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# phil1882

Member Since 27 Apr 2012
Offline Last Active Yesterday, 03:15 PM

### In Topic: Equilateral Triangle: Color and distance

26 March 2015 - 04:26 PM

Spoiler for agree with rainman

### In Topic: A Complicated Numbers Problem

13 March 2015 - 03:24 PM

i have no idea how you could solve this without computing at least a few decimal points of sqrt(5).

for example one possiblility might be multipying by 3 -sqrt(5), but then i would have to divide by this number at the end of the problem.

the fastest way i know of, would be to compute about 1000 decimal points of 3+sqrt(5),

and then use the fact that a^n * a^n = a^(2*n). ie something like

```v = 3 +sqrt(5)
while n != 0:
if n&1 == 0:
n -= 1
v *= (3+sqrt(5))
else:
n >>= 1
v *= v
print v
```

### In Topic: Rest in Peace, Games Forum

11 March 2015 - 07:33 PM

it was a goood run y-san hosted some fun ones. i'm not particuarly skilled at hosting forum games but if we had more poeple i probably could.

### In Topic: A mean, mean minimization problem

17 February 2015 - 11:21 PM

9*x*(sin x) +4/(x*sin x)

if x = pi/2:

16.68

if x = pi/4:

12.2

if x = pi/8:

27.97

if x = 3*pi/8:

13.47

if x = 3*pi/16:

15.17

so it looks like its pi/4.

### In Topic: A circle in a square hole.

22 January 2015 - 05:52 AM

in a 20x25 rectangle, 500 unit squares can be fitted.

spacing the 120 squares out such that slightly less than a unit square is between them, gives roughly 240 area that the circle cannot be.

rotating the squares in an alternating pattern of diamond and square gives roughly 324 area that the circle cannot enter.

moving the squares out of sync such that they are in a somewhat hexagonal pattern maximizes the area that the circle cannot be,  giving roughy 411 area the circle connot enter. this still leaves plenty of space for the circle, even in the worst case.