Try to find out what this is :

  • Thread starter kleinwolf
  • Start date
In summary, the conversation discusses using a sheet of paper, a straightliner, and a compass to create a cylinder with a circle of the same radius drawn on it. It is then unfolded and the big axis of the resulting curved is measured to be equal to pi/3. This distance is then tripled with the compass to construct a square with a perimeter of 4pi. The conversation also raises questions about drawing a circle on a cylinder and the purpose of creating a square with the same perimeter as a circle. The response clarifies that using a compass on a cylinder does not create a complete turn around the cylinder, but only 60 degrees or pi/3. This process is referred to as the quadrature of the circle.
  • #1
kleinwolf
295
0
Take a sheet of paper, a straightliner and a compass.

Make a cylinder out of the sheet of paper and use the compass to draw on the cylinder a "circle" with the same radius as the cylinder (let's put that radius R=1(whichever unit you want)).

Unfold the sheet and take the big axis of the closed curved obtained. One can show, this length is : [tex] L=\frac{\pi}{3} [/tex].

Triple this distance with compass, and you can now construct a square which perimeter is [tex]4\pi[/tex]

Now construct a circle of radius 2, and you built a circle of same perimeter as the square above...
 
Physics news on Phys.org
  • #2
wait how do you draw a circle on a cylinder? do you mean to go all the way around? because that would give you only [tex] 2 \pi r [/tex] i don't see where the [tex]\pi/3[/tex] comes from...

*edit* maybe you mean to draw it on sideways, and even then, why would you want a square with the same perimeter as a circle? forgive the naiveness of my questions :biggrin: (also, exactly how do you draw a circle on sideways like that if you don't want to crush your paper cylinder?)
 
  • #3
Well the point is exactly that taking the compass (carefully) on the cylinder doesn't draw a circle (neither an ellipse by the way).

If you want : look at the cylinder from the basis circle : take the radius of the cylinder on your compass : put (carefully), the compass on the surface of the cylinder. You immediatly see that this does not make the complete turn around of the cylinder, but only 60°=Pi/3...Is that clearer ?

Since you now unfold the paper, u get a length that is multiple of Pi u did the quadrature of the circle.
 

1. What is the purpose of trying to find out what this is?

The purpose of trying to find out what this is is to gain knowledge and understanding about something that is currently unknown.

2. How can I determine what this is?

To determine what this is, you can use various scientific methods such as observation, experimentation, and analysis of data.

3. What steps should I take to find out what this is?

The steps to finding out what this is may include conducting research, collecting data, forming a hypothesis, and testing that hypothesis through experimentation.

4. What tools or equipment do I need to find out what this is?

The tools and equipment needed to find out what this is may vary depending on the object being studied, but may include microscopes, chemical tests, and other scientific instruments.

5. Is it important to find out what this is?

Yes, it is important to find out what this is as it can lead to new discoveries and advancements in various fields of science and technology.

Similar threads

  • Special and General Relativity
Replies
29
Views
1K
  • Special and General Relativity
2
Replies
40
Views
2K
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Sci-Fi Writing and World Building
Replies
9
Views
2K
  • General Math
Replies
4
Views
2K
Replies
1
Views
525
  • Introductory Physics Homework Help
Replies
25
Views
1K
Replies
11
Views
3K
  • Astronomy and Astrophysics
Replies
7
Views
2K
Back
Top