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Euclid's Formula is a method of generating Pythagorean Triples. A Pythagorean Triple is a set of three positive integers (whole numbers), which satisfy the equation
a2 + b2 = c2. The smallest Pythagorean Triple is 3, 4, 5. Euclid's Formula says this: If you choose two positive integers m and n, with m < n, then the three numbers n2 - m2, 2mn and n2 + m2 form a Pythagorean Triple. For example, if m = 5 and n = 7, n2 - m2 = 49 - 25 = 24, 2mn = 70, and
n2 + m2 = 49 + 25 = 74.
24, 70, 74 is a PT, because 242 + 702 = 742. That's how to use Euclid's Formula. If the question means why does it work, then: (n2 - m2)2 + (2mn)2 = (n4 + m4 - 2n2m2) + (4m2n2) = n4 + m4 + 2n2m2, which is the same thing as (n2 + m2)2 . Two things to note are: The Formula does not generate all possible Triples, and it will generate Primitive Triples (ones with no common factor), only if m and n have no common factor, (except 1).
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Who are euclids parents?
eetrgrv
Books written by euclid?
euclids elements
How many books in euclids eiements?
There are 13 books in Euclid's Elements.
What is euclids full name?
Euclid of Alexandria or Eukleides
Did society accept Euclid ideas?
Those studying and using mathematics accepted Euclids work, which was a compilation of all the mathematics known at his time, and which has continued to be used as the basis of geometry taught is schools for over 2000 years.
Can you use euclids formula to generate integers 9, 12, andv15?
im not sure how to answer it
What is euclids theory?
need a simple explanation of Euclids theory.
Who are euclids parents?
eetrgrv
What are euclids most known accomplishmens?
His mathematical books called Elements. His work on geometry, particularly his famous axioms.
Books written by euclid?
euclids elements
What was euclids major maths discoveries?
geometry
What were euclids favorite areas of mathematics?
geometry
Title of thirteenth book in euclids elements?
compositions
Whats the oldest plane in the world?
euclids elements
What were some of euclids accomplishments?
His major accomplishment was in philosophy and mathematics
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How many books in euclids eiements?
There are 13 books in Euclid's Elements.
