Shape Symmetry

[drizzleRomanceGirl]

Re: Shape Symmetry

Speaking of overloading your mind, watch some of this video:

[cetaka]

Re: Shape Symmetry

How come squares can be horizontally divided into rectangles evenly and vice versa, while hexagons can be evenly divided into trapezoids without the opposite being true?

How come bears can be horizontally divided into organs evenly and vice versa, while lions can be evenly divided into isosceles triangles without the opposite being true?

[Arntonach]

Re: Shape Symmetry

how many points of symmetry exist on a circle?

Infinite, since any straight line that goes through a circle's epicenter divides it evenly into two domes.

[Pseudo Enigma]

Re: Shape Symmetry

Infinite, since any straight line that goes through a circle's epicenter divides it evenly into two domes.

not really. All you have to do is find the perimeter of the circle and divide it by 2. lol I was just being pretentious.

edit: my reasoning is that you have to have two points to cut a circle in half. You put those on opposite sides from each other, and you have a point of symmetry. There is only half of the perimeter of the circle worth of unique symmetry points.

[PaperclipGames]

Re: Shape Symmetry

not really. All you have to do is find the perimeter of the circle and divide it by 2. lol I was just being pretentious.

edit: my reasoning is that you have to have two points to cut a circle in half. You put those on opposite sides from each other, and you have a point of symmetry. There is only half of the perimeter of the circle worth of unique symmetry points.

No, Arntonach is right. There is an uncountably infinite amount of lines through any* circle's center (each of which intersecting with two unique points on the circle). All of these lines correspond with a mirror symmetry.
Note also that a circle has uncountably infinite amounts of rotational symmetry as well (each focussed on the center of the circle).

* Euclidian and in a field isomorphic to R²

[L.B.D.D]

Re: Shape Symmetry

become a math major

[Pseudo Enigma]

Re: Shape Symmetry

become a math major

that's his goal

also I guess you're probably talking about how a circle has infinite vertices, and going from there to say that the vertices/2 would be the number points of symmetry (infinity/2), right?

[PaperclipGames]

Re: Shape Symmetry

That is a very rough but I suppose equivalent way of putting it, yes (infinity/2 is not defined, though). More precisely I said there are infinite pairs of vertices such that the line through the two forms a symmetry - but the result is pretty much the same thing.

[L.B.D.D]

Re: Shape Symmetry

no u are wrong infinity is the name of a techno song

[FoJaR]

Re: Shape Symmetry

http://cosmometry.net/vector-equilib...-vector-matrix

korny seriously dude, you either need to stop taking hallucinogens or spend some time in a classroom or both