/sci/ - Science & Math

No calculator? hell no

>Is it possible to draw a square with the same surface as a circle, using only a ruler and a compass?'
>draw a square with the same surface as a circle
>same surface as a circle
>same surface

>>938694
Given that pi is irrational a calculator won't really help you.

>>938693

What the fuck's wrong with ''surface'' do you want me to type ''area'', well, ok, AREA

>>938687
No you can't square the circle

>>938699

>implying you can't approximate

>>938703

an circle the square?

>>938701
If you say same surface as a circle that could mean anything.

>>938707
an circle now!!!

break circle into dust particles, rearrange to make square

What the fuck will these do to help me?

>>938699
And transcendental. The fact that it is a transcendental number prevents us from squaring the circle.

If you know the exact surface area of the circle, why can't you?

I guess the real question is, can you make a circle and find it's EXACT surface area. In which case the answer is no since pi is irrational.

>>938704
You can't approximate.
area of circle = pi * (1/2 * d)^2 = pi * 1/4 * d^2
area of square = l^2
l^2 = pi/4 * d^2

The circle is going to be pi/4 times as wide as the square. Now comes the trigonometry...

use pirR^2 to get area of circle just measure the radius of the circle with the ruler

then just set up the L and W of the square when * to get the same answer as the first one

easy

>>938744 can you make a circle and find it's EXACT surface area. In which case the answer is no since pi is irrational.

Sure you can if its radius is sqrt(1/pi)

area = pi * (sqrt(1/pi))*2 = pi / pi = 1

protip: this is done without any calculations

>>938727
oh man lol

>>938758
how do with compass and ruler?

L= Pi
W= r^2

>>938687
Why, yes. Just draw any square. Some circle will have the same (size of) surface (area). You do not even need the compass! That was easy, OP.

draw circle of radius r. Surface=pir^2

length of each each side of the square must equal root Pi r. Thus it is impossible.

>>938839

ITT: classical trolling.

hey guys, I was just thinking about the square root of 2, and guess what?

>>938886


...what?

>>938886
You got a boner

Just a passerby, but I'll throw this out here for inspiration: A square drawn on the surface of a sphere is no longer the same square it would be in the 2D Cartesian coordinate system. If your coordinate axes are 3D hyperbolic, a square will have the same surface as a circle.

The constructable numbers form an algebraic field-extension over the rationals.
<span class="math">\pi[/spoiler] is transcendental over Q [note 1], thus it follows that <span class="math">sqrt{\pi}[/spoiler] is also transcendental and as such not constructable.


note 1: http://dialspace.dial.pipex.com/town/way/po28/maths/docs/pi.html

>>941011
DAMN YOU MATH-TAGS.
<span class="math">\sqrt{\pi}[/spoiler]
For fucks sake.

Is this what you are talking about OP?

>>941078
>square and circle should have same area
Looks legit.

>>941078
yeah man, same surface

now go die in a fire

http://en.wikipedia.org/wiki/Square_the_circle

>>938744
lulz, fucktard.
It's not because <span class="math">\pi[/spoiler] is irrational. haha.
<span class="math">\sqrt{2}[/spoiler] is also irrational, but you can construct it extremely easy. Just make a unit square and voila: the diagonal has length <span class="math">\sqrt{2}[/spoiler].

The answer to the question...
is "no."