Ahmed Amir

I'm looking on the sample question.. Thanks

What does "Cyclic equations" mean? Does it mean a symmetric system of equations?

@GFauxPas I noticed that the number of pages is different.

May I ask a question? Is there any difference between the Spivak's Calculus book (the fourth edition) and what is so called (World student series edition)?

@Ramanujan I was just curious about the problem you were discussing..

@Ramanujan thanks..

@Ramanujan May I ask about the name of this book?

I haven't received any answer yet. That maybe because of the way I asked..

Could you please suggest an edit to this question? math.stackexchange.com/questions/1996363/…

OK.. Thanks for your time and your clarification..

So the solutions that used Pythagorean triples isn't dense on the plane..

as "a" is smaller than "b".. in the triple

What you meant by a dense set is that like a set between, for example, 1 - 100 on the x axis.. Not like the example on that answer whose points on the x axis are smaller than one?

The other answer on my question shows that it's possible on aplane.. He used the fact that there are an infinte numbers of Pythagorean triples.. Take a look on that answer and the comment.. It's so simple

It's all clear now.. Sorry for my slow understanding as I'm studying these just by my own.. And thanks for your patience.

So the method to get such two or more points is to take the arctan of a rational number multiplying by four..

Points that have a rational distance between each others..

Like, point one has 30 degrees.. point two has 44 degrees..

Well, if I want to choose any two points on the unit circle to test if they have a rational distance between each others.. Just give me three or more points to test them..

I see, so in other words, The two points on the unit circle should have a specific angle between each others.. And by moving them we get an infinite set..

Just another question.. What did you exactly meant by thet part about tan 4 theta?

It makes sense now.. Will try to make it again by myself.. Thanks

No, I tried to use Pythagoras, but couldn't get the same formula.

Can you please explain this in more details, especially the tan part.