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Pythagorean Triples Video Lecture | Crash Course for GRE
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FAQs on Pythagorean Triples Video Lecture - Crash Course for GRE
| 1. What is a Pythagorean triple? |  |
Ans. A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy the equation a^2 + b^2 = c^2, where c is the length of the hypotenuse of a right-angled triangle, and a and b are the lengths of the other two sides.
| 2. How can I determine if a set of three numbers is a Pythagorean triple? | |
Ans. To determine if a set of three numbers (a, b, c) is a Pythagorean triple, you can use the Pythagorean theorem. Simply square the two smaller numbers, add them together, and check if the result is equal to the square of the largest number. If it is, then the set of numbers is a Pythagorean triple.
| 3. Can all positive integers form a Pythagorean triple? | |
Ans. No, not all positive integers can form a Pythagorean triple. Pythagorean triples must satisfy the condition a^2 + b^2 = c^2, where a, b, and c are positive integers. While there are infinitely many Pythagorean triples, not all positive integers can be part of one.
| 4. Are there any patterns or rules for generating Pythagorean triples? | |
Ans. Yes, there are patterns and rules for generating Pythagorean triples. One method is to use the formulas: a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, where m and n are positive integers. By varying the values of m and n, you can generate different Pythagorean triples.
| 5. How are Pythagorean triples useful in real-world applications? | |
Ans. Pythagorean triples have various real-world applications. For example, they are used in construction and engineering to ensure that right-angled corners are accurately measured. They are also used in navigation and GPS systems to calculate distances and angles. Additionally, Pythagorean triples have applications in computer graphics, where they help determine the lengths of sides in 3D models and animations.
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Dec 23, 2024 Last updated |
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