2 Eggs and A Building

[el22]

OK, my calculations:
triangle area=
8*r*r/(2*tan(30)) + 6*r*r = 2*r*r*(1/tan(30) + 3)
coin area = 3*pi*r*r

% = 100 * (1 - (3*pi)/(2(2/(tan(30) + 3)) = 50%

[Quasimodem]

All wrong.

Also, I would like to see your full calculations.

Would you like to continue guessing or do you perhaps want the answer?

After fixing a dumb mistake...~27%???

Don't give us the answer, by the way. And I'll show my calculations once/if I get it right!

EDIT: Are all these coins the same size?

[el22]

= 27.1% now
I give up

Strmstn can I go now?

[Hàkon]

After fixing a dumb mistake...~27%???

Don't give us the answer, by the way. And I'll show my calculations once/if I get it right!

≈ 27% is right!

My calculation:

r = the radius of the circles

The uniformity principle gives the distance from origo in a circle to the nearest triangle tip = 2r.

The third side of the triangle that is formed by the radius in a circle and origo to the triangle tip = sqr(4*r^2-r^2) = r*sqr(3)

Side in the outer triangle = 2*r*sqr(3)+2*r = 2*r(sqr(3)+1)

Height of the outer triangle = 2*r+sqr(3)*r+r = r*(sqr(3)+3)

Area of the triangle TA (YES, TA!) = 2*r*(sqr(3)+1)*r*(sqr(3)+3)/2 =
r^2*(6+4*sqr(3))

Total area of the circles CA: 3*pi*r^2

Area not covered by the circles = (r^2*(6+4*sqr(3))-3*pi*r^2)/(r^2*(6+4*sqr(3)))*100 = (6+4*sqr(3)-3*pi)/(6+4*sqr(3))*100 ≈ 27,1%

[el22]

StrmStn I gave you a more simple solution, without even being aware of the 'uniformity principle' (whatever it means), and (apart from a calculation error) my answer was right

[Hàkon]

StrmStn I gave you a more simple solution, without even being aware of the 'uniformity principle' (whatever it means), and (apart from a calculation error) my answer was right

I actually did not see the first post you made, I apologize for that.

I searched the thread hastily by Ctrl+F + %.

[Osprey]

keep the calculations to a minimum please...

[Quasimodem]

≈ 27% is right!

My calculation:

r = the radius of the circles

The uniformity principle gives the distance from origo in a circle to the nearest triangle tip = 2r.

The third side of the triangle that is formed by the radius in a circle and origo to the triangle tip = sqr(4*r^2-r^2) = r*sqr(3)

Side in the outer triangle = 2*r*sqr(3)+2*r = 2*r(sqr(3)+1)

Height of the outer triangle = 2*r+sqr(3)*r+r = r*(sqr(3)+3)

Area of the triangle TA (YES, TA!) = 2*r*(sqr(3)+1)*r*(sqr(3)+3)/2 =
r^2*(6+4*sqr(3))

Total area of the circles CA: 3*pi*r^2

Area not covered by the circles = (r^2*(6+4*sqr(3))-3*pi*r^2)/(r^2*(6+4*sqr(3)))*100 = (6+4*sqr(3)-3*pi)/(6+4*sqr(3))*100 ≈ 27,1%

Here's how I did it (unfortunately, some was cut off while scanning, but you can probably get the gist of it):