Math Is Fun Forum

this is the book shared bia google drive

https://drive.google.com/file/d/1eYeHtD4H-hnJdYAVTAxtSB_DY4zkhpS7/view?usp=sharing

I don't know if you can download it I found it on web
it's a translated version for the original book of john napier

also allow me to quote this :-

Arithmetical progressions : 1, 2, 3, 4, 5, 6, 7,
&c. ; or 2, 4, 6, 8, 10, 12, 14, 16,
Geometrical progressions: 1, 2, 4, 8, 16, 32, 64,
or 243,81, 27, 9, 3, 1.
in these progressions we require accuracy and ease in
working. Accuracy is obtained by taking large numbers
for a basis ; but large numbers are most easily made from
small by adding cyphers,

Thus instead of 100000, which the less experienced make the greatest sine, the more learned
put 10.000.000, whereby the difference of all sines
is better expressed. Wherefore also we use the
same for radius and for the greatest of our geometrical proportional.

what does he put? he just increase the zeros it's mean he changed the number is that accuracy?

They are supervisors the 4 employee
But at checkpoint fir example I need 21 employee at A shift and at D shift and at N shift less
At terminal I need 25 every A,D and N shift

Thier sum is 46 lets say 50 per shift
So how many extra employees I need to cover the OFF days  Don't know if they are enough or not
I want to know the specific number
To get less cost so no need to employee a lot of employees for nothing
For example if i got 50 and need 6 more
That's less cost from employee 17 extra one for nothing

I have a late question then I'll continue to work on this pattern you provided to me
but first may I know something
if I have 3 employee only I can't make a schedule lick that
because for example :
Sat    Sun     Mon     Tue     Wed      Thu       Fri
A       A       A        A      A      A      X     -------x1
D       D       D       D      D      X     D     -------x2
N       N       N       X      N      N     N     -------x3

mr bob every time the one of these employee goes off we miss someone at a specific time
for example look at Tuesday the X3 got off in that day so no one exist at NightShift(10PM-6AM) note that the 10PM started in monday and that shift ended 6AM in Tuesday we called it the nightshift

so obviously we need 1 extra employee to solve that problem

my question is what if we have 50 employees do I need 10 extra employees to solve the situation?
how to calculate how many extra employee I need in general

Why there is DDAD and AAAD
I want everyweek to still same like six days and sixs nights continuously how to do that

Also your schedule has a small mistake there is eight A it has to be 6 A then OFF
And is there general equation for that

Also the employees are security officers in airport
I Can't just do it with 28 days
They have to work the whole month I don't want the airport be empty from the officers every morning i need and officer at list and everynight and afternoon the other 225 are security inspectors also i need at least 70 of them at daylight and 70 at afternoon and 60 of them at night
No problem with night can be lesser because night is not important there is less passengers traveling at night

the second problem I got as you will see in the next photo..

the first photo I show to you was in month May
in the second photo it's the next month which is June schedule

in the May the day1 start at Monday until  Day5 which is Friday which is the OFF day of X1 employee
so I started to fill and trying and tests thier schedules according to this
but at Day31 of May it was Wed and it was (D) shift for the X1 employee the end of the month
then at June the sixth Month it most continue in (D) shift until his Friday OFF
so I can't save the pattern inside my mind and apply it for each month because it has to be a specific calculations for each months
because some month also start for example at Sunday which is the OFF of the X3 employee
I just want to make a schedule  so I make sure I don't make any mistakes
and I want to know how to customize it for example I want to change few things like I want in Day5 2 employee at afternoon shifts instead of them at Daylight shift

EPSILON = 1E-14;
r = sqrt(2.0)

if  abs(r * r - 2.0) < EPSILON
output :-
sqrt(2.0) squared is approximately 2.0

this when I use java but when I use Microsoft calculator it said false! the condition would be false not true as you can see in this picture :-

also as you can see in this example :-

double x = 9.999999999999999;
if (Math.abs(x- 10.0) < EPSILON)
{
System.out.println("the number is approximately 10"); 
    }
}
}

when I minus the 9.999999999999999 to 9.99 for example the condition will be false!

in short I just want to solve this question :-

Explain why it is more difficult to compare floating-point numbers than integers.
Write Java code to test whether an integer n equals 10 and whether a floating-point
number x is approximately equal to 10

So we record that in the answer space as not 4 subtracts but 0.4 subtracts because we shifted the carriage one place.

I mean we made 15 become 1.5 the number is changed who gives the right to do such a thing is that legal in math and clearly understandable? is there explaintion for that ..
I mean we chose a different number it's 1.5
I can't imagine that is there interactive example like 6 apples iver 16 people