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#1 |
rain of memories...
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![]() 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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#2 |
lil j the bad b-word
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![]() wow! great thread idea!
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#3 | |
rain of memories...
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..
Quote:
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#4 |
It's Saint Pepsi bitch
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#5 |
Banned
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Posts: 8,563
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#6 |
Kawaii Desu Ne?
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Location: The Kawaiian Island~
Age: 30
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![]() 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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#7 |
rain of memories...
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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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#8 | |
FFR Player
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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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#9 |
V's beta-male entourage
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![]() I like your curves
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#10 | |
rain of memories...
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#11 |
Forum User
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![]() 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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#12 | |
ごめんなさい (/ω\)
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Age: 28
Posts: 2,290
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stop it |
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#13 |
B^)
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![]() octagon
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#14 |
Digital Dancing!
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Age: 31
Posts: 12,982
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![]() How many circles can you fit into a bigger circle?
consider your mind fucked.
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#15 |
ごめんなさい (/ω\)
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Age: 28
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#16 |
rain of memories...
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![]() Speaking of overloading your mind, watch some of this video:
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#17 |
Dark Chancellor
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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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#18 |
Owlbears Rock!
Join Date: Mar 2012
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Infinite, since any straight line that goes through a circle's epicenter divides it evenly into two domes.
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#19 | |
ごめんなさい (/ω\)
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Age: 28
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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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#20 | |
Mrow~
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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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