We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Nobody downloaded yet

Pythagorean triples - Essay Example

Comments (0)
It is about a property of all right triangles showing a relationship between their sides given by the equation c2 = a2 + b2; that is, the square of the longest side is equal to the…
Download full paper
Pythagorean triples
Read TextPreview

Extract of sample
Pythagorean triples

Download file to see previous pages... The most popular example of which is the 3-4-5 triangle, the triple which, according to Knott (2009), was known to the Babylonians since way back 5,000 years and was possibly used as a basis in making true right angles in ancient building construction.
Then again, the 3-4-5 triangle is just one of the infinitely many Pythagorean Triples, and mind you, there are various ways of generating such triples. One is, given two integers n and m, where n > m, then sides a, b and c are define as n2 - m2, 2nm and n2 + m2, respectively, following a simple proof (Bogomolny 2009):
Taking for instance the triple 8-15-17, which is generated by taking n = 4 and m = 1, then a = n2 - m2 = 4­­2 - 12 = 16 - 1 = 15; b = 2mn = 2(1)(4) = 8, and; c = n2 + m2 = 4­­2 + 12 = 16 + 1 = 17. Another example is 7-24-25, which can be verified using n = 4 and m = 3. Such triples are examples of Primitive Pythagorean Triples, or those triples that are not multiples of another and are found using the n-m formula (Knott 2009). Other Pythagorean Triples can be found using a variety of methods as presented by Bogomolny (2009) and Knott (2009), some of which are:
c) by Two-fractions method—choose any two fractions whose product is 2, add 2 to each fraction, then cross multiply, getting the two shorter sides of the triple: 4/2, 2/2 → 8/2, 6/2 → 16, 12 → 162 + 122 = 202, and;
To sum it up, there are infinitely many Pythagorean Triples existing. But one thing is for sure, a variety of techniques are available that will serve useful in generating patterns among such triples. Hence, if you cannot list them all, be familiar of their patterns at least.
Knott, R. (2009). Pythagorean Triangles and Triples. Retrieved November 20, 2009, from The University of Surrey, Mathematics Web site: ...Download file to see next pagesRead More
Comments (0)
Click to create a comment or rate a document
: Visual learning
The visual aids commonly come in the form of objects, posters, charts and handouts. Visual aids reinforce the speech of the teacher with visual stimulants. Common visual learning styles include but are not limited to making outlines, making diagrams, copying the images or text on the board, mapping historic events, watching videos, and using flashcards.
1 Pages(250 words)Essay
How concerns of commerce and business spur on the development of mathematics
The oldest mathematical texts that were available included, the Rhind mathematical papyrus, which was of Egyptian mathematics between 2000-1800 BC, Plimpton 322 of Babylonian mathematics in 1900 BC and the Moscow mathematical papyrus in 1890 BC. These texts were all in accordance to the Pythagorean Theorem that is the oldest and known to many after geometry and basic arithmetic (Avner 87).
9 Pages(2250 words)Essay
Pythagorean triplets
2 Pages(500 words)Essay
He authored the book A Plaine Discovery of the Whole Revelation of St John in 1593 which became the first important Scottish interpretation of the bible. John Napier's invention of the system of logarithms, described in Canonis Descriptio in 1614 made him a name to be reckoned with until today.
5 Pages(1250 words)Essay
The Pythagorean Theorem
whose side is the hypotenuse is equal to the sum of the areas of the squares of the two sides that meet at a right angle i.e. whose sides are the two legs" Two of those triangles taken together, however, are equal to a rectangle whose sides are a, b. The area of such a rectangle is a times b: ab.
14 Pages(3500 words)Essay
Fibonacci, Mathematician of the Middle Ages
Nowadays, it is situated in the western arcade of the Campo Santo, chronological graveyard on the Piazza dei Mira coli. The sculpture had started off in the Camposanto. Then it had been stirred to the Giardino Scotto just to accumulate it from probable harm throughout the World War Two.
4 Pages(1000 words)Essay
Philosophy paper - 1000 words - Mind, Meaning and Metaphysics - Material Provided
However, Greek science did not start in Greece but in the city of Miletus in Asia Minor on the Mediterranean coast of modern-day Turkey as well as in the other cities of that region. The region, called
4 Pages(1000 words)Essay
Brief Summary of Historical Orientation of Mathematics
As far as the history of mathematics is concerned, the same can be traced back to 3000 BCE. The Base-60 place value system started to develop within Mesopotamia and the Egyptians used the base-10 for grouping different numbering systems. This was the time when Harappan civilization was getting its roots firm within India.
1 Pages(250 words)Essay
Pythagorean Thagorean equations
In all the triples identified, it was verified that a, b, and c are in the exact proportion and relationship in accordance with the Pythagorean Theorem equation. The two numbers of the
1 Pages(250 words)Essay
Pythagorean Theorem
Unlike any other mathematical theorem, the Pythagorean Theorem is supported by both geometric and algebraic proofs. This paper will discuss the Pythagorean Theorem in detail. The theorem is a statement about the three sides of a
3 Pages(750 words)Essay
Let us find you another Essay on topic Pythagorean triples for FREE!
Contact us:
Contact Us Now
FREE Mobile Apps:
  • About StudentShare
  • Testimonials
  • FAQ
  • Blog
  • Free Essays
  • New Essays
  • Essays
  • The Newest Essay Topics
  • Index samples by all dates
Join us:
Contact Us