The Ultimate Test
Previous puzzles I’ve posted in this publication involve very little mathematics.
Although they were quite difficult and involved plenty of mathematical thinking, they generally required very little mathematical knowledge. People who have studied mathematics formally at the high school (or even university level) may not have a significant advantage when solving those problems.
This time, I’m going to mix it up: a problem involving many areas of math; algebra, geometry, trigonometry, even number theory (depending on how you approach it).
It requires mathematical thinking, research skills, a strong grasp of fundamental knowledge, broad investigations into different areas of mathematics, and more importantly, interest.
It’s what I would consider an ultimate test of skill, at least for the stereotypically “good” math student. There’s a small chance you’ve been taught how to do this in school; in that case, try to do it in different ways.
And now, the ultimate reveal:
How do you rotate a rational function?
How can you extend a function?
And finally,
How will you work with a relation?
That’s it! Don’t ask me for any more instructions, because I really have nothing more to say.
You may say, that’s awfully vague. Yes, you’re right, and it’s intentional. If you have no idea where to begin, consider:
0. This question could mean many things. For all of the things you think of, attempt steps 1 to 4:
- Defining the problem, formally, using mathematical language
- Consider different approaches towards investigating this problem
- Consider different areas of mathematics
- Explore; build upon this problem, as much as you can. Extend into related problems. Expand on your lemmas. Look intuitively. Search aimlessly. Your imagination is the limit.
I’ll post a solution to this, discussing possible approaches to this problem. Meanwhile, I do suggest seeing how far you can go, and for how long you can push yourself to work on this problem.
If you wish (I really hope you do), send your solutions to my email: providence641@gmail.com. I’ll post all of them, unless you don’t want them to be publicized.
