![2000px-Square_root_of_2_triangle.svg[1].png](https://i.imgur.com/BC1g5FJ.png "2000px-Square_root_of_2_triangle.svg[1].png")
Math noob/filhty autodictat here, would like an elementary doubt cleared please
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?
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?
Pic related (sort of?)
>>7749810
This is the literature board.
Yes to both if you can prove it.
>>7749810
both are wrong
The "can(not) be represented as the length of the one of the sides of a 2D object" part is irrelevant.
If you delete this property and examine "All real numbers are not transcendental numbers" it is flat-out false since π is transcendental and π ∈ R. Same for the second proposition: it is false because 666 is not transcendental, but does ∈ R.
>>7749849
Of course that's true...
I'm curious about the length of the sides of a 2D figure.
I don't know what you mean by irrelevant, it seems like a hard term to define.
Do you have an answer to my question? If so bring it over to /sci/, sorry for posting on the wrong board guys, make this a literature of math or aesthetic beauty of maths thread if you like, or just delete.
>>7749861
The falsity of "All real numbers are (not) transcendental numbers" implies the falsity of "All real numbers that can(not) be represented as the length of the one of the sides of a 2D object are (not) transcendental numbers".
Just because you're trying to interpret it geometrically it doesn't mean it somehow changes the truth-value.
>>7749810
Both are wrong. All real numbers can be represented as the length of the one of the sides of a 2D object. However complex numbers cannot. Source: Used to study math at university.
>>7749876
You mean the Cartesian R^2 plane? How is that relevant to the problem at hand though?
>>7749875
Can you give me an example of a 2D object that has a side of length pi?
>>7749895
>The 2D object in question is an object that can be drawn with straight edge and compass in a finite number of steps.
This is what was in my head.
I mean, of course it's possible to have an "object" that is a square of side length pi.
Also, thread is now here: >>>/sci/7891918
>>7749895
If the condition is that it can be drawn with a finite number of steps then the object wouldn't reflect the real numbers and therefore your question would be stupid.
>>7749899
>>7749897
Eh
>>7749901
Of course, it wouldn't reflect all real numbers my question is:
1) Are those real numbers that can be represented in this way definitely not transcendental (this part seems true, quoting wikipedia below)
>Squaring the circle has been proven impossible, as it involves generating a transcendental number, that is, {\sqrt{\pi}}. Only certain algebraic numbers can be constructed with ruler and compass alone, namely those constructed from the integers with a finite sequence of operations of addition, subtraction, multiplication, division, and taking square roots. The phrase "squaring the circle" is often used to mean "doing the impossible" for this reason.
https://en.wikipedia.org/wiki/Compass-and-straightedge_construction
2) Are those real numbers that cannot be constructed this way transcendental?
>>7749904
Yes, yes, I suppose I asked for this by not being specific, let's exclude the case of circles.
>>7749895
>>7749891
Irrational numbers can only be approximated, both geometrically and decimally.
The decimal "3.14159265358979323846264338327950288419716939937510..." cannot be written out fully because there is not enough paper and ink in the universe to do so. That's why the number is named "π" because it is easier to refer to it that way.
This is a pseudo-problem. The "2D object ..." property is absolutely irrelevant here. Both propositions are false.
>>7749906
In this case then #1 is true. But #2 still false. For example you wouldn't be able to construct a irrational number and not all irrational numbers are transcendental.
>>7749904
What software btw?
>>7749904
What program is this?
>>7749916
You wouldn't say that you cannot draw a triangle like pic related with compass and straight edge would you?
Read the last line here:
https://en.wikipedia.org/wiki/Compass-and-straightedge_construction
>>7749917
https://en.wikipedia.org/wiki/Constructible_number
Irrational numbers can be "constructed" though.
>>7749935
>>7749916
>Irrational numbers can only be approximated, both geometrically and decimally.
Basically, give me a line segment of unit 1 and I can construct pic related, thereby constructing an irrational number.
So, irrational numbers can be "constructed" geometrically.
Now, transcendental numbers on the other hand...
>>7749940
the point is why do you assume that it is legit to draw the hypotenuse, aka ''does the hypotenuse exist ?''.
>>7749973
It can for pic related, read up on the definition of constructable numbers.
Got my answer from /sci/ anyway:
>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 (2√323 for example)
And 1 is true.
Thanks/no thanks I guess, sorry for polluting the board.
>>7749910
Yeah I get what you were asking though, I was just bored and having a giggle. It's actually pretty interesting and I'm glad some actual math people answered it.
>>7749918
>>7749920
CADWorx running on top of AutoCAD
Sage report and hide shit threads.
