Project Euler Forum

So, I can now correctly calculate V(x).

My last issue is getting the accuracy to 9 decimal places.

Are the provided x values, x=1.114785284, x=2.511167869, result in V(x) = 36.000000000.., and 49.000000000
-- ie with accuracy to 9 decimal places?

-- I am assuming so.. Any maybe hints on accuracy would be appreciated....

Thanks

What you are required to do is to give [sum]x accurate to 9 decimal places.
This doesn't directly mean that the V(x) need to be accurate to 9 decimal places.
That depends on the function V(x).

I just want to clarify something.

I compute V(0) for alpha = 30, and R = 3
and get 32.64838334800159 instead of 32.648388556.

I am assuming that 32.648388556 <-- is what should be expected after you do V(0) yes?

Thanks

RishadanPort wrote:...
I compute V(0) for alpha = 30, and R = 3
and get 32.64838334800159 instead of 32.648388556.
I am assuming that 32.648388556 <-- is what should be expected after you do V(0) yes? ...

Yes. For alpha = 30 deg. and R = 3, V(0) = 32.648388556 when rounded to 9 decimals.

Yep -- After a bit of analysis of the function... I have now realized why the error is cropping up.

Thanks

Edit: After a few days spent debugging, -- I found a few bugs in my code, and found why the errors were cropping up.
Great problem -- loved it.

I'm very confused on how the volume missing is 32.648388556

With A = 30 degrees, Radius = 3, x =0 I get ~28.2743
In fact I get this answer with twomethods leading me to believe I have misunderstood the question.

I used shell method to integrate the empty space integrate( 2 * pi * x * (sin(A)*x), x = 0 to R) = 28.2743

Alternately I calculate the volume of cone (1/3 * pi * R^2 * (sin(A) * R) = 9*pi/2) and subtract that from a cylinder (pi * R^2 * (sin(A) * R) = 27*pi/2) = 27*pi/2 - 9*pi/2 = 18*pi/2 = ~28.2743

So now I'm confused on where 32.648 came from.

kingvash wrote:I'm very confused on how the volume missing is 32.648388556

With A = 30 degrees, Radius = 3, x =0 I get ~28.2743
In fact I get this answer with twomethods leading me to believe I have misunderstood the question.

I used shell method to integrate the empty space integrate( 2 * pi * x * (sin(A)*x), x = 0 to R) = 28.2743

Alternately I calculate the volume of cone (1/3 * pi * R^2 * (sin(A) * R) = 9*pi/2) and subtract that from a cylinder (pi * R^2 * (sin(A) * R) = 27*pi/2) = 27*pi/2 - 9*pi/2 = 18*pi/2 = ~28.2743

So now I'm confused on where 32.648 came from.

The height of the cone is not sin(A)*R.

Hi,

I don't understand why 1.114785284 has 3 squared decimal places ...

At first sight, I see "1" twice and "4" twice too, giving thus 4 places... So this is not about single digits being squares...

Can someone please explain me the decision criterion ?

Many thanks for your help !

NMB wrote:Hi,

I don't understand why 1.114785284 has 3 squared decimal places ...

At first sight, I see "1" twice and "4" twice too, giving thus 4 places... So this is not about single digits being squares...

Can someone please explain me the decision criterion ?

Many thanks for your help !

It simply has 9 decimal places. That 9=3^2 is just part of Fred's obsession with squares.

Wow ok it was as simple as that ... Thank you very much

The problem statement says:

We shall let the amount of space wasted in cubic metres be given by $V(x)$. If $x = 1.114785284$, which happens to have three squared decimal places, then the amount of space wasted, $V(1.114785284) \approx 36$. Given the range of possible solutions to this problem there is exactly one other option: $V(2.511167869) \approx 49$.

It feels to me as though this question has been edited and lost some key explanation. Should this say something like the following?

We shall let the amount of space wasted in cubic metres be given by $V(x)$. If $x = 1.114785284$, which happens to have three squared decimal places, then the amount of space wasted, $V(1.114785284) \approx 36$, which is an integer square. Given this angle of repose and diameter, there is exactly one other value of $x$ which gives an integer square wastage: $V(2.511167869) \approx 49$.