Pythagorean Triples in Geometry

A Pythagorean triple is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2. For example, 3^2 + 4^2 = 5^2. If you’re a fan of the TV show The Big Bang Theory, then you might remember that this is the formula that Sheldon Cooper used to win Amy Farrah Fowler’s heart. 

How It Works?

Pythagorean triples are named after the Greek mathematician Pythagoras because he is credited with discovering the formula. In fact, the formula is sometimes called “Pythagoras’ Theorem.” The theorem states that in a right angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. 

Why Is It Important? 

The Pythagorean theorem is important in geometry and architecture because it helps us calculate distances and angles. For example, if you want to build a deck on your house and you know how long two of the sides are, you can use the Pythagorean theorem to figure out how long the third side needs to be. 

Conclusion: 

Pythagorean triples are sets of three natural numbers that follow the equation a^2 + b^2 = c^2. The theorem is named after Pythagoras because he discovered the formula and it is sometimes called “Pythagoras’ Theorem.” The theorem is important in geometry and architecture because it helps us calculate distances and angles.

FAQ

What is a Pythagorean triple?

A Pythagorean triple is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2.

What does the formula mean?

The formula means that in a right angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

How can we use Pythagorean triples?

Pythagorean triples are used in geometry and architecture to help calculate distances and angles. For example, a 3-4-5 triangle is often used to determine square corners in construction. They are also used to calculate the area of triangles and other shapes.

Are there any special Pythagorean triples?

Yes, there are some special Pythagorean triples that have interesting properties. The 3-4-5 triple is the simplest one, and there are also triples that have sums of their sides equal to a perfect square. These triples include (5, 12, 13) and (7, 24, 25). There are also infinitely many primitive Pythagorean triples which can be used to generate other pythagorean triples.