Math noob/filhty autodictat here, would like an elementary doubt

Bonus points for examples?

All trascendental numbers have length and limit. The only thing you can't do is use transcendental numbers as results to fractions.

Sorry, sorry, forgot to add a condition.

The 2D object in question is an object that can be drawn with straight edge and compass in a finite number of steps.

Exclude the case of circles.

>>7891937
Can't do that either with regular rational numbers.

Bump?
Someone please?

Also:
https://en.wikipedia.org/wiki/Constructible_number
https://en.wikipedia.org/wiki/Compass-and-straightedge_construction

What you are asking is true though, you can't construct transcendental numbers with just a straight edge and a compass.

>>7891953
I don't get what you mean?
I can't draw a 2D object with a straight edge and compass in a finite number of steps?

>>7891956
And are those the only real numbers I can't draw with straight edge and compass?

Or would there be certain irrational or other numbers too that I can't draw?

>>7891956
>>7891960
Pic related in OP can be "constructed" given a line segment of unit length so some irrational numbers can definitely be "constructed" does this hold true for all of them (that seems like a stupid question but still, it isn't obvious to me, sorry)?

>>7891960
Nope, there is a property that characterizes the numbers that can be constructed with a ruler and compass (check out Wantzel's theorem), which is considerably stronger than simply algebraic. There are many algebraic numbers that cannot be constructed with a ruler and a compass ([math]\sqrt[3]{2}[/math] for example)

>>7891973
Thanks maen.

>>7891957
You can't represent all rational numbers as the length of a side of a shape made only with a compass and straight edge in a finite number of steps.

>>7891989
Ah neat, example and further reading if possible?

>>7891993
On further thought, I could be wrong.. I don't know enough about geometry to answer, don't take my answer as fact.

>>7891918
What happens to the length of the other two sides if we redefine the triangle side sqrt(2) to have length 1.

>>7892005
they are both 1/sqrt(2)

>>7892007
Ok thanks. Makes sense

>>7892003
All rational numbers are constructible, so sayeth the wiki

>>7892024
Yeah makes sense, my apologies. Got my terms mixed up.

>>7891918
This is a good thread OP. Thanks for contributing.

>>7891918
>Can I say that all real numbers that can be represented as the length of the one of the sides of a 2D object are not transcendental numbers?

If you mean any segment that you can construct using compas and ruler, then yes.

>
Can I say that all real numbers that cannot be represented as the length of one of the sides of a 2D object are transcendental?

No, you cannot construct a cubic root of 2 (with compas and ruler), but cubic root of 2 is not transcendental.

>>7892408
Yes you can. Just draw the hypotenuse last.

>>7892928
Not him but, what?

>>7891931
What about infinite continued fractions?

File: 1450129044722.jpg (154KB, 1920x1200px) Image search: [Google]

154KB, 1920x1200px

>>7891918
the question is why do even think that you can get a length of 1 IRL.
the other question is why do you think that the your favorite numbers (typical the irrational) are a good formalization of the lengths that you observe IRL.

>>7893471
and the last question is why do you seek other numbers to prove that you can only deal with certain numbers through compasses and rulers.

>>7891918

OP's thread appears to be confused.

>Can I say that all real numbers that can be represented as the length of the one of the sides of a 2D object are not transcendental numbers?

The answer to this question is no.

>Can I say that all real numbers that cannot be represented as the length of one of the sides of a 2D object are transcendental?

The answer to this question is also no.

I will write a bit more about this in a lower post.

t. math grad

Other anons (and apparently even OP given the OP picture being at the wiki) have already pointed out the relevant topic of a constructible number, the notion of which comes from the actual practice (actually using compass and straight-edge to draw figures) of Euclidian geometry.

The three relevant notions to OP's questions are baked into the language themselves: constructible numbers, irrational numbers, and transcendental numbers.

However, OP's question by-itself is more general than Euclidian constructibility. In practice, there's nothing stopping us from imagining a regular polygon whose side lengths are exactly pi, or e (both transcendental numbers). The constructibility in terms of the above restrictions is a separate question, and other anons are making the mistake of thinking of OP's question only in those terms.

But we can get creative. I want to use more things: I want to use a (perfect-circle-drawing) compass, a (perfectly straight) straight-edge, and a perfectly-cutting scissors. Now I can construct a transcendental number easily!

Just set a length with the compass, define its radius as unity, then draw the circle whose perimeter is exactly pi. Now cut this circle out with the perfectly precise scissors. trace this disk for one revolution, against a straight edge, and draw the line. voila, a line that is transcendental, relative to an established radius. Now I can even make polygons with this basis.

>>7897302

of course, there is an irrelevant 2pi : "tau" thing going on here, before someone jumps all over me. Simply convert the radius/diameter before drawing.

>>7891961
No because some irrational numbers are transcendental, ie pi, e...

>>7897302
you can imagine anything you want and the rules who make your deliriums valid. what matters is why do you crave those deliriums.

>>7898399
>what matters is why do you crave those deliriums.
Because that guy's rules actually give a correct answer to OP's question.

>>7898399

You are correct that mathematics is an imaginative and creative process, involving a little abstraction, and "magical thinking".

One of the magical ideas is that there exists a perfect straight line (it actually does). But the other magical idea is that "a straight edge", a physical object that you or I can hold, can be "used" to "draw" a "straight line".

Another magical idea is that we can agree on an arbitrary "unit" of length.

Still other magical ideas have to do with ideal compasses, and what they are supposed to be able to do, and what the system described so far is capable and incapble of doing. Making things even more interesting and wonderfully DELERIOUS than they had already been, is my other piece of magical thinking, which is no more delerious than what came before.

Happily this nigga >>789846 gets me. But what will really bake everyone's noodle is that not only do I reject this constructibility autism for OP's actual question, but more, that the above "magical objects" are /real/.

Euclid was a hella mathemagician.