PlutonianEmpire
King of the Plutonian Empire
What exactly is _% less? Like, if one takes the number 100, and one says 30% less, is the new number 70, or something different?
Let's discuss Mathematics
- Thread starter ParadigmShifter
- Start date
It's 70.
First calculate what is 30% of the number. Then it's that much less than the original number.
First calculate what is 30% of the number. Then it's that much less than the original number.
azzaman333
meh
30% less of 100 is 70. 10% less of 50 is 45. Not much difficulty in interpreting a percentage of a raw number.
Where you might run into trouble is in a situation like this. 80% of men are happy. 10% less have girlfriends.
In this case, it's not exactly clear whether you mean 72% of men have girlfriends, or if you mean 70% of men have girlfriends. I believe that strictly speaking it means the former, but sometimes people incorrectly mean the latter. If you meant the latter you should say it's 10 percentage points less, as that removes the ambiguity.
Where you might run into trouble is in a situation like this. 80% of men are happy. 10% less have girlfriends.
In this case, it's not exactly clear whether you mean 72% of men have girlfriends, or if you mean 70% of men have girlfriends. I believe that strictly speaking it means the former, but sometimes people incorrectly mean the latter. If you meant the latter you should say it's 10 percentage points less, as that removes the ambiguity.
PlutonianEmpire
King of the Plutonian Empire
Yeah, that's why I asked, because science journalism seems to post confusing stuff like that once in a while.
Anyways, thanks.
PlutonianEmpire
King of the Plutonian Empire
New question: If I were to make a simplified, equi-rectangular map, say, 4096 by 2048 pixels, with just green and blue, and plaster it onto a sphere, how do I calculate or find out how much of that sphere is covered in blue, or what percentage, or something like that?
Mise
isle of lucy
It depends what kind of projection you're using and how the green and blue are distributed. If you're using an equal-area projection then the proportions on the 2D map will be the same as the proportions on the sphere.
So, just say that the map you've drawn is an equal area projection of your planet and be done with it
So, just say that the map you've drawn is an equal area projection of your planet and be done with it
PlutonianEmpire
King of the Plutonian Empire
I already stated it was an equirectangular map. AKA, simple cylindrical.It depends what kind of projection you're using and how the green and blue are distributed. If you're using an equal-area projection then the proportions on the 2D map will be the same as the proportions on the sphere.
So, just say that the map you've drawn is an equal area projection of your planet and be done with it
Then to be accurate, you need to convert it to equi-area or otherwise calculate the proportion of water at each latitude, and weigh that to the length of that latitude before summing all the latitudes together.I already stated it was an equirectangular map. AKA, simple cylindrical.
PlutonianEmpire
King of the Plutonian Empire
Yes, but HOW? I need numbers and formulae, dude; not just words.
That's what I guess too.
So, in practice, you just add up
cos(latitude(b)) and
cos(latitude(g))
for each blue pixel b and green pixel g. The sums tell the ratio of the total area of the sphere. Right?
So, in practice, you just add up
cos(latitude(b)) and
cos(latitude(g))
for each blue pixel b and green pixel g. The sums tell the ratio of the total area of the sphere. Right?
I know that one cubic foot can be defined as a cube whose sides are 1 foot long, but is a cube that has 10-ft sides defined as 10 cubic feet or 100 cubic feet? Also, if an area is 5 ft high, 3 ft wide and 3 ft deep, is that 45 cubic feet in volume?
In essence, is 10 feet cubed one hundred times larger than 10 cubic feet?
In essence, is 10 feet cubed one hundred times larger than 10 cubic feet?
azzaman333
meh
1m^3 * 10 = 10m^3
I think you're falsely extrapolating a definition that only applies to a single case, and confusing yourself as a result.
I think you're falsely extrapolating a definition that only applies to a single case, and confusing yourself as a result.
Mise
isle of lucy
a cube that has 10 ft sides is 1,000 cubic feet. 10 x 10 x 10 = 1,000. you can fit 1,000 of your original 1 ft cubes into this cube.
PlutonianEmpire
King of the Plutonian Empire
What happens when you convert it to the 4th dimension (aka, tesseract)? 
It's to the fourth power: 10 * 10 * 10 * 10 = 10 000 m^4.
This is a failure of English to be precise in its terminology. Atticus' explanation is spot on.
You are correct that your 5' x 3' x 3' encloses 45 cubic feet. However, I've also heard this volume referred to as 45 feet cubed, though I consider that to be wrong.
To me, 45' cubed = 45' x 45' x 45'
Mise
isle of lucy
feet cubed is perfectly fine, just like centimetres squared, or meters per second squared. It's not wrong; it's the convention for stating units.
That's what I always assumed, but if 45 cubic feet is the same thing as 45 feet cubed, then that is wrong and one logical combination (5' x 5' x 3') is correct.
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