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]

Re: Shape Symmetry

wow! great thread idea!

[drizzleRomanceGirl]

Re: Shape Symmetry

wow! great thread idea!

..

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]

Re: Shape Symmetry

http://cosmometry.net/vector-equilibrium-&-isotropic-vector-matrix

[choof]

Re: Shape Symmetry

..

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

[benguino]

Re: Shape Symmetry

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]

Re: Shape Symmetry

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]

Re: Shape Symmetry

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]

Re: Shape Symmetry

I like your curves

[drizzleRomanceGirl]

Re: Shape Symmetry

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]

Re: Shape Symmetry

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]

Re: Shape Symmetry

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]

Re: Shape Symmetry

octagon

[rushyrulz]

Re: Shape Symmetry

How many circles can you fit into a bigger circle?

consider your mind fucked.

[Pseudo Enigma]

Re: Shape Symmetry

How many circles can you fit into a bigger circle?

consider your mind fucked.

how many points of symmetry exist on a circle?