Shape Symmetry

[drizzleRomanceGirl]

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?

[JurseyRider734]

wow! great thread idea!

[drizzleRomanceGirl]

Originally Posted by JurseyRider734

wow! great thread idea!

..

Originally Posted by Synthlight

I know.. The thought that someone would come in here and chat about general stuff.

Quick! Time for the almost regular members to come out and try to make this person feel like an idiot in an attempt to elevate their worth on an internet forum.

Cheers,

Synthlight

[korny]

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

[choof]

Originally Posted by drizzleRomanceGirl

..

see this post would have been a perfect place to say "get fucen dunked on, son"

[reuben_tate]

You might want to check that vice-versa case. It is not the case that for every rectangle, you can cut horizontally divide it (once) and expect to form two squares.

[drizzleRomanceGirl]

Originally Posted by reuben_tate

You might want to check that vice-versa case. It is not the case that for every rectangle, you can cut horizontally divide it (once) and expect to form two squares.

Oops, I didn't think about that until now. I guess shapes must be both vertically and horizontally symmetrical to divided into each other indefinitely. I don't understand the reasoning behind this fact, though.

[Crashfan3]

Originally Posted by drizzleRomanceGirl

Oops, I didn't think about that until now. I guess shapes must be both vertically and horizontally symmetrical to divided into each other indefinitely. I don't understand the reasoning behind this fact, though.

A square has four equal sides and four equal 90deg angles. A rectangle has four equal 90deg angles, but not necessarily four equal sides. You can't take a rectangle that is 10cm in width and 2cm in height, and expect to come out with two square shapes with four equal sides when you divide it horizontally.

Dividing a hexagon from one vertex to the another directly across from it creates two trapezoids, which have four sides. But a trapezoid's vertices are not the same as a hexagon's, and to divide from one vertex to another will create triangles, because you will be down to three sides. Even if you create a dividing line between the vertexes (on the sides themselves), you will only end up with a four-sided polygon. There is no way to divide a trapezoid with a single line and have the end result be a six-sided shape.

[Snowcrafta]

I like your curves

[drizzleRomanceGirl]

Originally Posted by Crashfan3

A square has four equal sides and four equal 90deg angles. A rectangle has four equal 90deg angles, but not necessarily four equal sides. You can't take a rectangle that is 10cm in width and 2cm in height, and expect to come out with two square shapes with four equal sides when you divide it horizontally.

Dividing a hexagon from one vertex to the another directly across from it creates two trapezoids, which have four sides. But a trapezoid's vertices are not the same as a hexagon's, and to divide from one vertex to another will create triangles, because you will be down to three sides. Even if you create a dividing line between the vertexes (on the sides themselves), you will only end up with a four-sided polygon. There is no way to divide a trapezoid with a single line and have the end result be a six-sided shape.

Oh, I think I understand this reasoning. Thank you for explaining.

[Spenner]

Consider a hexagon to be a flattened view of a 3D cube, with no shading the give it it's depth. Then its like the trapezoids represent squares on an angle for the faces, and in a different view, would appear to be a square.

Maybe it doesn't matter if a hexagon can't be cut into little hexagons if it really only relates to a cube on an angle... !_!

[Pseudo Enigma]

Originally Posted by spenner

consider a hexagon to be a flattened view of a 3d cube, with no shading the give it it's depth. Then its like the trapezoids represent squares on an angle for the faces, and in a different view, would appear to be a square.

Maybe it doesn't matter if a hexagon can't be cut into little hexagons if it really only relates to a cube on an angle... !_!

what are you doing to my brain
stop it

[Tim Allen]

octagon

[rushyrulz]

How many circles can you fit into a bigger circle?

consider your mind fucked.

[Pseudo Enigma]

Originally Posted by rushyrulz

How many circles can you fit into a bigger circle?

consider your mind fucked.

how many points of symmetry exist on a circle?

[drizzleRomanceGirl]

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

[cetaka]

Originally Posted by drizzleRomanceGirl

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]

Originally Posted by Pseudo Enigma

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]

Originally Posted by Arntonach

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]

Originally Posted by Pseudo Enigma

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