- #1
Calixto
- 16
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how can I show that ... arctan(1/v) = (π/2) - arctan(v) ?
Calixto said:how can I show that ... arctan(1/v) = (π/2) - arctan(v) ?
An interesting proof is one that is unexpected or counterintuitive, yet logically sound. It may also involve creative and unique approaches to solving a problem.
A challenging proof is one that requires a high level of mathematical knowledge and problem-solving skills. It may involve complex concepts or require multiple steps to reach a conclusion.
Some common challenges in creating an interesting proof include identifying and understanding the key concepts and assumptions, finding a logical and elegant argument, and ensuring that the proof is rigorous and complete.
To improve your ability to create interesting yet challenging proofs, it is important to continually practice and develop your mathematical reasoning skills. This can involve studying different proof techniques, analyzing and understanding the logic behind existing proofs, and constantly challenging yourself to solve more difficult problems.
Interesting yet challenging proofs are important in science because they help to advance our understanding of the natural world and solve complex problems. They also demonstrate the power and beauty of mathematics as a tool for discovery and innovation.