• Current Events & Politics
    Welcome Guest
    Please read before posting:
    Forum Guidelines Bluelight Rules
  • Current Events & Politics Moderators: deficiT | tryptakid | Foreigner

Questions With Answers (cf. the "Universe Threads")

^ Good, you solved it way easier than I did.

I ended up applying the Root-Mean-Square Inequality* to the a_i and found what max(a_i) value would result in a contradiction.

* 1/n sum(a_(i^2)) >= A^2 for A= 1/n sum(a_i)

Good job though!

Edit: I guess ya you did do the same thing I did, I just missed the linear correlation between m and a_16 and thus went on a wild number chase :(
 
Last edited:
Weird and probably silly question

I had an unusual thought today,. I Want someone to either confirm this or explain where and why it is wrong.

How can a triangle have a side whose length is an irrational number?

Suppose we take a 45 45 90 triangle with base of length 1. That means the hypotenuse has length SQRT(2). How can a side have a length that is a non-terminating non-repeating decimal?

If we cut a triangle out of a sheet of paper and the bases are length 1 and the triangle is a right triangle, there should be no way for the hypotenuse to exist - No matter how precisely we measure it, no matter how many hundreds of decimal places we are accurate to, we should still be making a small + or - error from its true accurate length.

Does this mean it is impossible to construct in reality a perfect 45 45 90 triangle? I mean, I don't see how a "length" in reality can be an irrational number. What am I missing here?
 
the way i see it..

there are no "triangles" in reality. it's a mental tool/pattern that we can approximate spatial relationships in reality with

mathematics and reality are so odd when you think about it. everything spatial (aka any energy/matter we know of, and spacetime itself) seems to boil down to mathematics, but mathematics doesn't necessarily lead to spatial relationships--the same maths could be seen in totally other ways, as if the fundamental basis of reality could be something totally abstract and ungraspable to us (at least for now). it's interesting how many different ways of doing math can describe one spatial relationship, i wonder what's going on down there with those wavicles or whatever

i think the crazy relationship between maths & spatial reality could be something fundamental to how we percieve the universe
 
qwe said:
the way i see it..

there are no "triangles" in reality. it's a mental tool/pattern that we can approximate spatial relationships in reality with

mathematics and reality are so odd when you think about it. everything spatial (aka any energy/matter we know of, and spacetime itself) seems to boil down to mathematics, but mathematics doesn't necessarily lead to spatial relationships--the same maths could be seen in totally other ways, as if the fundamental basis of reality could be something totally abstract and ungraspable to us (at least for now). it's interesting how many different ways of doing math can describe one spatial relationship, i wonder what's going on down there with those wavicles or whatever

i think the crazy relationship between maths & spatial reality could be something fundamental to how we percieve the universe
Click to expand...

What about circles then? The perimeter of a circle with integer radius is an irrational number.
 
Fjones said:
What about circles then? The perimeter of a circle with integer radius is an irrational number.
Click to expand...

Construct a square with (rational) sides X. WLOG, let X=1. Then you have made something with rational sides but an irrational diagonal (sqrt(2)).

Irrational lengths come up all around us. However, most (if not all) of them are assessed by inference (a square...okay then a diagonal) rather than by construction (I'm going to make a square by starting with a diagonal...).
 
What we have here is that rational and irrational distances can't be measured with the same ruler, so to speak. But that don't mean irrational distances don't "exist".

In RL's example, we coulda just as well said X = the square root of two. Then the diagonal woulda been a rational number.
 
You must log in or register to reply here.
Top