The Too-Perfect Saint: Tossed Aside by My Fiancé and Sold to Another Kingdom - Ch. 18 - Secret Plan

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Too bad the saints seem a bit limited in their mathematical abilities. Even if they multiply their resources by 5, or to be generous let's make it an even 10, they are not going to be increasing the size of a purification circle by as much as they think.

Let's assume things in their favour, like that it is not a magical technique that does everything over a circular area, then it is a bit cheaper. Instead we only need to consider a purely 1-dimensional circular circumference. If we are this kind to our math, then yes, the radius is linearly proportional to the circumference. So having 10 times as much resources should lead to 10 times the circumference, which in turn is 10 times the radius. But even then I very much doubt it is enough to cover an entire continent, as the country (the area she covers right now) needs to be a full fifth the size of the continent, OR located in the center in which case it can be a tenth. Which is unlikely.

And that is when stacking everything in their favour. I am fairly sure the purification circle affects the area inside the circle too, meaning the radius is not linearly proportional. And so the radius should be only sqrt(multiplier) larger, which further makes it so the country needs to (approximately) be somewhere between a third to half a third of the entire continent. And if the factor of 10 times more resources (mana) is too high, things further devolve.
 
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I dont like this idea -~-
We need to get Julius first Philia. You try to solve it by yourself again. That stupid person doesnt deserve your salvation. Peace was never an option for him since this series started -~-
 
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Too bad the saints seem a bit limited in their mathematical abilities. Even if they multiply their resources by 5, or to be generous let's make it an even 10, they are not going to be increasing the size of a purification circle by as much as they think.

Let's assume things in their favour, like that it is not a magical technique that does everything over a circular area, then it is a bit cheaper. Instead we only need to consider a purely 1-dimensional circular circumference. If we are this kind to our math, then yes, the radius is linearly proportional to the circumference. So having 10 times as much resources should lead to 10 times the circumference, which in turn is 10 times the radius. But even then I very much doubt it is enough to cover an entire continent, as the country (the area she covers right now) needs to be a full fifth the size of the continent, OR located in the center in which case it can be a tenth. Which is unlikely.

And that is when stacking everything in their favour. I am fairly sure the purification circle affects the area inside the circle too, meaning the radius is not linearly proportional. And so the radius should be only sqrt(multiplier) larger, which further makes it so the country needs to (approximately) be somewhere between a third to half a third of the entire continent. And if the factor of 10 times more resources (mana) is too high, things further devolve.
Will your reasoning be right? Will it be wrong? Will the power of manga reasoning overpower yours? Dont worry, in just a few chapters more you'll know :p.
 
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Too bad [...]
Let's instead assume that the barrier actually draws mana from nature, through those barrier pillars she placed, and keeping it active is what requires the mana. Then she'd need more mana either for increasing the number of pillars, or to maintain the connection over a larger distance. The saint needing to stay in the centers points more towards a challenge of staying connected, but even then it's difficult to say if half that country is her own maximum distance or if moving too close to one side (it isn't circular) would disturb the balance to make the barrier unstable.

I can't remember if they said anything about whether the barrier is limited to the one country because her mana capacity coincidentally only covers that much, or just because they avoided diplomacy to work quicker. So it might still be mathematically possible to cover the entire continent with five times the mana. Let's see how the author decides to solve this.
 
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Let's instead assume that the barrier actually draws mana from nature, through those barrier pillars she placed, and keeping it active is what requires the mana. Then she'd need more mana either for increasing the number of pillars, or to maintain the connection over a larger distance. The saint needing to stay in the centers points more towards a challenge of staying connected, but even then it's difficult to say if half that country is her own maximum distance or if moving too close to one side (it isn't circular) would disturb the balance to make the barrier unstable.

I can't remember if they said anything about whether the barrier is limited to the one country because her mana capacity coincidentally only covers that much, or just because they avoided diplomacy to work quicker. So it might still be mathematically possible to cover the entire continent with five times the mana. Let's see how the author decides to solve this.
So you are thinking that the number of pillars is what matters, and that it is why they only have to use energy on the circumference? Still means she needs to travel around the entire continent's shores in the span of 4 days, but yeah, then we are back to a linear cost, and indeed possibly even lower as it might be something like "affected area is 30% larger than the area contained by the pillars" (so not just a margin of x meters, but rather proportional to the contained area).

The main issue will be the pillars that has to be placed directly in the sea though, as it is a purification circle and not a purification polygon.
 
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I agree with this feeling, but the original Japanese version calls the country Parunakoruta. So technically this translation is somewhere between Pannacotta and Parnacorta.
Parnacolta would also be a comfortable rendition.
 
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Too bad the saints seem a bit limited in their mathematical abilities. Even if they multiply their resources by 5, or to be generous let's make it an even 10, they are not going to be increasing the size of a purification circle by as much as they think.

Let's assume things in their favour, like that it is not a magical technique that does everything over a circular area, then it is a bit cheaper. Instead we only need to consider a purely 1-dimensional circular circumference. If we are this kind to our math, then yes, the radius is linearly proportional to the circumference. So having 10 times as much resources should lead to 10 times the circumference, which in turn is 10 times the radius. But even then I very much doubt it is enough to cover an entire continent, as the country (the area she covers right now) needs to be a full fifth the size of the continent, OR located in the center in which case it can be a tenth. Which is unlikely.

And that is when stacking everything in their favour. I am fairly sure the purification circle affects the area inside the circle too, meaning the radius is not linearly proportional. And so the radius should be only sqrt(multiplier) larger, which further makes it so the country needs to (approximately) be somewhere between a third to half a third of the entire continent. And if the factor of 10 times more resources (mana) is too high, things further devolve.
Also need to factor in MC's sister and perhaps the aunt.

The math won't check out with that alone, but there's a lot more you can do in the details that could change the formula.
 

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