# G H Hardy A course in pure mathematics

• storm4438
In summary: To determine any number of right-angle triangles, you would need to find a general expression or formula for the lengths of the sides of a triangle whose sides are rational. This would allow you to find the lengths of an infinite number of right-angle triangles with rational sides.
storm4438
1. Homework Statement [/b]
3. if X m and n are positive rational numbers, X(m^2 ~ n^2) , 2Xmn , and X(m^2+n^2) are positive rational numbers. Hence show how to determine any number of right-angle triangles the lengths of all whose sides are rational

## The Attempt at a Solution

What does the tilde mean in this context, he doesn't explain use it anywhere else or explain what it is. Also what does "determine any number of right-angle triangles..." mean? Is it asking you to find a general expresion for the lengths of the sides of a triangle whose sides are rational?
-Thanks

storm4438 said:
...
What does the tilde mean in this context, he doesn't explain use it anywhere else or explain what it is.
I believe that the tilde represents a modified form of subtraction. In this case it means to subtract the smaller number from the larger. In other words, it's the absolute value of the difference.
Also what does "determine any number of right-angle triangles..." mean? Is it asking you to find a general expression for the lengths of the sides of a triangle whose sides are rational?
-Thanks
A right-angle triangle, is a triangle having one right angle. It is usually referred to as simply a 'right triangle'.

## 1. What is "A Course in Pure Mathematics" by G H Hardy?

"A Course in Pure Mathematics" is a classic textbook written by G H Hardy, a renowned British mathematician. The book was first published in 1908 and has been a standard text in mathematics courses for over a century. It covers topics such as algebra, geometry, number theory, and calculus.

## 2. Who is the target audience for "A Course in Pure Mathematics"?

The book is primarily aimed at undergraduate students studying mathematics, but it has also been used by graduate students and even professional mathematicians as a reference text. It assumes a solid foundation in basic mathematics and is suitable for self-study or as a supplement to a course.

## 3. What sets "A Course in Pure Mathematics" apart from other textbooks?

One of the distinctive features of this book is its emphasis on rigorous mathematical proofs. Hardy believed that a student cannot truly understand mathematics without being able to prove theorems. The book also includes many challenging exercises, which help students develop their problem-solving skills.

## 4. Is "A Course in Pure Mathematics" still relevant in modern mathematics?

Although the book was first published over a century ago, its content is still highly relevant in modern mathematics. Many of the concepts and techniques covered in the book are still fundamental to current research in pure mathematics. Additionally, the book's approach to rigorous proof and problem-solving is still highly valuable to students.

## 5. Can "A Course in Pure Mathematics" be used as a standalone text?

While "A Course in Pure Mathematics" is a comprehensive text, it is not intended to be the sole resource for a mathematics course. It is best used in conjunction with lectures, class notes, and other textbooks. However, it can be used as a standalone text for self-study, as it includes thorough explanations and numerous exercises with solutions.

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