which shape is better: circle or square?

[IAM]

The circle is by far a better shape. The curve of the female body. Barrel of a gun. The sun great giver of life. The truthness is obvious the circle is the best shape.

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


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

 

[Cheezy the Wiz]

The circle was often considered to be the most divine of shapes, because all the points are equidistant from the center, just as we are all equally distant from, and equal before the eyes of, God. It is also the shape of the heavens, as seen from earth. In Paradiso, Dante describes God as appearing to be three circles within one another, sharing the same center point.

 

[Borachio]

The answer, as so often, is it depends.

As a symbol of all sorts of things the circle has much to recommend it.

But when it comes to things like packing, the square is the only thing. Or rather rectangles generally. For examples, a row of round houses wastes a great deal of space, while a circular shipping container would be an absolute nightmare.

Though in practical terms, square wheels don't really function too well.

The square symbolizes law and order. And the four directions.

 

[Terxpahseyton]

The square. He is a simple down-to-earth guy. Whou edges? Hm... maybe we start with four.
A gab?
Well, draw a line.
The square is bit sharp on the edges, I admit. But that is what makes him so authentic. I can trust a square, a reliable authentic and edgy anchor to cling to in the stormy sea. A strong line to lean on.
The circle? A crazy fanatic, knows no boundaries. Edges? I am all edges! A number? I give you Pi!
Try lean on this guy and he will be gone in a second as far as it goes.

 

[IAM]

For examples, a row of round houses wastes a great deal of space,

Round houses like those monolithic domes are far superior structurally to conventional building techniques. But i do agree about the shipping container.

http://www.monolithic.com/

 

[Borachio]

http://www.monolithic.com/topics/cabins-model15
Want one! Now!

 

[Cheezy the Wiz]

A number? I give you Pi!

The square root of 2 is an almost as crazy number.

 

[Borachio]

e^(i*pi) =-1

Spoiler :

spooky

 

[dutchfire]

Square isn't just a shape, it means we don't cut corners.

 

[IdiotsOpposite]

A circle is balanced. No matter how you rotate it, it's perfectly symmetric in all ways. It can be represented by simple equations on the x-y plane (where r is the circle's radius):

x^2 + y^2 = r^2

Or on the r-theta plane:

r=r

Or hell, even expressed parametrically:

x = r cos(t)
y = r sin(t)

Seriously, try expressing a square under ANY of those systems. Simply.

 

[Kennigit]

squares for 2d

spheres 3d

 

[Borachio]

A square can be represented simply by the area enclosed by the x and y axis and the lines x=a, y=a.

 

[IdiotsOpposite]

A square can be represented simply by the area enclosed by the x and y axis and the lines x=a, y=a, where a is the side length of the square.

You can't forget to define a!

 

[Borachio]

I don't think that's necessary. It's pretty much implicit. If you can draw two lines y=a and x=a and not have a square enclosed by those two and the x and y axes, I'd like to see it.

 

[dutchfire]

A circle is balanced. No matter how you rotate it, it's perfectly symmetric in all ways. It can be represented by simple equations on the x-y plane (where r is the circle's radius):

x^2 + y^2 = r^2

Or on the r-theta plane:

r=r

Or hell, even expressed parametrically:

x = r cos(t)
y = r sin(t)

Seriously, try expressing a square under ANY of those systems. Simply.

|(x,y)|_1 = 1, where | |_1 is the Manhattan metric.

 

[Antilogic]

OP has it right.

 

[IdiotsOpposite]

|(x,y)|_1 = 1, where | |_1 is the Manhattan metric.

Well, that's definitely one way to do it. I would have also accepted |x| + |y| = 1, although that IS a rotated square.

 

[Antilogic]

Dude, anyone who picks square is a square.

 

[Borachio]

Oooh. Is it a quiz? Do you have prizes? All the best quizzes have prizes.

And what difference does it make whether it's a rotated square or not?

Circular chess board with, ahem, circular squares are lame.

 

[IdiotsOpposite]

Oooh. Is it a quiz? Do you have prizes? All the best quizzes have prizes.

And what difference does it make whether it's a rotated square or not?

Some people like to have their squares with the side facing downwards, rather than the point.

And unfortunately, no prizes, although there are now three ways to write a square shown. I'll add a fourth that's an extension of yours:

|x| = a
|y| = a

With a being the side length of the square and suitable bounds on the domain of x and y, of course.