can be found in our GCSE Beyond Pythagoras section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Beyond Pythagoras essays

  1. Beyond Pythagoras

    Length of the shortest side: a=2n+1 I now need to test my formula to see if it works so: (2x1)+1=3 It works for that one, as I can see on my table that with term 1, the side length is 3.

  2. Beyond Pythagoras ...

    - (16n2+32n3+16n4) Now I will investigate the other Pythagorean triples because my theory says use the bases then you times them. For Example a=b+ (b+1)= c so a=3 b=4 c=5 So it's 5= 4+(2+1) So it's 52= 42+ 32 25=16+9 Then you times the bases 3,4, 5 by two to get a=b+(b+1)

  1. Beyond Pythagoras - I am investigating the relationships between the lengths of the three ...

    5)+(6 x 5)+2 =132 (4 x 6)+(6 x 6)+2 =182 (4 x 7)+(6 x 7)+2 =240 (4 x 8)+(6 x 8)+2 =306 etc.

  2. Pyhtagorean Theorem

    So with that knowledge, you substitute a and b with their formulae to get the formula. So (2n)(n�-1) 2 = n(n�-1) = n�-n We also know that to get the perimeter of any shape, not just a triangle, you add up the lengths of all of the sides.

  1. Beyond Pythagoras

    \ / \ / 2 2 2 2 2 Every time 2 is being added to the previous number. I can work out that the next numbers will be 9, 11, and then 13. Sequence for middle side 4 12 24 40 60 84 \ / \ / \ /

  2. Beyond Pythagoras

    I worked out that the formula = 2n + 1 I will make a prediction to prove my formula works: I predict that for no. 10 the sequence will be (10x2) + 1 = 21. How can I prove I'm right?

  1. Beyond Pythagoras

    � b� a�+b� = b�=2b+1 b+1� a� = 2b + 1 a�-1=b 2 Pythagoras theory is satisfied So now with 5 triplets that I have proved I will now find a general formula to find other pythagorean triplets in this family.

  2. Beyond Pythagoras

    Sequence 4,12,24,40,60,84 1st Difference 8,12,16,20,24 2nd Difference 4,4,4,4,4 4/2=2 So it's 2n2. Sequence 4,12,24,40,60,84 2n2 2,8,18,32,50, 72. Sequence minus 2n2 2,4,6,8,10,12 First Difference 2,2,2,2,2,2 Therefore the rule for finding the nth term of the middle side is: 2n2+2n Next I shall find the nth term of the longest side.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work