Calculate and fill with circle

[danuthorincas]

Apr 7, 2022 17:52:24 GMT plus said:

429 is what I got for air bubbles floating to top last row doesn't make cut inside 600 pixel square, almost but not quite.

Screenshot 600 x 600 window.

Now Easter Eggs is a different story!

How did you calculate ?Thanks

[plus]

pi = 3.141592
' cos(30) = x / hypt so x (the vertical dist between circle centers) = 50 cos(30) or 50*cos(2*pi/12)
' cos(30) = x/50 ' = the difference in vertical height of circle centers
' 30 degrees = 1/12 of circle = 2*pi/12
cch = 50 * cos(2*pi/12) ' circle center height from one layer to next is this
print "The first and last row are at least 25 away from edge."
print "The difference between each row height of circles is then ";cch
'the first layer of circle is 25 from edge
row = 1
h = 25 ' to middle of first row of circles
cnt = 12
toggle = 0
print "Row", "Height", "Count"
print row, h, cnt
[anotherRow]
if h + cch + 25 <= 600 then ' last row needs another radius height to clear the last edge
   'add another row
   row = row + 1
   if toggle then cnt = cnt + 12 else cnt = cnt + 11
   h = h + cch 'this is centers of circle stack height not the very top, another 25!
   toggle = 1 - toggle
   print row, h, cnt
   goto [anotherRow]
end if


The first and last row are at least 25 away from edge.
The diffeence between each row height of circles is then 43.3012729
Row           Height        Count
1             25            12
2             68.3012729    23
3             111.602546    35
4             154.903819    46
5             198.205092    58
6             241.506365    69
7             284.807637    81
8             328.10891     92
9             371.410183    104
10            414.711456    115
11            458.012729    127
12            501.314002    138
13            544.615275    150


Also confirmed on the Engineering Calculator here: www.engineeringtoolbox.com/circles-within-rectangle-d_1905.html

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[plus]

Here is an illustration to help with the Geometry / Trig of determining the Vertical Height between layers of Circles:

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