Sales: Sales: Support: Support:
Academic writing services  
 
Custom written essay Book report Research paper Dissertation Resume and CV Editing and proofreading  
main menu
discounts
discounts
By ordering custom paper you get
  • 24/7 Support
  • Over 100 professional US Writers
  • 300 words per page
  • Flexible discount system
  • FREE revision (within 2 days)
  • Anti-Plagiarism Software Check
we accept
sample essays
Accounting Essays
Admission Essays
Analysis Essays
Art Essays
Biography Essays
Biology Essays
Book Review Essays
Business Essays
Case Studies Essays
Cause and Effect Essays
Character Analysis Essays
Communication Essays
Communication and Media Essays
Compute Technologies Essays
Consideration Essays
Controversial Essays
Description Essays
Economics Essays
Education Essays
Evaluation Essays
Explanation Essays
History Essays
Job Essays
Law Essays
Management Essays
Medicine Essays
Music Essays
Personal Essays
Personal Experience Essays
Persuasive Essays
Persuasive Speech Essays
Philosophy Essays
Political science Essays
Politics Essays
Proposal Essays
Psychology Essays
Reflective Essays
Religion Essays
Research Essays
Response Essays
School Essays
Science Essays
Sociology Essays
Technology Essays
World Literature Essays
Pythagorean Triples essay
 
← The Primordial Soup Theory Last Natural Selection →

Pythagorean Triples. Custom Pythagorean Triples Essay Writing Service || Pythagorean Triples Essay samples, help

According to Laubenbache and Pengelley (1999)The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students.

A Pythagorean triple is a set of three integers a, b, c which form the sides of a right angled triangle. The smallest Pythagorean triple is the set of numbers 3,4,5. The Pythagorean Theorem states: In a right triangle, with sides (legs) a and b, and hypotenuse c, then c²=a²+b². A right triangle is a triangle with one right angle (an angle of 90°). Its hypotenuse is the side opposite the right angle (Maor 2007).

It is called "Pythagoras' Theorem" and can be written in one short equation:

a2 + b2 = c2

Note:

  • c is the longest side of the triangle
  • a and b are the other two sides

The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that: "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."

The Pythagorean theorem is used any time we have a right triangle, we know the length of two sides, and we want to find the third side. The Pythagorean theorem is also frequently used in more advanced math. The applications that use the Pythagorean theorem include computing the distance between points on a plane; converting between polar and rectangular coordinates; computing perimeters, surface areas and volumes of various geometric shapes; and calculating maxima and minima of perimeters, or surface areas and volumes of various geometric shapes (Tobey and Slater 2002)..

Example of application

a2 + b2 = c2

52 + 122 = c2

25 + 144 = c2

169 = c2

c2 = 169

c = √169

c = 13

Ecluid showed that there are unending Pythagorean triples.

The proof was based on the fact that the difference of the squares of any two consecutive numbers is always an odd number.

Examples:

22 - 12 = 4-1 = 3 (an odd number),

152 - 142 = 225-196 = 29 (an odd number)

And also every odd number can be expressed as a difference of the squares of two consecutive numbers. Have a look at this table as an example:

And there are an infinite number of odd numbers.

According to Laubenbacher and Pengelley, D. (1999)There is an infinite number of odd numbers. Since the perfect squares form a subset of the odd numbers, and a fraction of infinity is also infinity, it follows that there must also be an infinite number of odd squares. Therefore, there are an infinite number of Pythagorean Triples.

(3,4,5) (5,12,13) (7,24,25) (8,15,17) (9,40,41) (11,60,61) (12,35,37) (13,84,85) (15,112,113) (16,63,65) (17,144,145) (19,180,181) (20,21,29) (20,99,101) (21,220,221) (23,264,265) (24,143,145) (25,312,313) (27,364,365) (28,45,53) (28,195,197) (29,420,421) (31,480,481) (32,255,257) (33,56,65) (33,544,545) (35,612,613) (36,77,85) (36,323,325) (37,684,685)

One of the most common applications of the Pythagorean theorem is in the distance formula, to find the distance between two points.

Pythagorean Triples. Custom Pythagorean Triples Essay Writing Service || Pythagorean Triples Essay samples, help

Order Now
Order nowhesitating

Related essays

  1. Last Natural Selection
  2. Border Cave South Africa
  3. The Primordial Soup Theory
  4. Theories in Human Sciences


order now

 
 
3.6K
1.2K
Order now
Email
Password
 
why choose us
96% of satisfied returning customers
24/7 customer support
A wide range of services
Up-to-date sources
100% privacy guaranteed
MA/PhD writers
Custom written papers only
Free plagiarism report
Free revision (within 2 days)
Free extras by your request
Direct communication with a writer
faq
Are your writers qualified for the custom writing?
How quick can my order be accomplished?
Is it legal to buy custom essays, term papers or book reports from your company?
Are essays offered by your company truly custom-written?
Is it safe to buy from SupremeEssays.com?
How secure is the payment system of your company?
Can I submit custom essays or term papers done by your company as my own?
How can I contact your company if I've got problems with my ordered paper?
testimonials

Finally, I've found the real custom writing service . My grades are saying "Thank you, it's been a pleasure to work with you."

Jamal, South Africa

I can't believe you finished my essay under such a short deadline! You saved me from a disaster once again. You guys deliver exactly what you promise. I'll be back. That's for sure!

William H , Kansas, US

contact us
Toll free for US & Canada only. International callers are charged for outgoing calls.

Our phone numbers:
SupremeEssays.com provides custom term paper writing/rewriting services inclusive of research material for assistance purposes only. The term papers should be used with proper reference and are not meant to replace actual assignments.
 

Get 15% off your first custom essay order

Order now

PRICES
from $12.99/PAGE

X