interesting mathematical property

[Dickarms]

a hexagon and a square, of equal areas, will have different perimeters. seems simple, but crazy. discuss.
the hexagon will be smaller in perimeter, by the way.

[ovid9]

Slow sunday afternoon at the Youngblood residence eh?

[clipless bumper]

Caue a circle is the most efficient enclosure for area - a hexagon is closer to a circle than a square is.

[Dickarms]

samsung austin semiconductor, to be precise. buy more phones!

[Dickarms]

Caue a circle is the most efficient enclosure for area - a hexagon is closer to a circle than a square is.

true. still, it boggles the mind when you try to actually realize it, like if you had 100 skittles lying on the table, you could corral them with a shorter piece of string into a hexagon than you could a square. seems odd.

[Dickarms]

well i guess it becomes clear thinking of the opposite side of it, that you could create really long inefficient oval around them if placed side by side.



carry on.




i saw this on the article about the new space telescope using hexagonal mirrors instead of square panels because they are more efficient due to this principle.

[ovid9]

I guess it isn't odd to me as I grew up playing hexagonal based board games. I figured out young that it was more efficient to do so (as well as giving you 6 easy to track movement routes) but I never thought about the math in it.

I wish I'd thought of the math more as its interesting to me know and I know jack crap about it. I fumble through even the simplest geometry and algebra problems is so sad.

[Dickarms]

like...chinese checkers? i used to rule at that game.

[ovid9]

lol

Naw, bunch of old wargames mostly. Squad leader, the russian campaign, Gaudalcanal, The Battle of the Bulge, D-Day. Various others.

[rear naked]

Caue a circle is the most efficient enclosure for area - a hexagon is closer to a circle than a square is.

true. still, it boggles the mind when you try to actually realize it, like if you had 100 skittles lying on the table, you could corral them with a shorter piece of string into a hexagon than you could a square. seems odd.

What about a 2x2 meter square
P=8m
A=4m^2

compared with a rectangle of the same area, A=4m^2
short sides are length 10^-100m
long sides are length 4*10^100m

Perimeter is 800,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 meters

[clipless bumper]

About as far from a circle as you can get.....

[Dickarms]

that was the opposite solution i proposed.

i mean its all very simple in concept, just never bothered to stop and realize the significance of the ratio of perimeter to area. the more you know...

[Cirrus]

It's also the reason water tanks are often spherical or at least cylindrical - most storage space with the least surface area.

[clipless bumper]

It's also the reason water tanks are often spherical or at least cylindrical - most storage space with the least surface area.

and it's the strongest - less material needed.
The center of large flat sides would easily deflect (thus needing to be much stronger/thicker), compared to a sphere, where it's all strong by virtue of the shape.

[rear naked]

Here is one for you...

http://en.wikipedia.org/wiki/Gabriel's_Horn

A shape with finite volume but infinite surface area

[VTM]

lol

Naw, bunch of old wargames mostly. Squad leader, the russian campaign, Gaudalcanal, The Battle of the Bulge, D-Day. Various others.

You ever play dis?

[long standing member]

well, since I'm a biologist, might as well throw this one on the pile

http://www.guardian.co.uk/science/1999/aug/26/technology

Let's make a poll of this thread!

or