04-16-2014, 08:29 PM | #1 |
rain of memories...
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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?
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04-16-2014, 08:30 PM | #2 |
lil j the bad b-word
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Re: Shape Symmetry
wow! great thread idea!
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04-16-2014, 08:33 PM | #3 | |
rain of memories...
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Re: Shape Symmetry
..
Quote:
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04-16-2014, 08:34 PM | #4 |
It's Saint Pepsi bitch
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Re: Shape Symmetry
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04-16-2014, 08:36 PM | #5 |
Banned
Join Date: Nov 2013
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Re: Shape Symmetry
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04-16-2014, 08:48 PM | #6 |
Kawaii Desu Ne?
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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.
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04-16-2014, 08:52 PM | #7 |
rain of memories...
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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.
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04-18-2014, 08:05 PM | #8 | |
FFR Player
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Re: Shape Symmetry
Quote:
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.
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04-18-2014, 11:04 PM | #9 |
V's beta-male entourage
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Re: Shape Symmetry
I like your curves
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04-18-2014, 11:55 PM | #10 | |
rain of memories...
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Re: Shape Symmetry
Quote:
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04-19-2014, 12:14 AM | #11 |
Forum User
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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... !_!
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04-19-2014, 01:06 AM | #12 | |
ごめんなさい (/ω\)
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Re: Shape Symmetry
Quote:
stop it |
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04-19-2014, 01:08 AM | #13 |
B^)
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Re: Shape Symmetry
octagon
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04-19-2014, 01:48 AM | #14 |
Digital Dancing!
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Re: Shape Symmetry
How many circles can you fit into a bigger circle?
consider your mind fucked.
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04-19-2014, 03:13 AM | #15 |
ごめんなさい (/ω\)
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Re: Shape Symmetry
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04-19-2014, 03:36 AM | #16 |
rain of memories...
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Re: Shape Symmetry
Speaking of overloading your mind, watch some of this video:
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04-19-2014, 04:19 AM | #17 |
Dark Chancellor
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Re: Shape Symmetry
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?
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04-19-2014, 04:33 AM | #18 |
Owlbears Rock!
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Re: Shape Symmetry
Infinite, since any straight line that goes through a circle's epicenter divides it evenly into two domes.
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04-19-2014, 05:07 AM | #19 | |
ごめんなさい (/ω\)
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Re: Shape Symmetry
Quote:
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. Last edited by Pseudo Enigma; 04-19-2014 at 05:11 AM.. |
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04-19-2014, 05:50 AM | #20 | |
Mrow~
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Re: Shape Symmetry
Quote:
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 Rē
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