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Sigil Ciy of Doors (Topology of a Torus) - MATHS
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<blockquote data-quote="Rel" data-source="post: 4602972" data-attributes="member: 99"><p>One thing I thought of was that, if there is a gap in the torus then, depending on how big the whole thing is, it makes the idea that there is a "disturbing nothingness that is unsettling to look upon" kinda...cheap due to how visible that nothingness would be through the gap.</p><p></p><p>Let's assume that the shape is exactly like a car tire scaled up to very large size. If I'm standing almost anywhere on the inner surface of the tire, I can look up and see, not only across to the opposite side of the tire, but also up through the gap into the void. This effect varies in how pronounced it is based on how wide the gap is and also how big the donut hole is. </p><p></p><p>If the donut hole is very small compared to the total radius of the torus then your view from across the city, through the gap, is more likely to show some part of the other side of the city or some part of the outside of the city but still not the void. You have to get much closer to the gap in order to be at an angle to see past the other side and out into the void.</p><p></p><p>As the donut hole becomes larger compared to the total radius of the torus then it becomes easier and easier to see out into the void. If the torus is almost all "hole" and very little "donut" then you end up with the Ringworld where you can quite easily see out into the void on either side of "the arch".</p><p></p><p>Again, this effect can also be compensated for based on the size of the gap. The more donut hole you've got the narrower the gap has to be in order to conceal the void.</p></blockquote><p></p>
[QUOTE="Rel, post: 4602972, member: 99"] One thing I thought of was that, if there is a gap in the torus then, depending on how big the whole thing is, it makes the idea that there is a "disturbing nothingness that is unsettling to look upon" kinda...cheap due to how visible that nothingness would be through the gap. Let's assume that the shape is exactly like a car tire scaled up to very large size. If I'm standing almost anywhere on the inner surface of the tire, I can look up and see, not only across to the opposite side of the tire, but also up through the gap into the void. This effect varies in how pronounced it is based on how wide the gap is and also how big the donut hole is. If the donut hole is very small compared to the total radius of the torus then your view from across the city, through the gap, is more likely to show some part of the other side of the city or some part of the outside of the city but still not the void. You have to get much closer to the gap in order to be at an angle to see past the other side and out into the void. As the donut hole becomes larger compared to the total radius of the torus then it becomes easier and easier to see out into the void. If the torus is almost all "hole" and very little "donut" then you end up with the Ringworld where you can quite easily see out into the void on either side of "the arch". Again, this effect can also be compensated for based on the size of the gap. The more donut hole you've got the narrower the gap has to be in order to conceal the void. [/QUOTE]
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