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What are whole numbers that satisfy the pythagoreartheorm called?
Pythagorean Triples
What isa pythagorean triples?
That refers to any solution of the equation a2 + b2 = c2, where a, b, and c are positive integers. For example, 3, 4, 5; or 5, 12, 13.
How can you tell Pythagorean triples?
They are sets of three integers. The squares of two of them add up to the square of the third.
What was Fermat's original proof of his last theorem?
Fermat's last theorem says there does not exist three positive integers a, b, and c which can satisfy the equation an + bn = cn for any integer value of n greater than 2. (2 with be pythagoran triples so we don't include that) Fermat proved the case for n=4, but did not leave a general proof. The proof of this theorem came in 1995. Taylor and Wiles proved it but the math they used was not even known when Fermat was alive so he could not have done a similar proof.
What are the pythagorean theorem triples?
They are sets of integers such that the sum of the squares of two of the numbers equals the square of the third. For example, 5, 12 and 13 where 52 + 122 = 132
How many ordered triples of positive integers satisfy the equation a plus b plus c equals 6?
There are 6 such triples.
How many ordered triples of three prime numbers exist for which the sum of the members of the triple is 24?
There are three triples making 15 ordered triples.There are three triples making 15 ordered triples.There are three triples making 15 ordered triples.There are three triples making 15 ordered triples.
What are whole numbers that satisfy the pythagoreartheorm called?
Pythagorean Triples
What isa pythagorean triples?
That refers to any solution of the equation a2 + b2 = c2, where a, b, and c are positive integers. For example, 3, 4, 5; or 5, 12, 13.
How do you find a pythagorean triple?
There are infinitely many Pythagorean triples. To find a Pythagorean triple take two positive integers x, y with x > y. A Pythagorean triple is of the form x2 - y2, 2xy, x2 + y2.
How can you tell Pythagorean triples?
They are sets of three integers. The squares of two of them add up to the square of the third.
What was Fermat's original proof of his last theorem?
Fermat's last theorem says there does not exist three positive integers a, b, and c which can satisfy the equation an + bn = cn for any integer value of n greater than 2. (2 with be pythagoran triples so we don't include that) Fermat proved the case for n=4, but did not leave a general proof. The proof of this theorem came in 1995. Taylor and Wiles proved it but the math they used was not even known when Fermat was alive so he could not have done a similar proof.
Which set of integers is a Pythagorean triple?
Pythagorean triples: 3, 4 and 5 or 5, 12 and 13 are two of them
How does Euclid's Formula Work?
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).
Formula for midpoint of ordered triples?
You would use the midpoint formula on each axis, given that each ordered triple is represented by (x, y, z). The midpoint formula is another way of saying the mean of each axis.
What are the pythagorean theorem triples?
They are sets of integers such that the sum of the squares of two of the numbers equals the square of the third. For example, 5, 12 and 13 where 52 + 122 = 132
How do you generate pythagorean triples?
There are many different methods: the simpler methods will generate lots of triplets but not all. Comprehensive generators tend to be very complex. So here is a simple one: Euclid's formula Take any two positive integers x and y and suppose x > y. Then A = x2 - y2 B = 2xy C = x2 + y2 form a Pythagorean triplet.
