Exploring Pythagorean Triples | Examples, Applications, and Mathematical Significance

{3,4,5}{5,12,13}{8,15,17}{7,24,25}

These sets of numbers {3,4,5}, {5,12,13}, {8,15,17}, {7,24,25} represent Pythagorean triples

These sets of numbers {3,4,5}, {5,12,13}, {8,15,17}, {7,24,25} represent Pythagorean triples. A Pythagorean triple is a set of three positive integers that satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In the first set {3,4,5}, we can see that 3^2 + 4^2 = 5^2, thus satisfying the Pythagorean theorem.

In the second set {5,12,13}, we have 5^2 + 12^2 = 13^2, again satisfying the theorem.

In the third set {8,15,17}, we see that 8^2 + 15^2 = 17^2, fulfilling the Pythagorean theorem.

Finally, in the set {7,24,25}, we have 7^2 + 24^2 = 25^2, satisfying the theorem once more.

Pythagorean triples have been studied for centuries and have many applications in geometry and math. These sets of numbers are particularly useful when working with right triangles, as they allow for easy calculation of missing side lengths or checking if a given set of side lengths forms a right triangle.

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